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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<title>Analysis module | DIPlib | a library for quantitative image analysis</title>
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<a href="https://diplib.org"><img src="DIPlib_logo.svg" alt="" />DIPlib</a><span class="m-breadcrumb">┃</span><a href="index.html" class="m-thin">a library for quantitative image analysis</a><span class="m-breadcrumb">┃</span><a href="https://github.com/DIPlib/diplib/releases/tag/3.5.2" class="m-thin">version 3.5.2</a> </span>
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<h1>
Analysis <span class="m-thin">module</span> <div class="m-doc-include m-code m-thin m-text-right">#include <a href="file--diplib--analysis-h.html">"diplib/analysis.h"</a></div>
</h1>
<p>Assorted analysis tools.</p>
<div class="m-block m-default">
<h3>Contents</h3>
<ul>
<li>
Reference
<ul>
<li><a href="#nested-classes">Classes</a></li>
<li><a href="#alias-members">Aliases</a></li>
<li><a href="#function-members">Functions</a></li>
<li><a href="#operator-members">Operators</a></li>
</ul>
</li>
</ul>
</div>
<section id="nested-classes">
<h2>Classes</h2>
<dl class="m-doc">
<dt>
struct <a href="#dip-SubpixelLocationResult" class="m-doc">dip::<wbr />SubpixelLocationResult</a>
</dt>
<dd>Contains the result of the function <a href="analysis.html#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><code>dip::SubpixelLocation</code></a>. <a href="#dip-SubpixelLocationResult">more...</a></dd>
<dt>
class <a href="dip-Distribution.html" class="m-doc">dip::<wbr />Distribution</a>
</dt>
<dd>Holds probability density functions and other types of distribution</dd>
</dl>
</section>
<section id="alias-members">
<h2>Aliases</h2>
<dl class="m-doc">
<dt id="dip-SubpixelLocationArray">
using <a href="#dip-SubpixelLocationArray" class="m-doc-self">dip::<wbr />SubpixelLocationArray</a> = std::vector<SubpixelLocationResult>
</dt>
<dd>Contains the result of the functions <a href="analysis.html#dip-SubpixelMaxima-Image-CL-Image-CL-String-CL"><code>dip::SubpixelMaxima</code></a> and <a href="analysis.html#dip-SubpixelMinima-Image-CL-Image-CL-String-CL"><code>dip::SubpixelMinima</code></a>.</dd>
</dl>
</section>
<section id="function-members">
<h2>Functions</h2>
<dl class="m-doc">
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-Find-Image-CL-Image-CL" class="m-doc">dip::<wbr />Find</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask = {}) -> <a href="supporttypes.html#dip-CoordinateArray" class="m-doc">dip::CoordinateArray</a></span>
</dt>
<dd>Finds the coordinates for all non-zero pixels in the scalar image <code>in</code>, optionally constrained to the pixels selected by <code>mask</code>. <a href="#dip-Find-Image-CL-Image-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL" class="m-doc">dip::<wbr />SubpixelLocation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="supporttypes.html#dip-UnsignedArray" class="m-doc">dip::UnsignedArray</a> const& position,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& polarity = S::MAXIMUM,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::PARABOLIC_SEPARABLE) -> <a href="analysis.html#dip-SubpixelLocationResult" class="m-doc">dip::SubpixelLocationResult</a></span>
</dt>
<dd>Gets coordinates of a local extremum with sub-pixel precision <a href="#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-SubpixelMaxima-Image-CL-Image-CL-String-CL" class="m-doc">dip::<wbr />SubpixelMaxima</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask = {},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::PARABOLIC_SEPARABLE) -> <a href="analysis.html#dip-SubpixelLocationArray" class="m-doc">dip::SubpixelLocationArray</a></span>
</dt>
<dd>Gets coordinates of local maxima with sub-pixel precision <a href="#dip-SubpixelMaxima-Image-CL-Image-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-SubpixelMinima-Image-CL-Image-CL-String-CL" class="m-doc">dip::<wbr />SubpixelMinima</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask = {},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::PARABOLIC_SEPARABLE) -> <a href="analysis.html#dip-SubpixelLocationArray" class="m-doc">dip::SubpixelLocationArray</a></span>
</dt>
<dd>Gets coordinates of local minima with sub-pixel precision <a href="#dip-SubpixelMinima-Image-CL-Image-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-MeanShift-Image-CL-FloatArray-CL-dfloat-" class="m-doc">dip::<wbr />MeanShift</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& meanShiftVectorResult,
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& start,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> epsilon = 1e-3) -> <a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a></span>
</dt>
<dd>Finds the coordinates of a local maximum close to <code>start</code> <a href="#dip-MeanShift-Image-CL-FloatArray-CL-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-MeanShift-Image-CL-FloatCoordinateArray-CL-dfloat-" class="m-doc">dip::<wbr />MeanShift</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& meanShiftVectorResult,
<a href="supporttypes.html#dip-FloatCoordinateArray" class="m-doc">dip::FloatCoordinateArray</a> const& startArray,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> epsilon = 1e-3) -> <a href="supporttypes.html#dip-FloatCoordinateArray" class="m-doc">dip::FloatCoordinateArray</a></span>
</dt>
<dd>Finds the coordinates of local a maximum close to each point in <code>startArray</code>. <a href="#dip-MeanShift-Image-CL-FloatCoordinateArray-CL-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-GaussianMixtureModel-Image-CL-Image-L-dip-uint--dip-uint--dip-uint--StringSet-CL" class="m-doc">dip::<wbr />GaussianMixtureModel</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> dimension = 2,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> numberOfGaussians = 2,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> maxIter = 20,
<a href="supporttypes.html#dip-StringSet" class="m-doc">dip::StringSet</a> const& flags = {})</span>
</dt>
<dd>Determines the parameters for a Gaussian Mixture Model for every line in the image. <a href="#dip-GaussianMixtureModel-Image-CL-Image-L-dip-uint--dip-uint--dip-uint--StringSet-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL" class="m-doc">dip::<wbr />CrossCorrelationFT</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in1,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& in2,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& in1Representation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& in2Representation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& outRepresentation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& normalize = S::NORMALIZE)</span>
</dt>
<dd>Calculates the cross-correlation between two images of equal size. <a href="#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-AutoCorrelationFT-Image-CL-Image-L-String-CL-String-CL" class="m-doc">dip::<wbr />AutoCorrelationFT</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& inRepresentation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& outRepresentation = S::SPATIAL)</span>
</dt>
<dd>Computes the auto-correlation function. <a href="#dip-AutoCorrelationFT-Image-CL-Image-L-String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FindShift-Image-CL-Image-CL-String-CL-dfloat--UnsignedArray-" class="m-doc">dip::<wbr />FindShift</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in1,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& in2,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::MTS,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> parameter = 0,
<a href="supporttypes.html#dip-UnsignedArray" class="m-doc">dip::UnsignedArray</a> maxShift = {}) -> <a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a></span>
</dt>
<dd>Estimates the (sub-pixel) global shift between <code>in1</code> and <code>in2</code>. <a href="#dip-FindShift-Image-CL-Image-CL-String-CL-dfloat--UnsignedArray-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FourierMellinMatch2D-Image-CL-Image-CL-Image-L-String-CL-String-CL" class="m-doc">dip::<wbr />FourierMellinMatch2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in1,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& in2,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& interpolationMethod = S::LINEAR,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& correlationMethod = S::PHASE) -> <a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a></span>
</dt>
<dd>Finds the scaling, translation and rotation between two 2D images using the Fourier Mellin transform <a href="#dip-FourierMellinMatch2D-Image-CL-Image-CL-Image-L-String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-" class="m-doc">dip::<wbr />StructureTensor</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& gradientSigmas = {1.0},
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& tensorSigmas = {5.0},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::BEST,
<a href="supporttypes.html#dip-StringArray" class="m-doc">dip::StringArray</a> const& boundaryCondition = {},
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> truncation = 3)</span>
</dt>
<dd>Computes the structure tensor. <a href="#dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P" class="m-doc">dip::<wbr />StructureTensorAnalysis2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* orientation = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* energy = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* anisotropy1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* anisotropy2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* curvature = nullptr)</span>
</dt>
<dd>Computes useful image parameters from the 2D structure tensor. <a href="#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P" class="m-doc">dip::<wbr />StructureTensorAnalysis3D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* phi1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* theta1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* phi2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* theta2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l3 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* phi3 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* theta3 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* energy = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* cylindrical = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* planar = nullptr)</span>
</dt>
<dd>Computes useful image parameters from the 3D structure tensor. <a href="#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-StructureTensorAnalysis-Image-CL-ImageRefArray-L-StringArray-CL" class="m-doc">dip::<wbr />StructureTensorAnalysis</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html#dip-ImageRefArray" class="m-doc">dip::ImageRefArray</a>& out,
<a href="supporttypes.html#dip-StringArray" class="m-doc">dip::StringArray</a> const& outputs)</span>
</dt>
<dd>Interface to <a href="analysis.html#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis2D</code></a> and <a href="analysis.html#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis3D</code></a>. <a href="#dip-StructureTensorAnalysis-Image-CL-ImageRefArray-L-StringArray-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-StructureAnalysis-Image-CL-Image-CL-std-vector<dfloat>-CL-String-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-" class="m-doc">dip::<wbr />StructureAnalysis</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
std::vector<dfloat> const& scales = {},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& feature = "energy",
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& gradientSigmas = {1.0},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::BEST,
<a href="supporttypes.html#dip-StringArray" class="m-doc">dip::StringArray</a> const& boundaryCondition = {},
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> truncation = 3) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>Analyzes the local structure of the image at multiple scales. <a href="#dip-StructureAnalysis-Image-CL-Image-CL-std-vector<dfloat>-CL-String-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-MonogenicSignal-Image-CL-Image-L-FloatArray-CL-dfloat--String-CL-String-CL" class="m-doc">dip::<wbr />MonogenicSignal</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& wavelengths = {3.0,24.0},
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> bandwidth = 0.41,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& inRepresentation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& outRepresentation = S::SPATIAL)</span>
</dt>
<dd>Computes the monogenic signal, a multi-dimensional generalization of the analytic signal. <a href="#dip-MonogenicSignal-Image-CL-Image-L-FloatArray-CL-dfloat--String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-MonogenicSignalAnalysis-Image-CL-ImageRefArray-L-StringArray-CL-dfloat--dfloat--dfloat--dfloat--String-CL" class="m-doc">dip::<wbr />MonogenicSignalAnalysis</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html#dip-ImageRefArray" class="m-doc">dip::ImageRefArray</a>& out,
<a href="supporttypes.html#dip-StringArray" class="m-doc">dip::StringArray</a> const& outputs,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> noiseThreshold = 0.2,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> frequencySpreadThreshold = 0.5,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> sigmoidParameter = 10,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> deviationGain = 1.5,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& polarity = S::BOTH)</span>
</dt>
<dd>Computes useful image parameters from the monogenic signal. <a href="#dip-MonogenicSignalAnalysis-Image-CL-ImageRefArray-L-StringArray-CL-dfloat--dfloat--dfloat--dfloat--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-OrientationSpace-Image-CL-Image-L-dip-uint--dfloat--dfloat--dip-uint-" class="m-doc">dip::<wbr />OrientationSpace</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> order = 8,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> radCenter = 0.1,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> radSigma = 0.8,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> orientations = 0)</span>
</dt>
<dd>Creates an orientation space for a 2D image <a href="#dip-OrientationSpace-Image-CL-Image-L-dip-uint--dfloat--dfloat--dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-PairCorrelation-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL-StringSet-CL" class="m-doc">dip::<wbr />PairCorrelation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& object,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Random.html" class="m-doc">dip::Random</a>& random,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 1000000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM,
<a href="supporttypes.html#dip-StringSet" class="m-doc">dip::StringSet</a> const& options = {}) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>Estimates the pair correlation function of the different phases in <code>object</code>. <a href="#dip-PairCorrelation-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL-StringSet-CL">more...</a></dd>
<dt id="dip-PairCorrelation-Image-CL-Image-CL-dip-uint--dip-uint--String-CL-StringSet-CL">
<span class="m-doc-wrap-bumper">auto <a href="#dip-PairCorrelation-Image-CL-Image-CL-dip-uint--dip-uint--String-CL-StringSet-CL" class="m-doc-self">dip::<wbr />PairCorrelation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& object,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 1000000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM,
<a href="supporttypes.html#dip-StringSet" class="m-doc">dip::StringSet</a> const& options = {}) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>like above, using a default-initialized <a href="dip-Random.html"><code>dip::Random</code></a> object.</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-ProbabilisticPairCorrelation-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL-StringSet-CL" class="m-doc">dip::<wbr />ProbabilisticPairCorrelation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& phases,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Random.html" class="m-doc">dip::Random</a>& random,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 1000000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM,
<a href="supporttypes.html#dip-StringSet" class="m-doc">dip::StringSet</a> const& options = {}) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>Estimates the probabilistic pair correlation function of the different phases in <code>phases</code>. <a href="#dip-ProbabilisticPairCorrelation-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL-StringSet-CL">more...</a></dd>
<dt id="dip-ProbabilisticPairCorrelation-Image-CL-Image-CL-dip-uint--dip-uint--String-CL-StringSet-CL">
<span class="m-doc-wrap-bumper">auto <a href="#dip-ProbabilisticPairCorrelation-Image-CL-Image-CL-dip-uint--dip-uint--String-CL-StringSet-CL" class="m-doc-self">dip::<wbr />ProbabilisticPairCorrelation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& object,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 1000000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM,
<a href="supporttypes.html#dip-StringSet" class="m-doc">dip::StringSet</a> const& options = {}) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>like above, using a default-initialized <a href="dip-Random.html"><code>dip::Random</code></a> object.</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-Semivariogram-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL" class="m-doc">dip::<wbr />Semivariogram</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Random.html" class="m-doc">dip::Random</a>& random,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 1000000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>Estimates the expected value of half the square difference between field values at a distance <code>d</code>. <a href="#dip-Semivariogram-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL">more...</a></dd>
<dt id="dip-Semivariogram-Image-CL-Image-CL-dip-uint--dip-uint--String-CL">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Semivariogram-Image-CL-Image-CL-dip-uint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />Semivariogram</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& object,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 1000000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>like above, using a default-initialized <a href="dip-Random.html"><code>dip::Random</code></a> object.</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-ChordLength-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL" class="m-doc">dip::<wbr />ChordLength</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& object,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Random.html" class="m-doc">dip::Random</a>& random,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 100000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>Estimates the chord length distribution of the different phases in <code>object</code>. <a href="#dip-ChordLength-Image-CL-Image-CL-Random-L-dip-uint--dip-uint--String-CL">more...</a></dd>
<dt id="dip-ChordLength-Image-CL-Image-CL-dip-uint--dip-uint--String-CL">
<span class="m-doc-wrap-bumper">auto <a href="#dip-ChordLength-Image-CL-Image-CL-dip-uint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />ChordLength</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& object,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> probes = 100000,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& sampling = S::RANDOM) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>like above, using a default-initialized <a href="dip-Random.html"><code>dip::Random</code></a> object.</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-DistanceDistribution-Image-CL-Image-CL-dip-uint-" class="m-doc">dip::<wbr />DistanceDistribution</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& object,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& region,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> length = 100) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>Computes the distribution of distances to the background of <code>region</code> for the different phases in <code>object</code>. <a href="#dip-DistanceDistribution-Image-CL-Image-CL-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-Granulometry-Image-CL-Image-CL-std-vector<dfloat>-CL-String-CL-String-CL-StringSet-CL" class="m-doc">dip::<wbr />Granulometry</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
std::vector<dfloat> const& scales = {},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& type = "isotropic",
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& polarity = S::OPENING,
<a href="supporttypes.html#dip-StringSet" class="m-doc">dip::StringSet</a> const& options = {}) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a></span>
</dt>
<dd>Computes the granulometric function for an image <a href="#dip-Granulometry-Image-CL-Image-CL-std-vector<dfloat>-CL-String-CL-String-CL-StringSet-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FractalDimension-Image-CL-dfloat-" class="m-doc">dip::<wbr />FractalDimension</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> eta = 0.5) -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Estimates the fractal dimension of the binary image <code>in</code> the sliding box method. <a href="#dip-FractalDimension-Image-CL-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-swap-Sample-L-Sample-L" class="m-doc">dip::<wbr />swap</a>(</span><span class="m-doc-wrap">Sample& a,
Sample& b)</span>
</dt>
<dd>Swaps two samples, copying the data from <code>other</code> to <code>*this</code>, and that from <code>*this</code> to <code>other</code>.
Both must have the same number of values. <a href="#dip-swap-Sample-L-Sample-L">more...</a></dd>
</dl>
</section>
<section id="operator-members">
<h2>Operators</h2>
<dl class="m-doc">
<dt>
<span class="m-doc-wrap-bumper">auto <a href="dip-Distribution.html#dip-operator%3C%3C-std-ostream-L-Distribution-CL" class="m-doc">dip::<wbr />operator<<</a>(</span><span class="m-doc-wrap">std::ostream& os,
<a href="dip-Distribution.html" class="m-doc">dip::Distribution</a> const& distribution) -> std::ostream&</span>
</dt>
<dd>Writes the distribution to a stream <a href="dip-Distribution.html#dip-operator%3C%3C-std-ostream-L-Distribution-CL">more...</a></dd>
</dl>
</section>
<section>
<h2>Class documentation</h2>
<section class="m-doc-details" id="dip-SubpixelLocationResult"><div>
<h3>
struct <a href="#dip-SubpixelLocationResult" class="m-doc-self">dip::<wbr />SubpixelLocationResult</a>
</h3>
<p>Contains the result of the function <a href="analysis.html#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><code>dip::SubpixelLocation</code></a>.</p>
<table class="m-table m-fullwidth m-first-tight m-flat m-doc">
<thead><tr><th>Variables</th><th></th></tr></thead>
<tbody>
<tr>
<td>
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> <a href="#dip-SubpixelLocationResult-coordinates" class="m-doc-self" id="dip-SubpixelLocationResult-coordinates">coordinates</a> </td>
<td>
Coordinates of local extremum
</td>
</tr>
<tr>
<td>
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> <a href="#dip-SubpixelLocationResult-value" class="m-doc-self" id="dip-SubpixelLocationResult-value">value</a> </td>
<td>
Interpolated value at local extremum
</td>
</tr>
</tbody>
</table>
</div></section>
</section>
<section>
<h2>Function documentation</h2>
<section class="m-doc-details" id="dip-Find-Image-CL-Image-CL"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="supporttypes.html#dip-CoordinateArray" class="m-doc">dip::CoordinateArray</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-Find-Image-CL-Image-CL" class="m-doc-self">dip::<wbr />Find</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask = {})</span></span>
</h3>
<p>Finds the coordinates for all non-zero pixels in the scalar image <code>in</code>, optionally constrained to the pixels selected by <code>mask</code>.</p>
<p><code>in</code> must be scalar, but can have any data type. <code>mask</code>, if forged, must be of the same sizes as <code>in</code>, or be
singleton expandable to that size, and must be binary.</p>
<p>The output array contains the coordinates for all non-zero pixels, in linear index order (that is, the image is
traversed row-wise to find the pixels). Note that this function is intended to be used with images that have
relatively few non-zero pixels, and there usually is a better alternative than to list the coordinates of
all non-zero pixels.</p>
<aside class="m-note m-default">
<h4>See also</h4>
<p><a href="math_statistics.html#dip-Count-Image-CL-Image-CL"><code>dip::Count</code></a></p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="analysis.html#dip-SubpixelLocationResult" class="m-doc">dip::SubpixelLocationResult</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL" class="m-doc-self">dip::<wbr />SubpixelLocation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="supporttypes.html#dip-UnsignedArray" class="m-doc">dip::UnsignedArray</a> const& position,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& polarity = S::MAXIMUM,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::PARABOLIC_SEPARABLE)</span></span>
</h3>
<p>Gets coordinates of a local extremum with sub-pixel precision</p>
<p>Determines the sub-pixel location of a local maximum or minimum close to <code>position</code>. <code>position</code> should point
to a pixel whose value is larger than its direct neighbors’ (if <code>polarity</code> is <code>"maximum"</code>) or smaller than
its direct neighbors’ (<code>polarity</code> is <code>"minimum"</code>).</p>
<p>The <code>coordinates</code> member of the output struct will contain the the sub-pixel location of this local
extremum. The <code>value</code> member will contain the interpolated grey value at the location of the extremum.</p>
<p><code>method</code> determines which method is used. These are the allowed values:</p>
<ul>
<li><code>"linear"</code>: Computes the center of gravity of 3 pixels around the extremum, in each dimension independently.
The value at the extremum is that of the pixel at <code>position</code>.</li>
<li><code>"parabolic"</code>: Fits a parabola to a 3-pixel-wide block around the extremum (for up to 3D only).</li>
<li><code>"parabolic separable"</code>: Fits a parabola in each dimension independently. The value at the extremum
is the maximum/minimum of the values obtained in each of the 1D processes, and thus not equivalent
to the grey value obtained by true interpolation.</li>
<li><code>"gaussian"</code>: Fits a Gaussian to a 3-pixel-wide block around the extremum (for up to 3D only).</li>
<li><code>"gaussian separable"</code>: Fits a Gaussian in each dimension independently. The value at the extremum
is the maximum/minimum of the values obtained in each of the 1D processes, and thus not equivalent
to the grey value obtained by true interpolation.</li>
<li><code>"integer"</code>: Doesn’t look for sub-pixel locations, returning the integer coordinates of the extremum.</li>
</ul>
<p>The image <code>in</code> must be scalar and real-valued.</p>
</div></section>
<section class="m-doc-details" id="dip-SubpixelMaxima-Image-CL-Image-CL-String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="analysis.html#dip-SubpixelLocationArray" class="m-doc">dip::SubpixelLocationArray</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-SubpixelMaxima-Image-CL-Image-CL-String-CL" class="m-doc-self">dip::<wbr />SubpixelMaxima</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask = {},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::PARABOLIC_SEPARABLE)</span></span>
</h3>
<p>Gets coordinates of local maxima with sub-pixel precision</p>
<p>Detects local maxima in the image, and returns their coordinates, with sub-pixel precision.
Only pixels where <code>mask</code> is on will be examined. Local maxima are detected using <a href="segmentation.html#dip-Maxima-Image-CL-Image-L-dip-uint--String-CL"><code>dip::Maxima</code></a>,
then their position is determined more precisely using <a href="analysis.html#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><code>dip::SubpixelLocation</code></a>.</p>
<p>A local maximum can not touch the edge of the image. That is, its integer location must be one
pixel away from the edge.</p>
<p>See <a href="analysis.html#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><code>dip::SubpixelLocation</code></a> for the definition of the <code>method</code> parameter.</p>
</div></section>
<section class="m-doc-details" id="dip-SubpixelMinima-Image-CL-Image-CL-String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="analysis.html#dip-SubpixelLocationArray" class="m-doc">dip::SubpixelLocationArray</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-SubpixelMinima-Image-CL-Image-CL-String-CL" class="m-doc-self">dip::<wbr />SubpixelMinima</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask = {},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::PARABOLIC_SEPARABLE)</span></span>
</h3>
<p>Gets coordinates of local minima with sub-pixel precision</p>
<p>Detects local minima in the image, and returns their coordinates, with sub-pixel precision.
Only pixels where <code>mask</code> is on will be examined. Local minima are detected using <a href="segmentation.html#dip-Minima-Image-CL-Image-L-dip-uint--String-CL"><code>dip::Minima</code></a>,
then their position is determined more precisely using <a href="analysis.html#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><code>dip::SubpixelLocation</code></a>.</p>
<p>A local minimum can not touch the edge of the image. That is, its integer location must be one
pixel away from the edge.</p>
<p>See <a href="analysis.html#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><code>dip::SubpixelLocation</code></a> for the definition of the <code>method</code> parameter.</p>
</div></section>
<section class="m-doc-details" id="dip-MeanShift-Image-CL-FloatArray-CL-dfloat-"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-MeanShift-Image-CL-FloatArray-CL-dfloat-" class="m-doc-self">dip::<wbr />MeanShift</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& meanShiftVectorResult,
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& start,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> epsilon = 1e-3)</span></span>
</h3>
<p>Finds the coordinates of a local maximum close to <code>start</code></p>
<p>The mean shift method iteratively finds the center of gravity of a Gaussian-shaped neighborhood around <code>start</code>,
moving <code>start</code> to this location, until convergence. The location that the process converges to is a local
maximum. Convergence is assumed when the magnitude of the shift is smaller than <code>epsilon</code>.</p>
<p>To speed up the computation within this function, the output of <a href="linear.html#dip-MeanShiftVector-Image-CL-Image-L-FloatArray--String-CL-StringArray-CL-dfloat-"><code>dip::MeanShiftVector</code></a> is used. This filter
pre-computes the center of gravity of all neighborhoods in the image. Specify the neighborhood sizes in that
function.</p>
</div></section>
<section class="m-doc-details" id="dip-MeanShift-Image-CL-FloatCoordinateArray-CL-dfloat-"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="supporttypes.html#dip-FloatCoordinateArray" class="m-doc">dip::FloatCoordinateArray</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-MeanShift-Image-CL-FloatCoordinateArray-CL-dfloat-" class="m-doc-self">dip::<wbr />MeanShift</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& meanShiftVectorResult,
<a href="supporttypes.html#dip-FloatCoordinateArray" class="m-doc">dip::FloatCoordinateArray</a> const& startArray,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> epsilon = 1e-3)</span></span>
</h3>
<p>Finds the coordinates of local a maximum close to each point in <code>startArray</code>.</p>
<p>Repeatedly calls the <a href="analysis.html#dip-MeanShift-Image-CL-FloatArray-CL-dfloat-"><code>dip::MeanShift</code></a> function described above, for each point in <code>startArray</code>. Duplicate maxima
are not removed, such that <code>out[ii]</code> is the local maximum arrived to from <code>startArray[ii]</code>.</p>
</div></section>
<section class="m-doc-details" id="dip-GaussianMixtureModel-Image-CL-Image-L-dip-uint--dip-uint--dip-uint--StringSet-CL"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-GaussianMixtureModel-Image-CL-Image-L-dip-uint--dip-uint--dip-uint--StringSet-CL" class="m-doc-self">dip::<wbr />GaussianMixtureModel</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> dimension = 2,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> numberOfGaussians = 2,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> maxIter = 20,
<a href="supporttypes.html#dip-StringSet" class="m-doc">dip::StringSet</a> const& flags = {})</span></span>
</h3>
<p>Determines the parameters for a Gaussian Mixture Model for every line in the image.</p>
<p><code>in</code> must be real-valued and scalar. For each image line along <code>dimension</code>, a Gaussian Mixture Model (GMM)
is fitted to find the <code>numberOfGaussians</code> most important Gaussian components. In the output image, <code>dimension</code>
indexes the Gaussian component. The components are stored in order of importance, the component with the largest
amplitude first. The parameters to each Gaussian are stored as tensor components, in the order
position, amplitude and sigma.</p>
<p><code>out</code> is a double-precision floating-point image with three tensor components. It has a size of <code>numberOfGaussians</code>
along <code>dimension</code>, and the same size as <code>in</code> along all other dimensions.</p>
<p><code>maxIter</code> sets how many iterations are run. There is currently no other stopping criterion.</p>
<p><code>flags</code> can contain the following values:</p>
<ul>
<li><code>"periodic"</code> specifies that the image is periodic along <code>dimension</code>.</li>
<li><code>"pixel size"</code> scales the parameters written to the output image with the pixel size along <code>dimension</code>.
By default these parameters are in pixels.</li>
</ul>
<aside class="m-note m-default">
<h4>See also</h4>
<p><a href="numeric.html#dip-GaussianMixtureModel-ConstSampleIterator<dfloat>--SampleIterator<dfloat>--dip-uint--dip-uint--dip-uint--Option-Periodicity-"><code>dip::GaussianMixtureModel</code></a></p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL" class="m-doc-self">dip::<wbr />CrossCorrelationFT</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in1,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& in2,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& in1Representation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& in2Representation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& outRepresentation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& normalize = S::NORMALIZE)</span></span>
</h3>
<p>Calculates the cross-correlation between two images of equal size.</p>
<p>The <code>normalize</code> flag determines whether to compute the regular cross-correlation (<code>"don't normalize"</code>)
or to normalize the frequency-domain inputs so that only the phase information is of importance
(<code>"normalize"</code> or <code>"phase"</code>). The normalization results as a very sharp peak in the spatial domain, which
increases the precision with which a shift between the two images can be determined.
Note that this normalization is not related to what is commonly referred to as “normalized cross-correlation”,
where the input images are whitened (in the spatial domain) before the cross-correlations is computed. The
method is instead related to the “phase correlation” as proposed by Kuglin and Hines (1975).</p>
<p>When <code>normalize</code> is <code>"normalize"</code>, the computation performed in the Fourier Domain is (as per Luengo & van Vliet, 2000)</p>
<div class="m-code"><pre><span></span><span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="w"> </span><span class="n">in1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Conjugate</span><span class="p">(</span><span class="n">in2</span><span class="p">)</span><span class="w"> </span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">SquareModulus</span><span class="p">(</span><span class="n">in1</span><span class="p">);</span>
</pre></div>
<p>When <code>normalize</code> is set to <code>"phase"</code>, the computation is (as per Kuglin & Hines, 1975)</p>
<div class="m-code"><pre><span></span><span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="w"> </span><span class="n">in1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Conjugate</span><span class="p">(</span><span class="n">in2</span><span class="p">)</span><span class="w"> </span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Modulus</span><span class="p">(</span><span class="n">in1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Modulus</span><span class="p">(</span><span class="n">in2</span><span class="p">)</span><span class="w"> </span><span class="p">);</span>
</pre></div>
<p>(See <a href="math_arithmetic.html#dip-Conjugate-Image-CL-Image-L"><code>dip::Conjugate</code></a>, <a href="math_arithmetic.html#dip-SquareModulus-Image-CL-Image-L"><code>dip::SquareModulus</code></a> and <a href="math_arithmetic.html#dip-Modulus-Image-CL-Image-L"><code>dip::Modulus</code></a>.)</p>
<p>These two approaches are identical if the only difference between <code>in1</code> and <code>in2</code> is a shift, except that
<code>"normalize"</code> is computationally cheaper than <code>"phase"</code>. If the images are otherwise not identical, then
the <code>"phase"</code> method might be the better choice. If there exist strong differences, the non-normalized
method can be the best option.</p>
<p>As elsewhere, the origin is in the middle of the image, on the pixel to the right of
the center in case of an even-sized image. Thus, for <code>in1==in2</code>, only this pixel will be set.
See <a href="analysis.html#dip-FindShift-Image-CL-Image-CL-String-CL-dfloat--UnsignedArray-"><code>dip::FindShift</code></a> with the <code>"CC"</code>, <code>"NCC"</code> or <code>"PC"</code> methods for localizing this peak.</p>
<p>If <code>in1</code> or <code>in2</code> is already Fourier transformed, set <code>in1Representation</code> or <code>in2Representation</code>
to <code>"frequency"</code>. Similarly, if <code>outRepresentation</code> is <code>"frequency"</code>, the output will not be
inverse-transformed, so will be in the frequency domain.</p>
<p><code>in1</code> and <code>in2</code> must be scalar images with the same dimensionality and sizes. Spatial-domain
images must be real-valued, and frequency-domain images are assumed (but not tested) to be
conjugate-symmetric (i.e. be Fourier transforms of real-valued images).
<code>out</code> will be real-valued if <code>outRepresentation</code> is <code>"spatial"</code>.</p>
<aside class="m-note m-default">
<h4>Literature</h4>
<ul>
<li>C.D. Kuglin and D.C. Hines, “The phase correlation image alignment method”, International
Conference on Cybernetics and Society (IEEE), pp 163-165, 1975.</li>
<li>C.L. Luengo Hendriks and L.J. van Vliet, “Improving resolution to reduce aliasing in an undersampled image sequence”,
in: Proceedings of SPIE 3965:214–222, 2000.</li>
</ul>
</aside>
</div></section>
<section class="m-doc-details" id="dip-AutoCorrelationFT-Image-CL-Image-L-String-CL-String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-AutoCorrelationFT-Image-CL-Image-L-String-CL-String-CL" class="m-doc-self">dip::<wbr />AutoCorrelationFT</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& inRepresentation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& outRepresentation = S::SPATIAL)</span></span>
</h3>
<p>Computes the auto-correlation function.</p>
<p>Equivalent to calling <a href="analysis.html#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><code>dip::CrossCorrelationFT</code></a> with the same image as the two inputs, and the
<code>normalize</code> flag set to <code>"don't normalize"</code> (normalization would yield a very boring output indeed).</p>
<p>As elsewhere, the origin is in the middle of the image, on the pixel to the right of
the center in case of an even-sized image.</p>
<p>If <code>in</code> is already Fourier transformed, set <code>inRepresentation</code> to <code>"frequency"</code>.
Similarly, if <code>outRepresentation</code> is <code>"frequency"</code>, the output will not be
inverse-transformed, so will be in the frequency domain.</p>
<p><code>in</code> must be a scalar image. Spatial-domain images must be real-valued, and a frequency-domain image
is assumed (but not tested) to be conjugate-symmetric (i.e. the Fourier transform of real-valued image).
<code>out</code> will be real-valued if <code>outRepresentation</code> is <code>"spatial"</code>.</p>
</div></section>
<section class="m-doc-details" id="dip-FindShift-Image-CL-Image-CL-String-CL-dfloat--UnsignedArray-"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-FindShift-Image-CL-Image-CL-String-CL-dfloat--UnsignedArray-" class="m-doc-self">dip::<wbr />FindShift</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in1,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& in2,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::MTS,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> parameter = 0,
<a href="supporttypes.html#dip-UnsignedArray" class="m-doc">dip::UnsignedArray</a> maxShift = {})</span></span>
</h3>
<p>Estimates the (sub-pixel) global shift between <code>in1</code> and <code>in2</code>.</p>
<p>The numbers found represent the shift of <code>in2</code> with respect to <code>in1</code>, or equivalently, the position of the
top-left pixel of <code>in2</code> in the coordinate system of <code>in1</code>. Shifting <code>in1</code> by the returned shift aligns the
two images. See <a href="geometry.html#dip-Shift-Image-CL-Image-L-FloatArray-CL-String-CL-StringArray-CL"><code>dip::Shift</code></a>.</p>
<p>There are various methods that can be used to determine the shift, see below.
For the methods that require that the shift be small, first the integer pixel is calculated using cross
correlation, and both images are cropped to the common part. <code>maxShift</code> can be used to restrict the shift
found. This is useful, for example, when the images contain a repeating pattern. Noise in the images can
cause a shift of several pattern periods to be “optimal” (e.g. the cross-correlation yields a larger value),
even if a much smaller shift would also explain the differences. In this case, set <code>maxShift</code> to be slightly
smaller than the pattern period along each dimension.</p>
<p>Valid strings for <code>method</code> are:</p>
<ul>
<li>
<p><code>"integer only"</code>: The cross-correlation method simply computes the cross-correlation, using
<a href="analysis.html#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><code>dip::CrossCorrelationFT</code></a>, and then finds the position of the pixel with the largest value.
This method works for any number of dimensions. <code>parameter</code> is ignored.</p>
</li>
<li>
<p><code>"CC"</code>: The cross-correlation method computes the cross-correlation, using <a href="analysis.html#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><code>dip::CrossCorrelationFT</code></a>,
and then uses <a href="analysis.html#dip-SubpixelLocation-Image-CL-UnsignedArray-CL-String-CL-String-CL"><code>dip::SubpixelLocation</code></a> to find the location of the largest peak with sub-pixel precision.
This method works for any number of dimensions. <code>parameter</code> is ignored.</p>
</li>
<li>
<p><code>"NCC"</code>: As <code>"CC"</code>, but using the normalized cross-correlation, which makes the peak much sharper
(Luengo Hendriks, 1998). This method works for any number of dimensions. <code>parameter</code> is ignored.
See the notes in <a href="analysis.html#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><code>dip::CrossCorrelationFT</code></a> regarding the normalization of the cross-correlation using the
<code>"normalize"</code> flag, which is not as what is commonly referred to as “normalized cross-correlation”.</p>
</li>
<li>
<p><code>"PC"</code>: As <code>"CC"</code>, but using phase correlation. This method works for any number of dimensions.
<code>parameter</code> is ignored. See the notes in <a href="analysis.html#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><code>dip::CrossCorrelationFT</code></a> regarding the normalization of the
cross-correlation using the <code>"phase"</code> flag.</p>
</li>
<li>
<p><code>"CPF"</code>: The CPF method (see Luengo Hendriks (1998), where it is called FFTS) uses the phase of the
cross-correlation (as calculated by <a href="analysis.html#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><code>dip::CrossCorrelationFT</code></a>) to estimate the shift. <code>parameter</code> sets
the largest frequency used in this estimation. The maximum value that makes sense is <code>sqrt(0.5)</code>.
Any larger value will give the same result. Choose smaller values to ignore the higher frequencies, which
have a smaller SNR and are more affected by aliasing. If <code>parameter</code> is <= 0, the optimal found for images
sub-sampled by a factor four will be used (parameter = 0.2).
This method only supports 2-D images.</p>
</li>
<li>
<p><code>"MTS"</code>: The MTS method (see Luengo Hendriks (1998), where it is called GRS) uses a first order Taylor
approximation of the equation <code>in1(t) = in2(t-s)</code> at scale <code>parameter</code>. If <code>parameter</code> is <= 0, a scale
of 1 will be used. This means that the images will be smoothed with a Gaussian kernel of 1. This method is
more accurate than CPF.
This method supports images with a dimensionality between 1 and 3.</p>
</li>
<li>
<p><code>"ITER"</code>: The ITER method is an iterative version of the MTS method. It is known that a single estimation
with MTS has a bias due to truncation of the Taylor expansion series (Pham et al., 2005). The bias can be
expressed as a polynomial of the subpixel displacements. As a result, if the MTS method is applied iteratively,
and the shift is refined after each iteration, the bias eventually becomes negligible. By using just 3
iterations, and noticing that <code>log(bias_increment)</code> is a linear sequence, it is possible to correct for the
bias up to O(10<sup>6</sup>).</p>
</li>
</ul>
<p>Set <code>parameter</code> to 0 for normal behavior. <code>parameter</code> in the range (0,0.1] specifies the desired accuracy.
A negative <code>parameter</code> causes <code>round(-parameter)</code> iterations to be run.
This method supports images with a dimensionality between 1 and 3.</p>
<ul>
<li><code>"PROJ"</code>: The PROJ method computes the shift in each dimension separately, applying the ITER method on the
projection of the image onto each axis. It is fast and fairly accurate for high SNR. Should not be used for
low SNR. <code>parameter</code> is passed unchanged to the ITER method. This method supports images with any number of
dimensions.</li>
</ul>
<p><code>in1</code> and <code>in2</code> must be scalar images with the same dimensionality and sizes.</p>
<aside class="m-note m-default">
<h4>Literature</h4>
<ul>
<li>C.L. Luengo Hendriks, “Improved Resolution in Infrared Imaging Using Randomly Shifted Images”, M.Sc. Thesis,
Delft University of Technology, The Netherlands, 1998.</li>
<li>T.Q. Pham, M. Bezuijen, L.J. van Vliet, K. Schutte and C.L. Luengo Hendriks, “Performance of Optimal
Registration Estimators”, in: Visual Information Processing XIV, Proceedings of SPIE 5817, 2005.</li>
</ul>
</aside>
</div></section>
<section class="m-doc-details" id="dip-FourierMellinMatch2D-Image-CL-Image-CL-Image-L-String-CL-String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-FourierMellinMatch2D-Image-CL-Image-CL-Image-L-String-CL-String-CL" class="m-doc-self">dip::<wbr />FourierMellinMatch2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in1,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& in2,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& interpolationMethod = S::LINEAR,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& correlationMethod = S::PHASE)</span></span>
</h3>
<p>Finds the scaling, translation and rotation between two 2D images using the Fourier Mellin transform</p>
<p>The output array represents a 2x3 affine transform matrix (in column-major order) that can be used as input
to <a href="geometry.html#dip-AffineTransform-Image-CL-Image-L-FloatArray-CL-String-CL"><code>dip::AffineTransform</code></a> to transform <code>in2</code> to match <code>in1</code>. <code>out</code> is the <code>in2</code> image transformed in this way.</p>
<p>The two images must be real-valued, scalar and two-dimensional, and have the same sizes.</p>
<p><code>interpolationMethod</code> has a restricted set of options: <code>"linear"</code>, <code>"3-cubic"</code>, or <code>"nearest"</code>.
See <a href="geometry.html#interpolation_methods">Interpolation methods</a> for their definition. If <code>in</code> is binary, <code>interpolationMethod</code> will be
ignored, nearest neighbor interpolation will be used.</p>
<p><code>correlationMethod</code> determines the normalization applied in the cross correlation. It can be
<code>"don't normalize"</code>, <code>"normalize"</code> or <code>"phase"</code>. See <a href="analysis.html#dip-CrossCorrelationFT-Image-CL-Image-CL-Image-L-String-CL-String-CL-String-CL-String-CL"><code>dip::CrossCorrelationFT</code></a> for an explanation of
these flags.</p>
<p>Example:</p>
<div class="m-code"><pre><span></span><span class="n">dip</span><span class="o">::</span><span class="n">Image</span><span class="w"> </span><span class="n">in1</span><span class="p">,</span><span class="w"> </span><span class="n">in2</span><span class="p">,</span><span class="w"> </span><span class="n">out</span><span class="p">;</span>
<span class="c1">// assign to in1 and in2 two similar images</span>
<span class="k">auto</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">FourierMellinMatch2D</span><span class="p">(</span><span class="w"> </span><span class="n">in1</span><span class="p">,</span><span class="w"> </span><span class="n">in2</span><span class="p">,</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="p">);</span>
<span class="c1">// out is a transformed version of in2, as per</span>
<span class="n">dip</span><span class="o">::</span><span class="n">AffineTransform</span><span class="p">(</span><span class="w"> </span><span class="n">in2</span><span class="p">,</span><span class="w"> </span><span class="n">out</span><span class="p">,</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">);</span>
</pre></div>
</div></section>
<section class="m-doc-details" id="dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-" class="m-doc-self">dip::<wbr />StructureTensor</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& gradientSigmas = {1.0},
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& tensorSigmas = {5.0},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::BEST,
<a href="supporttypes.html#dip-StringArray" class="m-doc">dip::StringArray</a> const& boundaryCondition = {},
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> truncation = 3)</span></span>
</h3>
<p>Computes the structure tensor.</p>
<p>The structure tensor is a tensor image that contains, at each pixel, information about the local image structure.
The eigenvalues of the structure tensor are larger when there are stronger gradients locally. That is, if all
eigenvalues are small, the image is locally uniform. If one eigenvalue is large, then there is a unique line
or edge orientation (in 2D), or a plane-like edge or structure (in 3D). In 3D, if two eigenvalues are large
then there is a line-like structure. The associated eigenvalues indicate the orientation of this structure.
See the literature references below for more information.</p>
<p><code>in</code> must be a scalar, real-valued image. <code>out</code> will be a symmetric NxN tensor image, where N is the number
of dimensions in <code>in</code>. Out is computed by:</p>
<div class="m-code"><pre><span></span><span class="n">dip</span><span class="o">::</span><span class="n">Image</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Gradient</span><span class="p">(</span><span class="w"> </span><span class="n">in</span><span class="p">,</span><span class="w"> </span><span class="n">gradientSigmas</span><span class="w"> </span><span class="p">);</span>
<span class="n">dip</span><span class="o">::</span><span class="n">Image</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Gauss</span><span class="p">(</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Transpose</span><span class="p">(</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">),</span><span class="w"> </span><span class="n">tensorSigmas</span><span class="w"> </span><span class="p">);</span>
</pre></div>
<p>If <code>mask</code> is given (not a raw image), then it is interpreted as confidence weights for the input pixels. It
should have values between 0 and 1 (or be binary). Normalized differential convolution is used to compute the
gradients. This method applies Gaussian gradients taking missing and uncertain values into account. See
<a href="linear.html#dip-NormalizedDifferentialConvolution-Image-CL-Image-CL-Image-L-dip-uint--FloatArray-CL-String-CL-StringArray-CL-dfloat-"><code>dip::NormalizedDifferentialConvolution</code></a>.</p>
<p>See <a href="linear.html#dip-Gauss-Image-CL-Image-L-FloatArray--UnsignedArray--String-CL-StringArray-CL-dfloat-"><code>dip::Gauss</code></a> for the meaning of the parameters <code>method</code>, <code>boundaryCondition</code> and <code>truncation</code>.</p>
<p>The functions <a href="analysis.html#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis2D</code></a> and <a href="analysis.html#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis3D</code></a> can be used with the output
of this function to obtain useful image parameters.</p>
<aside class="m-note m-default">
<h4>Literature</h4>
<ul>
<li>B. Jahne, “Practical Handbook on Image Processing for Scientific Applications”, chapter 13, CRC Press, 1997.</li>
<li>L.J. van Vliet and P.W. Verbeek, “Estimators for Orientation and Anisotropy in Digitized Images”,
in: Proceedings First Annual Conference of the Advanced School for Computing and Imaging, pp. 442-450, ASCI, Delft, 1995.</li>
<li>C.F. Westin, “A Tensor Framework for Multidimensional Signal Processing”, PhD thesis, Linköping University, Sweden, 1994.</li>
</ul>
</aside>
</div></section>
<section class="m-doc-details" id="dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P" class="m-doc-self">dip::<wbr />StructureTensorAnalysis2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* orientation = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* energy = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* anisotropy1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* anisotropy2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* curvature = nullptr)</span></span>
</h3>
<p>Computes useful image parameters from the 2D structure tensor.</p>
<p><code>in</code> must be a 2D, symmetric 2x2 tensor image obtained from <a href="analysis.html#dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-"><code>dip::StructureTensor</code></a>. This function takes a pointer
to output images, instead of taking them by reference. Set pointers to <code>nullptr</code> if you do not want the given
output computed. Use this function as follows:</p>
<div class="m-code"><pre><span></span><span class="n">dip</span><span class="o">::</span><span class="n">Image</span><span class="w"> </span><span class="n">st</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">StructureTensor</span><span class="p">(</span><span class="w"> </span><span class="n">img</span><span class="w"> </span><span class="p">);</span>
<span class="n">dip</span><span class="o">::</span><span class="n">Image</span><span class="w"> </span><span class="n">energy</span><span class="p">,</span><span class="w"> </span><span class="n">orientation</span><span class="p">;</span>
<span class="n">dip</span><span class="o">::</span><span class="n">StructureTensorAnalysis2D</span><span class="p">(</span><span class="w"> </span><span class="n">st</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">orientation</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">energy</span><span class="w"> </span><span class="p">);</span>
</pre></div>
<p>(note how the last two parameters were not given, they default to <code>nullptr</code>). The code above computes both the
orientation and energy values of the structure tensor.</p>
<p>The output images will be reallocated to be the same size as the input image. They will be scalar and of a
floating-point type.</p>
<p>The output images are defined as follows:</p>
<table class="m-table">
<thead>
<tr>
<th>Image</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><code>l1</code></td>
<td>The largest eigenvalue.</td>
</tr>
<tr>
<td><code>l2</code></td>
<td>The smallest eigenvalue.</td>
</tr>
<tr>
<td><code>orientation</code></td>
<td>Orientation. Lies in the interval (-π/2, π/2).</td>
</tr>
<tr>
<td><code>energy</code></td>
<td>Sum of the two eigenvalues <code>l1</code> and <code>l2</code>.</td>
</tr>
<tr>
<td><code>anisotropy1</code></td>
<td>Measure for local anisotropy: <code>( l1 - l2 ) / ( l1 + l2 )</code>.</td>
</tr>
<tr>
<td><code>anisotropy2</code></td>
<td>Measure for local anisotropy: <code>1 - l2 / l1</code>, where <code>l1 > 0</code>.</td>
</tr>
<tr>
<td><code>curvature</code></td>
<td>Magnitude of the curvature (1/bending radius).</td>
</tr>
</tbody>
</table>
<p>Curvature sign cannot be computed because the structure tensor does not distinguish the direction of
the gradient.</p>
<p>Note that <code>l1</code> and <code>l2</code> will both reference data within the same data segment, and therefore will likely not
have normal strides.</p>
<p>For a 3D structure tensor analysis, see the function <a href="analysis.html#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis3D</code></a>.
A different interface to this function is available in <a href="analysis.html#dip-StructureTensorAnalysis-Image-CL-ImageRefArray-L-StringArray-CL"><code>dip::StructureTensorAnalysis</code></a>.
Note that eigenvalues and eigenvectors can also be computed using <a href="math_tensor.html#dip-Eigenvalues-Image-CL-Image-L"><code>dip::Eigenvalues</code></a>
and <a href="numeric.html#dip-EigenDecomposition-dip-uint--ConstSampleIterator<dfloat>--SampleIterator<dcomplex>--SampleIterator<dcomplex>-"><code>dip::EigenDecomposition</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P" class="m-doc-self">dip::<wbr />StructureTensorAnalysis3D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* phi1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* theta1 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* phi2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* theta2 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* l3 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* phi3 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* theta3 = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* energy = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* cylindrical = nullptr,
<a href="dip-Image.html" class="m-doc">dip::Image</a>* planar = nullptr)</span></span>
</h3>
<p>Computes useful image parameters from the 3D structure tensor.</p>
<p><code>in</code> must be a 3D, symmetric 3x3 tensor image obtained from <a href="analysis.html#dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-"><code>dip::StructureTensor</code></a>. This function takes a pointer
to output images, instead of taking them by reference. Set pointers to <code>nullptr</code> if you do not want the given
output computed. Use this function as follows:</p>
<div class="m-code"><pre><span></span><span class="n">dip</span><span class="o">::</span><span class="n">Image</span><span class="w"> </span><span class="n">st</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">StructureTensor</span><span class="p">(</span><span class="w"> </span><span class="n">img</span><span class="w"> </span><span class="p">);</span>
<span class="n">dip</span><span class="o">::</span><span class="n">Image</span><span class="w"> </span><span class="n">energy</span><span class="p">;</span>
<span class="n">dip</span><span class="o">::</span><span class="n">StructureTensorAnalysis3D</span><span class="p">(</span><span class="w"> </span><span class="n">st</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">energy</span><span class="w"> </span><span class="p">);</span>
</pre></div>
<p>(note how the last two parameters were not given, they default to <code>nullptr</code>). The code above computes the
energy value of the structure tensor.</p>
<p>The output images will be reallocated to be the same size as the input image. They will be scalar and of a
floating-point type.</p>
<p>The output images are defined as follows:</p>
<table class="m-table">
<thead>
<tr>
<th>Image</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><code>l1</code></td>
<td>The largest eigenvalue.</td>
</tr>
<tr>
<td><code>phi1</code></td>
<td>First component of the orientation of the eigenvector for <code>l1</code>.</td>
</tr>
<tr>
<td><code>theta1</code></td>
<td>Second component of the orientation of the eigenvector for <code>l1</code>.</td>
</tr>
<tr>
<td><code>l2</code></td>
<td>The middle eigenvalue.</td>
</tr>
<tr>
<td><code>phi2</code></td>
<td>First component of the orientation of the eigenvector for <code>l2</code>.</td>
</tr>
<tr>
<td><code>theta2</code></td>
<td>Second component of the orientation of the eigenvector for <code>l2</code>.</td>
</tr>
<tr>
<td><code>l3</code></td>
<td>The smallest eigenvalue.</td>
</tr>
<tr>
<td><code>phi3</code></td>
<td>First component of the orientation of the eigenvector for <code>l3</code>.</td>
</tr>
<tr>
<td><code>theta3</code></td>
<td>Second component of the orientation of the eigenvector for <code>l3</code>.</td>
</tr>
<tr>
<td><code>energy</code></td>
<td>Sum of the three eigenvalues <code>l1</code>, <code>l2</code> and <code>l3</code>.</td>
</tr>
<tr>
<td><code>cylindrical</code></td>
<td>Measure for local anisotropy: <code>( l2 - l3 ) / ( l2 + l3 )</code>.</td>
</tr>
<tr>
<td><code>planar</code></td>
<td>Measure for local anisotropy: <code>( l1 - l2 ) / ( l1 + l2 )</code>.</td>
</tr>
</tbody>
</table>
<p>For a 2D structure tensor analysis, see the function <a href="analysis.html#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis2D</code></a>.
A different interface to this function is available in <a href="analysis.html#dip-StructureTensorAnalysis-Image-CL-ImageRefArray-L-StringArray-CL"><code>dip::StructureTensorAnalysis</code></a>.
Note that eigenvalues and eigenvectors can also be computed using <a href="math_tensor.html#dip-Eigenvalues-Image-CL-Image-L"><code>dip::Eigenvalues</code></a>
and <a href="numeric.html#dip-EigenDecomposition-dip-uint--ConstSampleIterator<dfloat>--SampleIterator<dcomplex>--SampleIterator<dcomplex>-"><code>dip::EigenDecomposition</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-StructureTensorAnalysis-Image-CL-ImageRefArray-L-StringArray-CL"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-StructureTensorAnalysis-Image-CL-ImageRefArray-L-StringArray-CL" class="m-doc-self">dip::<wbr />StructureTensorAnalysis</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html#dip-ImageRefArray" class="m-doc">dip::ImageRefArray</a>& out,
<a href="supporttypes.html#dip-StringArray" class="m-doc">dip::StringArray</a> const& outputs)</span></span>
</h3>
<p>Interface to <a href="analysis.html#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis2D</code></a> and <a href="analysis.html#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis3D</code></a>.</p>
<p><code>in</code> is as in <a href="analysis.html#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis2D</code></a> or <a href="analysis.html#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis3D</code></a>. That is, either a 2D
symmetric 2x2 tensor image or a 3D symmetric 3x3 tensor image, real-valued, as obtained from <a href="analysis.html#dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-"><code>dip::StructureTensor</code></a>.
<code>out</code> is an array with references to output images. It should have exactly as many elements as <code>outputs</code>.</p>
<p><code>outputs</code> is an array with one or more of the following strings, indicating which outputs are needed:</p>
<ul>
<li>For 2D inputs: <code>"l1"</code>, <code>"l2"</code>, <code>"orientation"</code>, <code>"energy"</code>, <code>"anisotropy1"</code>, <code>"anisotropy2"</code>, <code>"curvature"</code>.</li>
<li>For 3D inputs: <code>"l1"</code>, <code>"phi1"</code>, <code>"theta1"</code>, <code>"l2"</code>, <code>"phi2"</code>, <code>"theta2"</code>, <code>"l3"</code>, <code>"phi3"</code>, <code>"theta3"</code>,
<code>"energy"</code>, <code>"cylindrical"</code>, <code>"planar"</code>.</li>
</ul>
<p>The order of the strings in <code>outputs</code> indicates the order they will be written to the <code>out</code> array.</p>
<p>See the functions <a href="analysis.html#dip-StructureTensorAnalysis2D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis2D</code></a> and <a href="analysis.html#dip-StructureTensorAnalysis3D-Image-CL-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P-Image-P"><code>dip::StructureTensorAnalysis3D</code></a> for more information
on these outputs.</p>
</div></section>
<section class="m-doc-details" id="dip-StructureAnalysis-Image-CL-Image-CL-std-vector<dfloat>-CL-String-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-StructureAnalysis-Image-CL-Image-CL-std-vector<dfloat>-CL-String-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-" class="m-doc-self">dip::<wbr />StructureAnalysis</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
std::vector<dfloat> const& scales = {},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& feature = "energy",
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& gradientSigmas = {1.0},
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& method = S::BEST,
<a href="supporttypes.html#dip-StringArray" class="m-doc">dip::StringArray</a> const& boundaryCondition = {},
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> truncation = 3)</span></span>
</h3>
<p>Analyzes the local structure of the image at multiple scales.</p>
<p>Computes the structure tensor, smoothed with each of the values in <code>scales</code> multiplied by <code>gradientSigmas</code>,
determines the feature <code>feature</code> from it, and averages across the image for each scale. This leads to a series
of data points showing how the selected feature changes across scales. <code>scales</code> and <code>gradientSigmas</code> are
given in pixels, the image’s pixel size is not taken into account.</p>
<p>The reason that each element of <code>scales</code> is multiplied by <code>gradientSigmas</code> is to allow analysis of
non-isotropic images. The <code>gradientSigmas</code> corrects for the non-isotropy, allowing <code>scales</code> to be a scalar
value for each scale.</p>
<p><code>scales</code> defaults to a series of 10 values geometrically spaced by <code>sqrt(2)</code>, and starting at 1.0. Units are
pixels.</p>
<p><code>feature</code> can be any of the strings allowed by <a href="analysis.html#dip-StructureTensorAnalysis-Image-CL-ImageRefArray-L-StringArray-CL"><code>dip::StructureTensorAnalysis</code></a>, but <code>"energy"</code>, <code>"anisotropy1"</code>,
and <code>"anisotropy2"</code> (in 2D), and <code>"energy"</code>, <code>"cylindrical"</code>, and <code>"planar"</code> (in 2D) make the most sense.</p>
<p>See <a href="linear.html#dip-Gauss-Image-CL-Image-L-FloatArray--UnsignedArray--String-CL-StringArray-CL-dfloat-"><code>dip::Gauss</code></a> for the meaning of the parameters <code>method</code>, <code>boundaryCondition</code> and <code>truncation</code>.</p>
<p><code>in</code> must be scalar and real-valued, and either 2D or 3D. <code>mask</code> must be of the same size, and limits the
region over which the structure tensor feature is averaged.</p>
<p>See <a href="analysis.html#dip-StructureTensor-Image-CL-Image-CL-Image-L-FloatArray-CL-FloatArray-CL-String-CL-StringArray-CL-dfloat-"><code>dip::StructureTensor</code></a> for more information about the structure tensor.</p>
</div></section>
<section class="m-doc-details" id="dip-MonogenicSignal-Image-CL-Image-L-FloatArray-CL-dfloat--String-CL-String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-MonogenicSignal-Image-CL-Image-L-FloatArray-CL-dfloat--String-CL-String-CL" class="m-doc-self">dip::<wbr />MonogenicSignal</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-FloatArray" class="m-doc">dip::FloatArray</a> const& wavelengths = {3.0,24.0},
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> bandwidth = 0.41,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& inRepresentation = S::SPATIAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& outRepresentation = S::SPATIAL)</span></span>
</h3>
<p>Computes the monogenic signal, a multi-dimensional generalization of the analytic signal.</p>
<p>The monogenic signal of an <em>n</em>-dimensional image has <em>n</em>+1 components. The first component has been
filtered with the even (symmetric) filter component, and the other <em>n</em> components have been filtered
with the odd (antisymmetric) filter components, where each of those filter components is antisymmetric
along a different dimension.</p>
<p>This function splits the frequency spectrum of the image into <code>wavelengths.size()</code> components. The radial
component of a log-Gabor filter bank will be used. These radial frequency filters are defined by
<code>wavelengths</code> (in pixels) and <code>bandwidth</code>. See <a href="linear.html#dip-LogGaborFilterBank-Image-CL-Image-L-FloatArray-CL-dfloat--dip-uint--String-CL-String-CL"><code>dip::LogGaborFilterBank</code></a> for details.</p>
<p>The filters are always applied in the frequency domain. If <code>outRepresentation</code> is <code>"spatial"</code>, the inverse
Fourier transform will be applied to bring the result back to the spatial domain. Otherwise, it should be
<code>"frequency"</code>, and no inverse transform will be applied. Likewise, <code>inRepresentation</code> specifies whether <code>in</code>
has already been converted to the frequency domain or not.</p>
<p><code>in</code> must be scalar and real-valued if given in the spatial domain. If <code>in</code> is in the frequency domain, it is
expected to be conjugate symmetric, and thus have a real-valued inverse transform (the imaginary part of the
inverse transform will be discarded).
Out will be a tensor image with <code>wavelengths.size()</code> tensor columns and <em>n</em>+1 tensor rows. The data type will be
single-precision float for spatial-domain output, or single-precision complex for frequency-domain output.</p>
<aside class="m-note m-default">