S53_diffdrive_sensing.ipynb

{
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   "source": [
    "# Cameras for Robot Vision"
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {
    "colab_type": "text",
    "tags": [
     "no-tex"
    ]
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   "source": [
    "<a href=\"https://colab.research.google.com/github/gtbook/robotics/blob/main/S53_diffdrive_sensing.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "l9PoxhNACByz",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install -q -U gtbook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "Xanc4Al-lQIn",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import plotly.graph_objects as go\n",
    "try:\n",
    "    import google.colab\n",
    "except:\n",
    "    import plotly.io as pio\n",
    "    pio.renderers.default = \"png\"\n",
    "\n",
    "import gtsam\n",
    "from gtbook import diffdrive\n",
    "from gtbook.html import ROW\n",
    "\n",
    "FIG5 = \"https://raw.githubusercontent.com/gtbook/robotics/main/Figures5\""
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "-Bdg85pwVWJ9",
   "metadata": {},
   "source": [
    "```{index} sensing; vision\n",
    "```\n",
    "\n",
    "> A camera is a super-sensor."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f263a08e",
   "metadata": {
    "tags": [
     "no-pdf"
    ]
   },
   "source": [
    "<img src=\"Figures5/S53-Two-wheeled_Toy_Robot-04.jpg\" alt=\"Splash image with steampunk robot sporting a stereo camera\" width=\"40%\" align=center style=\"vertical-align:middle;margin:10px 0px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "m4uKhYmjMpES",
   "metadata": {},
   "source": [
    "In this section, we introduce cameras, which are among the most powerful sensors available to robots. We focus mainly on the geometric aspects of image formation, namely the relationships between 3D objects in the world and their 2D camera images. We will describe how to estimate the relevant parameters of the imaging process (camera calibration), and how two cameras can be used to estimate the 3D structure of the environment using two 2D images."
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "## Cameras throughout History\n",
    "\n",
    "```{index} Camera Obscura, photography, pinhole\n",
    "```\n",
    "> The basic ideas behind cameras have been around for centuries.\n",
    "\n",
    "Everyone knows what a camera is these days, and you probably have between 1 and 5 on your phone, depending on what model you have.\n",
    "\n",
    "Historically, a **Camera Obscura**, literally \"dark room\", showed people that focused *upside-down* images can be formed on a surface, provided the light rays coming from outside the room were constricted to a small **pinhole**. If you have never experienced this in real life, it is a worthwhile experience to see this with your own eyes. One of the surprising but obvious properties of a camera obscura is that the images *move*: the \"camera\" or room does not apply a still photo!\n",
    "\n",
    "```{index} Daguerreotype\n",
    "```\n",
    "The question then is how to capture these fleeting images. Da Vinci wrote extensively about using the camera obscura for drawing, and several 17th century painters may have used it in their painting process, the most famous of them being [Johannes Vermeer](https://en.wikipedia.org/wiki/Johannes_Vermeer).\n",
    "The invention of **photography** (painting with light!) is usually credited to [Niépce](https://en.wikipedia.org/wiki/Nic%C3%A9phore_Ni%C3%A9pce), who used a light-sensitive material to capture the light around 1825. However, it was his partner [Daguerre](https://en.wikipedia.org/wiki/Louis_Daguerre) who introduced photography to the world on a large scale via his *Daguerreotype* process, released into the public domain in 1839.\n",
    "\n",
    "```{index} digital cameras, pixel\n",
    "```\n",
    "```{index} pair: CCD; charged-coupled device\n",
    "```\n",
    "```{index} pair: CMOS; complementary metal-oxide-semiconductor\n",
    "```\n",
    "Since the 1990s, **digital cameras** have replaced cameras based on chemical emulsions, using CCDs (charged-coupled devices) or CMOS (complementary metal-oxide-semiconductor) sensors as the underlying technology. Both sensor types capture photons in an array of picture elements or **pixels**. We will not discuss in detail how these devices work, but in essence both sensor types count how many photons fall onto each pixel's area over a given time period. Below we discuss the more practical matter of the format in which images come to us, and how they can be used for robot vision."
   ]
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   "source": [
    "## Cameras for Robot Vision\n",
    "\n",
    "> A camera is two sensors in one.\n",
    "\n",
    "Cameras are amazing devices, and actually pack *two* sensors in one. First, a camera accurately measures the direction to points in space. Second, the 2D images formed on the sensor\n",
    "contain photometric information about the scene.\n",
    "This information can be analyzed by computer vision algorithms to recognize objects and analyze the scene in front of the robot. In this section we focus on the basics of image formation,\n",
    "however, and leave algorithms for Section 5.4.\n",
    "\n",
    "```{index} lens, pinhole, depth of field\n",
    "```\n",
    "A pinhole by itself is rather amazing, as it renders the entire scene in front entirely *in focus*. However, it has a large drawback, in that it only lets in a tiny amount of light. The solution is to use a **lens**, which *collects* light over a larger diameter and *focuses* the light onto the image sensor. The upshot is that we can collect a lot more light (photons) in the same amount of time. The *downside* is that only part of the scene can be in focus at a given time - a phenomenon that leads to the *depth of field* of a camera: the (possibly narrow) area between where objects are too close or too far to be in focus.\n",
    "\n",
    "```{index} resolution, focal length\n",
    "```\n",
    "```{index} pair: FOV; field of view\n",
    "```\n",
    "The most important properties associated with a digital camera are its \n",
    "**resolution**, typically specified as $W \\times H$ in pixels; \n",
    "its **focal length**, which, as we will see below, can be measured either in meters or pixels;\n",
    "and its **field of view** (FOV), typically specified in degrees (horizontal, vertical, or diagonal). \n",
    "The resolution is a property of the *sensor*, whereas focal length and field of view depend on the lens.\n",
    "We will investigate the relationships between these quantities below, where we describe the camera imaging geometry."
   ]
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   "cell_type": "markdown",
   "id": "LoAMnjvB3qXE",
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   "source": [
    "```{index} RGB\n",
    "```\n",
    "In essence, we get access to images as multi-dimensional arrays. Expensive CCD cameras have three sensors, one per color channel (red, green, and blue or **RGB**), and hence their raw output can be represented as three arrays of numbers that represent light levels in a specific frequency band, roughly corresponding to the same frequency bands that receptors in our eye are sensitive to. However, most cameras now have a *single* CMOS sensor with a color filter on top (called a Bayer pattern), and specialized algorithms that hallucinate three color channels. Actually, most cameras do a great deal more processing to improve the color and lighting; this sometimes gets in the way of algorithms that rely on measuring light exactly, but those are rather rare. In most cases, we are content to simply think of a (color) image as a $H \\times W \\times 3$ array of numbers, where $H$ is the height of the image, and $W$ the width."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2bba525",
   "metadata": {},
   "source": [
    "As an example on how to deal with images in code, in Figure [1](#fig:outdoor-lagr) we show an image on the left, taken by the differential-drive robot on the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dWfNJ6RBxQ8U",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table width=\"100%\" class={cls}>\n",
       "\n",
       "<tr>\n",
       "<td style=\"text-align:left;\"><img src=\"https://raw.githubusercontent.com/gtbook/robotics/main/Figures5/LL_color_1201754063.387872.jpeg?raw=1\" alt=\"Outdoor, beaten down path\"></td>\n",
       "<td style=\"text-align:left;\"><img src=\"https://raw.githubusercontent.com/gtbook/robotics/main/Figures5/lagr-robot.jpg?raw=1\" alt=\"LAGR robot\" height=\"359\"></td>\n",
       "</tr></table>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "#| caption: An outdoor scene on the left, taken by the \"LAGR\" robot on the right.\n",
    "#| label: fig:outdoor-lagr\n",
    "image_name = \"LL_color_1201754063.387872.jpeg\"\n",
    "ROW([f'<img src=\"{FIG5}/{image_name}?raw=1\" alt=\"Outdoor, beaten down path\">',\n",
    "     f'<img src=\"{FIG5}/lagr-robot.jpg?raw=1\" alt=\"LAGR robot\" height=\"359\">'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pTSfIaJPutVb",
   "metadata": {},
   "source": [
    "```{index} pair: Python Imaging Library; PIL\n",
    "```\n",
    "A python library, the [Python Imaging Library](https://pillow.readthedocs.io/en/stable/) or PIL provides some basic capabilities to deal with digital images. We can load an image using the `PIL.Image` class, examine its dimensions, and create a numpy array view (you can also use `display` in a notebook to show it):"
   ]
  },
  {
   "cell_type": "code",
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   "id": "Fn-WSMx83Co6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "resolution = 512x384\n",
      "image_data.shape = (384, 512, 3)\n",
      "[76 54 56]\n"
     ]
    }
   ],
   "source": [
    "image = diffdrive.read_image(image_name) # locally: PIL.Image.open(image_name)\n",
    "print(f\"resolution = {image.width}x{image.height}\")\n",
    "image_data = np.asarray(image)\n",
    "print(f\"image_data.shape = {image_data.shape}\")\n",
    "print(image_data[383,511])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "wpwvFOsHjp3_",
   "metadata": {},
   "source": [
    "We see that the image width and height are $512$ and $384$, respectively. But when we access the array with `numpy`, the first (slowest changing) dimension is the *height*, followed by the width and then the color dimension. Hence, the `numpy` array has to be indexed using the $(\\text{row},\\text{column})$ convention, after which you get the RGB value in the array, as shown in the last line of code above.\n",
    "\n",
    "It is customary to use variables $(i,j)$ or $(r,c)$ to index pixels, where the latter is slightly preferred as it emphasizes the *row* and *column* semantics of these *integer* coordinates."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1VSEd0UFqClr",
   "metadata": {},
   "source": [
    "## Camera Imaging Geometry\n",
    "\n",
    "> Points in the 3D environment project to points in a 2D image.\n",
    "\n",
    "```{index} pinhole camera model\n",
    "```\n",
    "In order to use a camera to infer the properties of the robot's 3D environment,\n",
    "we need to fully under stand the geometry of image formation.\n",
    "We already did so at a superficial level, but the geometry involved needs more detail: exactly what light falls into what pixel?\n",
    "The simplest model for geometric image formation is the **pinhole camera model**. \n",
    "Imagine a three-dimensional, orthonormal coordinate frame with its origin at center of the lens.\n",
    "Computer vision folks use a very specific camera convention which will make the math easy:\n",
    "- the x-axis points to the *right*;\n",
    "- the y-axis points *down*; and \n",
    "- the z-axis points into the scene.\n",
    "\n",
    "{raw:tex}`\\noindent`\n",
    "When we express 3D points in the scene according to this convention, in a coordinate frame that is attached the camera, we speak of specifying an object in *camera coordinates*. For example, a 2 meter tall person, standing 5 meters away, and 3 meters to the left, would be in between these two 3D coordinates: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "whBvZ0qA36zj",
   "metadata": {},
   "outputs": [],
   "source": [
    "feet = gtsam.Point3(-3,1.7,5) # point at the feet of the person, 5 meters in front of camera, 3 meters to the left\n",
    "head = gtsam.Point3(-3,-0.3,5) # point at the top of the head (note, Y = *minus* 2 meters)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "k7BMtCQeRNCc",
   "metadata": {},
   "source": [
    "Note that we specify the location of the person's feet in *camera coordinates*, and if we are holding the camera level at a height of 1.7 meters, the feet will be 1.7 meters *below* the pinhole position.\n",
    "\n",
    "Thinking back to the camera obscura example, the pinhole camera model specifies that a 3D point $(X,Y,Z)$ in camera coordinates will be projected onto an image plane *behind* the camera:\n",
    "\\begin{equation}\n",
    "X_I = - F \\frac{X}{Z} ~~~~\n",
    "Y_I = - F \\frac{Y}{Z} ~~~~\n",
    "Z_I = -F\n",
    "\\end{equation}\n",
    "Here, $F$ denotes the focal length measured in meters,\n",
    "which is defined as the distance from the image plane to the pinhole, i.e., the center of the lens. \n",
    "We show the geometry in Figure [2](#fig:pinhole_geometry). Note that the coordinate frame is rendered in color such that the x-axis is red, the y-axis green, and the z-axis blue, i.e., XYZ=RGB."
   ]
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  {
   "cell_type": "code",
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   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: The geometry of the pinhole camera model.\n",
    "#| label: fig:pinhole_geometry\n",
    "F = 1 # meter\n",
    "from gtbook.diffdrive import axes, plane, ray, show_3d\n",
    "show_3d(go.Figure(data = plane(-F) + [ray(feet, -F), ray(head, -F)] + axes()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "gdN6XBG6zVu5",
   "metadata": {},
   "source": [
    "However, it is not easy to debug algorithms with a true *upside down*  pinhole image. Instead, we can define a *virtual image plane* at a distance $F$ *in front* of the pinhole, which is non-physical, but has the advantage that the image now appears right-side up. We simply have to reflect the projected coordinates:\n",
    "\\begin{equation}\n",
    "X_V = F \\frac{X}{Z} ~~~~\n",
    "Y_V = F \\frac{Y}{Z} ~~~~\n",
    "Z_V = F\n",
    "\\end{equation}\n",
    "The virtual image geometry, with the virtual image *in front* of the camera, is shown in Figure [3](#fig:virtual_image)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98ReH9s8q8BU",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: The virtual image is *in front* of the camera.\n",
    "#| label: fig:virtual_image\n",
    "show_3d(go.Figure(data = plane(F) + [ray(feet, F), ray(head, F)] + axes()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "AmG9i2PH6JE3",
   "metadata": {},
   "source": [
    "```{index} intrinsic camera coordinates, principal point, optical axis\n",
    "```\n",
    "The above has the disadvantage that we still have to take into account the focal length $F$ when doing the projection. Dividing by the focal length yields the fundamental *pinhole projection equation*:\n",
    "\\begin{equation}\n",
    "x = \\frac{X}{Z} ~~~~ y = \\frac{Y}{Z}\n",
    "\\end{equation}\n",
    "The dimensionless $x$ and $y$ coordinates are called the **intrinsic camera coordinates**, and can be thought of as the image of the scene in a virtual image plane situated at a focal length of 1.0. \n",
    "Note that the image origin at $(x,y)=(0,0)$ is the location where the **optical axis** (the blue z-axis above) pierces the image plane. \n",
    "This point is commonly refered to as the **principal point**.\n",
    "The intrinsic coordinates are in essence measuring a direction in space,\n",
    "parameterized by a location in the virtual image plane."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "yOy6v--GgxhV",
   "metadata": {},
   "source": [
    "## Camera Calibration\n",
    "\n",
    "> From intrinsic to sensor coordinates.\n",
    "\n",
    "```{index} sensor coordinates\n",
    "```\n",
    "Intrinsic coordinates are dimensionless, but what *pixels* in an image do they correspond to?\n",
    "Also, when we project real-valued 3D coordinates in an image, we get *real-valued* intrinsic coordinates $(x,y)$. How does that relate to integer pixel coordinates? \n",
    "To translate from intrinsic coordinates to pixel coordinates, we introduce real-valued **sensor coordinates** $(u,v)$, with the following conventions (try to draw this out for a $4\\times3$ image!):\n",
    "- the top-left of the sensor corresponds to $(u, v)=(0.0, 0.0)$;\n",
    "- the bottom-right of the sensor corresponds to $(u, v)=(W, H)$.\n",
    "\n",
    "Some things to note:\n",
    "- the vertical $v$-axis points *down*;\n",
    "- the units are in pixels (*fractional* pixels, if being precise);\n",
    "- we swapped the convention from $(r,c)\\Leftrightarrow(\\text{row},\\text{column})$ to $(u,v)\\Leftrightarrow(\\text{horizontal}, \\text{vertical})$;\n",
    "- the middle of pixel $(r, c)=(0, 0)$ has sensor coordinates $(u, v)=(0.5, 0.5)$;\n",
    "- the middle of pixel $(r, c)=(H-1, W-1)$ has sensor coordinates $(u, v)=(W-0.5, H-0.5)$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5BGVnm-ZbzMI",
   "metadata": {},
   "source": [
    "```{index} camera calibration model\n",
    "```\n",
    "The simplest **camera calibration model** is just a linear mapping, which is most appropriate for lenses with a small field of view. For this we need four parameters $\\alpha$, $\\beta$, $u_0$, and $v_0$, to convert from intrinsic coordinates $(x,y)$ to sensor coordinates $(u,v)$:\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "u &= u_0 + \\alpha x \\\\\n",
    "v &= v_0 + \\beta y\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "As an example, consider the [FireFly S](https://www.flir.com/products/firefly-s/?model=FFY-U3-04S2C-C) machine vision camera, which has the following specifications:\n",
    "- sensor: [Sony IMX297](https://www.phase1vision.com/userfiles/product_files/imx273_287_296_297_flyer.pdf) (CMOS)\n",
    "- resolution: 720 x 540\n",
    "- pixel size: 6.9 $\\mu m$ (H) x 6.9 $\\mu m$ (V)\n",
    "- sensor size: 6.3mm diagonally"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "F-k1W_8AjMk9",
   "metadata": {},
   "source": [
    "{raw:tex}`\\noindent`\n",
    "We typically expect the *image center*, corresponding to $(x,y)=(0.0,0.0)$, to be close to $(u_0,v_0)=(W/2,H/2)$. \n",
    "For the sensor above this would be $(u_0,v_0)=(364.0, 272.0)$. \n",
    "To compute $\\alpha$ and $\\beta$ we have to take into account the lens focal length $F$. Since $u$ and $v$ are expressed in pixels, and $x$ and $y$ are dimensionless, it is clear that $\\alpha$ and $\\beta$ must also be expressed in pixels. They can be computed as\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\alpha = F k &= 8\\text{mm}/6.9\\mu\\text{m} \\approx 1160\\text{px}\\\\\n",
    "\\beta = F l &= 8\\text{mm}/6.9\\mu\\text{m} \\approx 1160\\text{px}\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "where \n",
    "\\begin{equation}\n",
    "k = \\text{px}/6.9\\mu\\text{m}\\,\\,\\,\\,\\,\\mathrm{and}\\,\\,\\,\\,l = \\text{px}/6.9\\mu\\text{m}\n",
    "\\end{equation}\n",
    "are sensor-specific constants that indicated the number of pixels per unit of length."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hjo-6_yxgoM5",
   "metadata": {},
   "source": [
    "Whenever $k=l$, the sensor has *square pixels*, and we can just use one proportionality constant, $f=\\alpha=\\beta$.\n",
    "In this case, $f$ again denotes the *focal length*, but this time, expressed in pixels. This is a slight abuse of terminology, as $f$ is a property of both the lens *and* the image sensor plane, but its use is in widespread and we will adopt it here as well."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ovtBgfyyQioE",
   "metadata": {},
   "source": [
    "## Pinhole Projection Equations\n",
    "\n",
    "> From 3D to pixel coordinates.\n",
    "\n",
    "```{index} pinhole projection\n",
    "```\n",
    "Putting all of the above together,\n",
    "we finally obtain the fundamental **pinhole projection** equation, projecting a point $P$ in 3D camera coordinates $P=(X,Y,Z)$, to its 2D image projection $p=(u,v)$ in sensor coordinates:\n",
    "\\begin{equation}\n",
    "u = u_0 + f \\frac{X}{Z} ~~~~ v = v_0 + f \\frac{Y}{Z}.\n",
    "\\end{equation}\n",
    "To obtain integer pixel coordinates $(r,c)$, we simply need to use the *floor* function, truncating the fractional pixel sensor coordinates to a location in the image array. Note that in doing so we also flip horizontal and vertical:\n",
    "\\begin{equation}\n",
    "(r,c) = (\\lfloor v \\rfloor, \\lfloor u \\rfloor)\n",
    "\\end{equation}\n",
    "We can also go the other way, *calibrating* the sensor coordinates $(u,v)$ to the dimensionless intrinsic coordinates $(x,y)$:\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "x &= (u-u_0)/f \\\\\n",
    "y &= (v-v_0)/f\n",
    "\\end{aligned}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "KWxgnvqUR5Et",
   "metadata": {},
   "source": [
    "## Camera Calibration in GTSAM\n",
    "\n",
    "> Everything above and more.\n",
    "\n",
    "In GTSAM you have access to several calibration models, with the simple one above corresponding to `Cal3_S2`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8zshTv8tpiYp",
   "metadata": {},
   "outputs": [],
   "source": [
    "cal_8mm_FireFlyS = gtsam.Cal3_S2(fx=1160, fy=1160, s=0, u0=364, v0=272)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "qPKWCDNV4o0Y",
   "metadata": {},
   "source": [
    "{raw:tex}`\\noindent`\n",
    "The arguments `fx` and `fy` above correspond to $\\alpha$ and $\\beta$, and for now you can ignore the extra `s` argument, denoting *skew* which is almost always zero for modern sensors.\n",
    "We can then convert from integer pixel coordinates to intrinsic coordinates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "hwWvq16WV14s",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "image[0,0] -> (u,v)=(0.5px,0.5px) -> (x,y)=(-0.313,-0.234) \n",
      "image[272,364] -> (u,v)=(364.5px,272.5px) -> (x,y)=(0.0,0.0) \n",
      "image[543,727] -> (u,v)=(727.5px,543.5px) -> (x,y)=(0.313,0.234) \n"
     ]
    }
   ],
   "source": [
    "def calibration_demo(cal:gtsam.Cal3_S2, row:int, col:int):\n",
    "    \"\"\"Convert from integer pixel coordinates to sensor and then intrinsic coordinates.\"\"\"\n",
    "    assert isinstance(row,int) and isinstance(col,int)\n",
    "    u, v = 0.5+col, 0.5+row\n",
    "    x, y = cal.calibrate([u,v])\n",
    "    print(f\"image[{row},{col}] -> (u,v)=({round(u,2)}px,{round(v,2)}px) -> (x,y)=({round(x,3)},{round(y,3)}) \")\n",
    "\n",
    "calibration_demo(cal_8mm_FireFlyS, row=0, col=0)\n",
    "calibration_demo(cal_8mm_FireFlyS, row=272, col=364)\n",
    "calibration_demo(cal_8mm_FireFlyS, row=543, col=727)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "oM3xiPf5ACMG",
   "metadata": {},
   "source": [
    "Note that although the intrinsic coordinates are the dimensionless, you can interpret them as fractions of the focal length. \n",
    "Also, the above was a \"calibration\" example where we go from pixel coordinates to intrinsic coordinates. The calibration objects in GTSAM also provide an `uncalibrate` method which goes the other way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "WblXPqZhKlrb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x,y)=(0,0) -> (u,v)=(364.0px,272.0px)\n"
     ]
    }
   ],
   "source": [
    "u,v = cal_8mm_FireFlyS.uncalibrate([0,0])\n",
    "print(f\"(x,y)=(0,0) -> (u,v)=({round(u,2)}px,{round(v,2)}px)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "uA9J968r9whb",
   "metadata": {},
   "source": [
    "## Camera Field of View\n",
    "\n",
    "```{index} pair: field of view; FOV\n",
    "```\n",
    "The last concept we need to define the camera imaging geometry\n",
    "is the camera's **field of view** or **FOV**.\n",
    "Because the *left-most* ray we can see has $u=0$, it corresponds to $x=-u_0/f\\approx-W/2f$.\n",
    "The horizontal FOV can then be calculated by\n",
    "\\begin{equation}\n",
    "\\mathrm{HFOV} = 2 \\arctan(W/2f)\\,\\,\\mathrm{rad} = 360 \\arctan(W/2f) / \\pi\\,\\,\\mathrm{degrees}\n",
    "\\end{equation}\n",
    "For the sensor-lens combination above we get a relatively narrow field of view of about 35 degrees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "_fd099Uf0Occ",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HFOV for f=1160 is 34.84 degrees\n"
     ]
    }
   ],
   "source": [
    "f = 1160\n",
    "hfov = 360 * math.atan(728/(2*f)) / math.pi\n",
    "print(f\"HFOV for f={f} is {hfov:.2f} degrees\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "_iL5ho22Rgii",
   "metadata": {},
   "source": [
    "Field of view *increases* with decreasing focal length, e.g., a lens of 4mm will give us a bit less than double that HFOV, of around 64 degrees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "xd-dKVfnbMPL",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HFOV for f=579.7 is 64.25 degrees\n"
     ]
    }
   ],
   "source": [
    "f_wide = 4e-3/6.9e-6\n",
    "hfov_wide = 360 * math.atan(728/(2*f_wide)) / math.pi\n",
    "print(f\"HFOV for f={f_wide:.1f} is {hfov_wide:.2f} degrees\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Q70tEVv3AB3z",
   "metadata": {},
   "source": [
    "We can also ask the opposite question: what lens focal length should we choose to get a certain filed of view. For example, for a *diagonal* field of view we have\n",
    "\\begin{equation}\n",
    "\\mathrm{DFOV} = 360 \\arctan(\\sqrt{W^2+H^2}/2f) / \\pi~~\\mathrm{degrees}\n",
    "\\end{equation}\n",
    "and hence\n",
    "\\begin{equation}\n",
    "f = \\frac{\\sqrt{W^2+H^2}}{2 \\tan(\\mathrm{DFOV} \\pi/360)}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ZyB4w8y_7E2C",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f45 = 454.0 pixels, F45 = 3.1 mm\n"
     ]
    }
   ],
   "source": [
    "f45 = math.sqrt(728**2+544**2)/2/math.tan(math.pi/4)\n",
    "F45 = f45*6.9e-3\n",
    "print(f\"f45 = {np.round(f45)} pixels, F45 = {np.round(F45,1)} mm\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fDmYJIfr6Z0o",
   "metadata": {},
   "source": [
    "## Stereo Vision\n",
    "\n",
    "> Given two cameras, we can calculate depth."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mwhW-KuCEhOX",
   "metadata": {},
   "source": [
    "When using two cameras, we can triangulate a feature that is seen in both cameras to calculate its location in space. \n",
    "Given a projection $p=(u,v)$ of a point $P=(X,Y,Z)$ in a single camera we can only determine the *ray* on which the point $P$ must lie.\n",
    "However, if we see *two* projections of the same feature in two cameras, placed side by side, we can *triangulate* the location of $P$.\n",
    "In particular, let us name the cameras \"Left\" and \"Right\", abbreviated as \"L\" and \"R\", and let the two projections be $p_L=(u_L,v_L)$ and $p_R=(u_R,v_R)$. How could we recover the coordinates $(X,Y,Z)$ in, say, the *left* camera coordinate frame?\n",
    "\n",
    "```{index} stereo baseline\n",
    "```\n",
    "We can easily work out the answer *if* the cameras have the same calibration *and* the camera pair is in a \"stereo\" configuration. The latter means that the cameras have exactly the same orientation with respect to the world, and the right camera is displaced only horizontally with respect to the left camera. We call the displacement the **stereo baseline** $B$. In that case we have\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "u_L &= u_0 + f \\frac{X}{Z}, \\,\\,\\,\\,\\, &v_L = v_0 + f \\frac{Y}{Z} \\\\\n",
    "\\\\\n",
    "u_R &= u_0 + f \\frac{X-B}{Z}, \\,\\,\\,\\,\\, &v_R = v_0 + f \\frac{Y}{Z}\n",
    "\\end{aligned}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hwI9xsRWkJST",
   "metadata": {},
   "source": [
    "```{index} disparity, fundamental stereo equation\n",
    "```\n",
    "Two interesting things to note: (a) $u_L$ and $u_R$ differ only because the $X$ coordinate of the point $P$, measured in the right camera, is $B$ less than its value in the left camera.\n",
    "and (b) $v_L$ and $v_R$ have the same value: *corresponding* points in a stereo pair lie on the same scanline in the images. We can use the first fact to calculate the *unknown depth* $Z$, by defining the **disparity** $d$ as the difference of $u_L$ and $u_R$,\n",
    "\\begin{equation}\n",
    "d \\doteq u_L - u_R = f \\frac{X}{Z} - f \\frac{X-B}{Z},\n",
    "\\end{equation}\n",
    "and then performing some algebraic manipulation to obtain the **fundamental stereo equation**:\n",
    "\\begin{equation}\n",
    "Z = B \\frac{f}{d}.\n",
    "\\end{equation}\n",
    "The fraction $f/d$ is dimensionless, as both disparity $d$ and focal length $f$ are expressed in pixels, and hence the resulting depth $Z$ is expressed in the units of the baseline $B$. \n",
    "Using this together with the projection equations above,\n",
    "we can now completely reconstruct the location of the point $P$ in (left) camera coordinates:\n",
    "\\begin{equation}\n",
    "\\begin{bmatrix}X\\\\Y\\\\Z\\end{bmatrix}\n",
    "= \\begin{bmatrix}Z(u_L-u_0)/f\\\\Z(v_L-v_0)/f\\\\B f/d\\end{bmatrix}\n",
    "= B \\frac{f}{d} \\begin{bmatrix}(u_L-u_0)/f\\\\(v_L-v_0)/f\\\\1\\end{bmatrix}\n",
    "\\end{equation}\n",
    "Stereo cameras are used very often on robotics platforms because of this ability to reconstruct the world in 3D, at least in principle. This is akin to our own (human) ability to perceive depth by virtue of having two eyes, a feature we have in common with many animals - primarily predators, who need accurate depth vision to hunt prey. In practice, using a stereo camera is not as easy, as it has to be carefully calibrated and finding *correspondences* between left and right cameras is not always straightforward. However, the latter has been alleviated quite a bit by recent advances in neural networks, which we will discuss below."
   ]
  }
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