Computer Vision: Stereo Techniques
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What does the disparity represent in the context of depth from disparity?

  • The distance between the left and right optical centers
  • The ratio of the depth to the baseline
  • The total depth of the scene
  • The difference in pixel coordinates of corresponding points (correct)

    • In the formula $Z = B rac{f}{x_l - x_r}$, what does 'B' represent?

  • The pixel disparity
  • The focal length of the camera
  • The baseline distance between the two cameras (correct)
  • The depth of the object

    • What are the epipolar lines used for in stereo correspondence?

  • To identify matching pairs of pixels for the same scene element (correct)
  • To increase the depth resolution
  • To estimate the focal length of the cameras
  • To correct lens distortion between images

    • Which of the following is true regarding the triangles formed by the projections of a 3D point in stereo vision?

    <p>The triangles formed by the left and right images are similar</p> Signup and view all the answers

    Which mathematical relationship can be derived from the disparity in depth perception?

    <p>Depth is inversely proportional to disparity</p> Signup and view all the answers

    What does the term 'disparity' refer to in stereo vision?

    <p>The difference in the position of an object in the two images</p> Signup and view all the answers

    Which of the following is a key application of stereo vision?

    <p>3D Reconstruction</p> Signup and view all the answers

    What is the role of camera calibration in stereo reconstruction?

    <p>To rectify and standardize image data</p> Signup and view all the answers

    Which of the following describes a common challenge in stereo vision?

    <p>Occlusions in the image scene</p> Signup and view all the answers

    What is the purpose of stereo matching in stereo vision?

    <p>To find corresponding points in the stereo images</p> Signup and view all the answers

    What technique assists in computing depth in stereo vision?

    <p>Triangulation principles</p> Signup and view all the answers

    Which of the following methods is commonly used for depth map generation?

    <p>Block matching</p> Signup and view all the answers

    What is the significance of the baseline distance between two cameras in stereo vision?

    <p>It influences the magnitude of disparity</p> Signup and view all the answers

    What does the term 'baseline' refer to in the context of stereo vision?

    <p>The distance between the optical centers of the cameras.</p> Signup and view all the answers

    In the depth from disparity formula, what is represented by 'f'?

    <p>The focal length of the camera.</p> Signup and view all the answers

    Which of the following correctly describes the relationship between xl and xr in the depth from disparity formula?

    <p>xl is positive while xr is negative.</p> Signup and view all the answers

    What geometric shape is used to derive the formula for depth from disparity?

    <p>Triangle</p> Signup and view all the answers

    What does the height-to-base ratio in the triangle Cl PCr : Z represent?

    <p>The perceived depth from stereo images.</p> Signup and view all the answers

    When considering the geometry of stereo vision, what is the significance of the point P = (X,Y,Z)?

    <p>It provides the coordinates of a point in 3D space.</p> Signup and view all the answers

    Which observation is correct concerning the disparity between left and right images?

    <p>Disparity offers a measure of depth in the stereo correspondence problem.</p> Signup and view all the answers

    In the context of stereo vision, what role does camera calibration play?

    <p>It helps in accurately determining the distance between camera optical centers.</p> Signup and view all the answers

    What does disparity represent in stereo imaging?

    <p>The inverse depth of a scene point</p> Signup and view all the answers

    In the context of stereo matching, which assumption is made regarding pixel brightness?

    <p>Brightness constancy is assumed</p> Signup and view all the answers

    What is the primary challenge of stereo matching algorithms?

    <p>Finding accurate matches across epipolar lines</p> Signup and view all the answers

    How does changing the window size impact stereo matching results?

    <p>Larger windows reduce detail but decrease noise</p> Signup and view all the answers

    What does the Sum of Squared Differences (SSD) calculate in stereo matching?

    <p>The best matching disparity</p> Signup and view all the answers

    Which of the following statements is true regarding epipolar lines in stereo vision?

    <p>They represent a 3D point's projections in both images</p> Signup and view all the answers

    Which aspect defines a good stereo correspondence?

    <p>The quality of the pixel match in the other image</p> Signup and view all the answers

    What effect does using an adaptive window size have on stereo matching results?

    <p>It can improve detail while managing noise</p> Signup and view all the answers

    What is window cost commonly defined as?

    <p>Either the sum of squared differences (SSD) or the sum of absolute differences (SAD)</p> Signup and view all the answers

    Which of the following statements is true about SSD and SAD?

    <p>SAD is more robust to outliers compared to SSD.</p> Signup and view all the answers

    What is the result when comparing the SSD values for window costs despite different disparities?

    <p>A unique best cost location can be identified.</p> Signup and view all the answers

    When calculating the SSD cost, how does a pixel's value influence the result?

    <p>Its square contributes disproportionately to the total cost.</p> Signup and view all the answers

    What is the primary advantage of using integral images in computing costs?

    <p>They reduce the computational complexity significantly.</p> Signup and view all the answers

    What does the term disparity refer to in the context of window costs?

    <p>The difference in pixel brightness between two images.</p> Signup and view all the answers

    In the process of window matching, which approach is likely to yield faster results?

    <p>Using integral images instead of direct computations.</p> Signup and view all the answers

    How many additions and multiplications are required to compute one window cost for an 11x11 matching window?

    <p>121 additions and multiplications</p> Signup and view all the answers

    What is the SSD value computed from the window example comparing two images?

    <p>12454</p> Signup and view all the answers

    When might SSD become less effective for pixel comparisons?

    <p>When substantial noise is present in the images.</p> Signup and view all the answers

    Which of the following describes the SAD method in comparison to SSD?

    <p>SAD is less influenced by individual pixel outliers than SSD.</p> Signup and view all the answers

    What is a drawback of using large window sizes in matching algorithms?

    <p>They lead to increased computational time.</p> Signup and view all the answers

    In pixel matching evaluations, what does the best SSD window cost indicate?

    <p>It assigns a unique pixel to a specific disparity.</p> Signup and view all the answers

    What is the mathematical representation for SSD window cost in pixel comparison?

    <p>$ ext{Cost} = ext{Sum}(( ext{Value}_1 - ext{Value}_2)^2)$</p> Signup and view all the answers

    How many operations are required to compute the sum over any rectangular window using the integral image?

    <p>Four</p> Signup and view all the answers

    Which formula represents the computation needed when finding the sum over a rectangular window with corners (x1,y1) and (x2,y2) after computing the integral image?

    <p>I(x2,y2) - I(x1-1,y2) - I(x2,y1-1) + I(x1-1,y1-1)</p> Signup and view all the answers

    What does the SAD (sum of absolute differences) cost measure in the context of window matching?

    <p>The difference in pixel values between the left and right images</p> Signup and view all the answers

    What strategy does the new efficient algorithm employ for calculating the window cost in window matching?

    <p>Utilizing integral image for rapid computation</p> Signup and view all the answers

    In the context of integral images, what is the primary benefit of using a larger window size when measuring disparity?

    <p>It leads to more distinct patterns for matching</p> Signup and view all the answers

    What is the significance of the disparity value in the context of window matching in the algorithm?

    <p>It represents the amount of shift in the left image</p> Signup and view all the answers

    How does the presence of low texture area affect the performance of 3x3 and 7x7 windows in disparity matching?

    <p>They may lead to indistinct pattern recognition</p> Signup and view all the answers

    In a situation with a central pixel matching a lamp, what might occur when using small window sizes?

    <p>Small windows may primarily match the corresponding features on the wall.</p> Signup and view all the answers

    Which of the following practices enhances the accuracy of disparity measurements?

    <p>Employing varying window sizes corresponding to texture area</p> Signup and view all the answers

    What is the main disadvantage of an old algorithm for window matching compared to the new approach?

    <p>It requires more computational resources.</p> Signup and view all the answers

    What is a typical characteristic of a good matching window size in a disparity matching algorithm?

    <p>It should be large enough to capture clear patterns.</p> Signup and view all the answers

    In the integral image algorithm for window matching, what operation is applied to calculate the disparity cost effectively?

    <p>Overlaying the left and right images</p> Signup and view all the answers

    What does an increase in the window size generally lead to in terms of disparity matching outcomes?

    <p>Greater likelihood of accurate depth perception</p> Signup and view all the answers

    Study Notes

    Computer Vision: Stereo

    • Stereo vision is a technique that mimics human binocular vision to perceive depth and 3D structure from two or more images.
    • It is inspired by the way humans use their two eyes to estimate distances to objects.
    • Key components of stereo vision include two images (stereo pair) captured from two cameras positioned slightly apart (baseline distance), these images represent the same scene but from different perspectives.
    • Disparity refers to the difference in the position of an object in the two images. Nearby objects have larger disparity and distant objects have smaller disparity.
    • Depth estimation calculates depth using disparity, camera parameters, and the geometry of the stereo setup. This is based on triangulation principles.

    Stereo Reconstruction

    • Stereo reconstruction involves reconstructing a 3D model of a scene or object.
    • Camera calibration and rectification is an easier problem than stereo correspondence.
    • Camera calibration is largely solved and is frequently used in many programs like OpenCV.
    • Stereo correspondence is a more challenging problem.

    Applications of Stereo Vision

    • 3D Reconstruction: Creating a 3D model of a scene or object.
    • Autonomous Vehicles: Detecting obstacles, estimating distances, and understanding the 3D layout of the environment.
    • Robotics: Enabling robots to perceive depth for navigation and manipulation.
    • AR/VR: Creating immersive environments that require depth perception.
    • Medical Imaging: Reconstructing 3D models of organs or tissues.
    • Object Tracking and Gesture Recognition: Recognizing and analyzing movements in 3D space

    Common Challenges

    • Occlusions: Parts of a scene might be visible in one image, but not the other.
    • Matching Ambiguity: Difficulty in matching corresponding points between images, especially in areas with little texture.
    • Lighting and Reflection Variations: Differences in lighting or reflections between viewpoints.

    Algorithms and Techniques

    • Stereo Matching: Finding corresponding points in the stereo pair using methods like block matching, semi-global matching (SGM), or learning-based approaches.
    • Depth Map Generation: Creating a dense representation of the depth of each pixel.

    Binocular Stereo

    • A single image stereogram (or autostereogram) is a technique used to create a 3D illusion from a 2D image.

    Stereo Vision as Localizing Points in 3D

    • An object point projects to some point in our image
    • That image point corresponds to a ray in the world.
    • Two rays intersect at a single point, so two eyes (or cameras) are needed to localize points in 3D.

    Why Two Eyes?

    • Charles Wheatstone first explained stereopsis in 1838.
    • Disparity (d) is the difference in x-coordinates of corresponding points in the left and right images.

    3D Shape from Stereo

    • Use two cameras instead of two eyes.

    Stereo

    • Given two images from different viewpoints, how can the depth of each point in the image be computed? Depth is based on how much each pixel moves between the two images, reflecting the concept of epipolar geometry.

    Epipolar Geometry

    • Two images, captured by a purely horizontal translating camera, are used.
    • X2 - X1 = the disparity of pixel (x1, y1).

    Disparity = Inverse Depth

    • The smaller the disparity, the further away the object is.

    Your Basic Stereo Matching Algorithm

    • Match Pixels in Conjugate Epipolar Lines
    • Assume brightness constancy, though this is a challenging problem with many approaches.
    • A good survey and evaluation is available on the Middlebury website.

    Stereo Matching Algorithm Details

    • For each epipolar line: Compare each pixel in the left image to every corresponding pixel in the right image on that same line and select the pixel with the minimum match cost.
    • Improvement: Match windows is also an improved approach.

    Stereo Matching based on SSD (Sum of Squared Differences)

    • The SSD graph shows the disparity vs. SSD. The minimum point on the graph indicates the best matching disparity.

    Window size

    • Smaller windows yield more details but more noise. Larger windows contain less noise but less detail. Adaptive windows are often better.

    Stereo Results

    • Data from University of Tsukuba.
    • Similar results on other images without ground truth.

    Stereo as Energy Minimization

    • What defines a good stereo correspondence?
      • Match quality: Want each pixel to find a good match in the other image.
      • Smoothness: If two pixels are adjacent, they should (usually) move about the same amount.

    Stereo as Energy Minimization (Cont.)

    • Find disparity map d that minimizes an energy function E(d)
    • Simple pixel/window matching, E(d) is determined by the sum of cost functions for all image pixels

    Cost Function

    • Sum of squared differences (SSD) between small patches, or windows.
    • C(x, y, d(x, y)) = SSD distance between windows I(x, y) and J(x + d(x, y), y).

    Stereo System

    • Unlike eyes, stereo cameras are usually not on the same plane, which is more numerically stable.

    Stereo System: Triangulation

    • Depth by triangulation uses rays cast through the optical centers of the left and right cameras.
    • The intersection determines the 3D world point P, where depth is based on camera position and parameters.

    Triangulation Requirements

    • Distance between cameras and camera focal length, solved via camera calibration.
    • Pairs of corresponding pixels in the left and right images (stereo correspondence problem).

    Depth from Disparity

    • Formula: Z = B*f / (x - x')

    Formula: Depth from Disparity (Alternative Formulation)

    • Height (or Z) to base ratio of triangle 𝝝₁Px₂, formed by the projections of the 3D point P and the two camera centers is given as:
      • Z = B * f / (x₁ - x₂).

    Coordinate Signs

    • Left image coordinates (x₁) are positive because they lie to the right of the left optical center.
    • Right image coordinates (x₂) are negative because they are measured leftward from the right optical center.

    Depth Formula

    • Geometric relationship between depth and disparity provide the formula of depth.
    • Disparity is inversely proportional to depth.

    Stereo Correspondence: Epipolar Lines

    • Finding corresponding pixels in stereo images reduces calculations to 1D searches along epipolar lines.

    Stereo Rectification

    • Epipolar lines, computed from camera calibration, can be made horizontal by rectifying the stereo pair.

    Stereo Correspondence

    • If the stereo pair is rectified, the corresponding pixels in the left and right images should be similar in intensity or color.

    Difficulties in Stereo Correspondence

    • Image noise affects pixel matching.
    • Regions with constant intensity make pixel matching unreliable.

    Window Matching Correspondence

    • Use a window (patch) of pixels for more robust noise resistance and distinguishable patterns.

    Window Matching: Basic Algorithm

    • For each pixel p in the left image, compare many windows around p with shifted windows in the same epipolar line in the right image.
    • Choose the location corresponding to the best matching window based on minimal matching cost.

    Which Locations to Try?

    • Disparity cannot be negative.
    • Disparity is limited by the camera setup, often known as maxDisp.
    • Disparity can range from zero to maxDisp (x-1, y),..., (x - maxDisp, y) in the right image (x,y) pixel

    Window Matching Cost

    • Define a window cost function, such as sum of squared differences (SSD) or sum of absolute differences (SAD).
    • Pick the window with the best (smallest matching cost).

    SSD Window Cost - Example

    (Numerical values of an example are given; not for students to reproduce.)

    Algorithm with SSD Window Cost

    • Describe the step-by-step algorithm and the meaning of how the shifting corresponds to disparity.

    Algorithm with SSD Window Cost Example

    (See numerical example showing the calculations and result; not for students to manually reproduce.)

    Correspondence with SSD Matching Example

    • Unique best cost location

    Compare to One Pixel "Window" Example

    • No unique best cost location.

    SAD Window Cost

    • SSD is fragile to outliers, and SAD is more robust.

    Definition of SAD

    • Sum of absolute differences pixel-left minus pixel-right

    Example 1: Comparing Windows

    (Provide a numerical example showing SAD calculation.)

    Example 2: Comparing Windows

    (Provide a numerical example showing SAD calculation.)

    Window Matching Efficiency

    • Matching a single 11x11 pixel window requires substantial calculations to search over locations which is slow.

    Speedups: Integral Image

    • Given image f(x, y), the integral image I(x, y) is the cumulative sum of values in f(x, y) from the top-left corner to (x, y) including (x, y).

    Example of Integral Image Calculation

    (Show examples calculating I(2, 2) and I(4, 1).)

    Efficiently Computing Integral Image

    • Computing integral image requires fewer operations. I(x, y) = f(x, y) + I(x - 1, y) + I(x, y - 1) - I(x - 1, y - 1)

    Integral Image: Order of Computation

    • Computation order for speed up purposes.

    Using Integaral Image

    • Summation over any rectangular window involves four operations using already computed integer values.

    Integral Image for Window Matching

    • Describe how to use the integral image to compute the window cost for every pixel and disparity

    Integral Image for Window Matching (Implementation)

    • Show examples of how this computation would look for disparities in a given grid of image pixel values

    Integral Image for Window Matching - Old and New Algorithms

    • Show how the old approach, without using integral images, is less efficient. Show how a new approach, leveraging integral images, can be more efficient

    Integral Image for Window Matching (Example)

    • Suppose the current disparity is 1, describe how to compute the AD image
    • Compute the AD image for a disparity of 1.

    Integral Image for Window Matching (Cont.)

    • Apply integral image to the AD image for a current disparity.

    Efficient Algorithm for Window Matching

    • Explain the efficient algorithm to find the best matching window for each disparity and pixel.

    Effect of Window Size

    • The effect on the result of different window sizes is shown in various graphics.

    Effect of Window Size: Low Texture Area

    • The different window sizes have different amounts of effect in the results and are shown for varying levels of disparity.

    Effect of Window Size: Near Discontinuities

    • The effect on the result with varying window sizes are compared.

    Stereo Reconstruction Pipeline

    • Steps involved starting with calibrating the cameras, rectifying the images, calculating disparity, and finally estimating the depth.
    • Common causes of error, including errors in calibration, low image resolution, occlusions, violation of intensity constancy, large image motions, or low-contrast regions.

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    Computer Vision - Stereo Ch5 PDF

    Description

    Explore the principles of stereo vision in computer science, mimicking human depth perception using two images. Understand the key components such as disparity and depth estimation, and learn about stereo reconstruction for 3D modeling.

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