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Computer Vision - Optical Flow
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Computer Vision - Optical Flow

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Questions and Answers

What is the goal of finding optical flow for each pixel in an image?

To find a velocity vector for each pixel indicating how quickly and in which direction it is moving across the image.

Which method is used for determining optical flow by assuming constant image intensity?

  • Differential methods
  • Block-based methods
  • Phase correlation methods
  • Lucas-Kanade method (correct)
  • The Aperture Problem can be solved by using local information.

    True

    In Lucas-Kanade method, the overconstrained linear system can be solved using the __________ method.

    <p>Least-Squares</p> Signup and view all the answers

    How does multi-scale flow estimation improve optical flow estimation?

    <p>It runs the Lucas-Kanade algorithm at different scales to capture motion details.</p> Signup and view all the answers

    Study Notes

    Optical Flow

    • Optical flow is the pattern of motion of objects, surfaces, and edges in a visual scene
    • It is used to understand the motion of the camera and objects in a scene

    Scene Interpretation

    • Given a video sequence, we can find the motion of the camera and objects by:
      • Recovering camera ego-motion
      • Motion segmentation
      • Structure from motion

    Applications

    • Optical flow has applications in:
      • Recovering camera ego-motion
      • Motion segmentation
      • Structure from motion
      • Multi-body segmentation
      • Recognizing the type of motion (e.g., walking, running, etc.)

    Motion Field and Optical Flow

    • Motion field: the real-world 3D motion
    • Optical flow field: the projection of the motion field onto a 2D image

    Examples of Motion Fields

    • Forward motion
    • Rotation
    • Horizontal translation
    • Closer objects appear to move faster

    When Does It Break?

    • The optical flow field can break when:
      • The screen is stationary, but objects generate motion
      • Non-rigid objects change shape
      • The light source changes

    Methods for Determining Optical Flow

    • Phase correlation methods
    • Block-based methods
    • Differential methods, including:
      • Lucas-Kanade method
      • Horn-Schunck method
      • Buxton-Buxton method
      • Black-Jepson method

    Estimating Optical Flow

    • Assume the image intensity is constant
    • Use the brightness constancy equation: I(x, y, t) = I(x + dx, y + dy, t + dt)
    • First-order Taylor expansion: I(x, y, t) + Ix * dx + Iy * dy + It * dt = 0

    Brightness Constancy Equation

    • Simplify the notation: Ix * u + Iy * v = -It

    Problem I: One Equation, Two Unknowns

    • The brightness constancy equation has one equation and two unknowns (u and v)

    Problem II: The Aperture Problem

    • For points on a line of fixed intensity, we can only recover the normal flow
    • We need additional constraints to solve the aperture problem

    Local Smoothness and Lucas-Kanade

    • Use local information to solve the aperture problem
    • Lucas-Kanade method (1984): assume constant (u, v) in a small neighborhood

    Least-Squares Method

    • Solve the overconstrained linear system using the least-squares method
    • Minimize the sum of squares of "errors" between the right- and left-hand sides of the equations

    How Does Lucas-Kanade Behave?

    • Edge regions: A^T * A becomes singular
    • Homogeneous regions: A^T * A is close to zero
    • Textured regions: two high eigenvalues

    Other Break-Downs

    • Brightness constancy is not satisfied
    • A point does not move like its neighbors
    • The motion is not small (Taylor expansion doesn't hold)

    Multi-Scale Flow Estimation

    • Use multi-scale estimation to handle large motions
    • Run Lucas-Kanade at multiple scales and warp and upsample the results

    Example: Motion-Based Segmentation

    • Input: a video sequence
    • Segmentation result: separate objects moving in different ways

    Affine Motion

    • For panning camera or planar surfaces, use affine motion: u = p1 + p2 * x + p3 * y, v = p4 + p5 * x + p6 * y
    • Only 6 parameters to solve for, resulting in better results

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    Related Documents

    09-Optical Flow.pptx

    Description

    This quiz covers optical flow in computer vision, understanding motion in video sequences, and scene interpretation. It involves tracking pixel movements between images and analyzing camera/object motion.

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