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Optical Flow. 10-24-2005. Problem. Problems in motion estimation Noise, color (intensity) smoothness, lighting (shadowing effects), occlusion, abrupt movements, etc Approaches: Block matching, Generalized block matching, Optical flow (block-based, Horn-Schunck etc) Bayesian, etc.

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Optical flow

Optical Flow

10-24-2005


Problem
Problem

  • Problems in motion estimation

    • Noise,

    • color (intensity) smoothness,

    • lighting (shadowing effects),

    • occlusion,

    • abrupt movements, etc

  • Approaches:

    • Block matching,

    • Generalized block matching,

    • Optical flow (block-based, Horn-Schunck etc)

    • Bayesian, etc.

  • Applications

    • Video coding and compression,

    • Segmentation

    • Object reconstruction (structure-from-motion)

    • Detection and tracking, etc.


Motion description

=

ì

x

X

í

=

y

Y

î

Motion description

  • 2D motion:

  • p = [x(t),y(t)]p’= [x(t+ t0), y(t+t0)]

  • d(t) = [x(t+ t0)-x(t),y(t+t0)-y(t)]

  • 3D motion:

  • Α= [ Χ1, Υ1, Ζ1 ]ΤΒ = [ Χ2, Υ2, Ζ2 ]Τ

  • = R+T

  • Basic projection models:

    • Orthographic

    • Perspective


Optical flow1
Optical Flow

  • Basic assumptions:

    • Image is smooth locally

    • Pixel intensity does not change over time (no lighting changes)

  • Normal flow:

  • Second order differential equation:


Block based optical flow estimation

and

Block-based Optical Flow Estimation

  • Optical flow estimation within a block (smoothness assumption): all pixels of the block have the same motion

  • Error:

  • Motion equation:


Horn schunck

Gauss-Seidel

Horn-Schunck

  • We want an optical flow field that satisfies the Optical Flow Equation with the minimum variance between the vectors (smoothness)







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