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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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