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Optical flow estimation plays a crucial role in understanding motion in visual data. This field faces multiple challenges, including noise, color smoothness, lighting effects, and occlusion. Various approaches like block matching, generalized block matching, and Bayesian methods are employed to tackle these issues. The applications of optical flow extend to video coding, segmentation, object reconstruction, detection, and tracking. Understanding 2D and 3D motion models and projection methods is vital for accurate motion description. Advanced methods, including the Horn-Schunck approach, help refine optical flow estimation amidst these complexities.
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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. • Applications • Video coding and compression, • Segmentation • Object reconstruction (structure-from-motion) • Detection and tracking, etc.
= 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 ]ΤΒ = [ Χ2, Υ2, Ζ2 ]Τ • = R+T • Basic projection models: • Orthographic • Perspective
Optical Flow • Basic assumptions: • Image is smooth locally • Pixel intensity does not change over time (no lighting changes) • Normal flow: • Second order differential equation:
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:
Gauss-Seidel Horn-Schunck • We want an optical flow field that satisfies the Optical Flow Equation with the minimum variance between the vectors (smoothness)
