# lect831h - Anandan Affine Affine(0,0(0,0(x,y x x(x,y(1,1 u...

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•1 Anandan Affine Affine (0,0) (1,1) (x,y) (0,0) (1,1) (x’,y’) 2 4 3 1 2 1 ) , ( ) , ( b y a x a y x v b y a x a y x u + + = + + = U X X - =

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•2 Anandan 2 4 3 1 2 1 ) , ( ) , ( b y a x a y x v b y a x a y x u + + = + + = = 2 4 3 1 2 1 1 0 0 0 0 0 0 1 ) , ( ) , ( b a a b a a y x y x y x v y x u •Affine a x X x u ) ( ) ( = a x X x u ) ( ) ( = 2 ) ( ) ( u f f a E T x t d d x + = 2 ) ( ) ( a f f a E T x t d d X x + = = y x f f f X min Optical flow constraint eq t y x f v f u f - = +
•3 Anandan [ ] t T T f X x X T f X a X f f X - = d ) )( ( Homework 1.1 Basic Components • Pyramid construction • Motion estimation • Image warping • Coarse-to-fine refinement

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•4 Image Warping warp ) , ( t X f ) 1 , ( - t X f ) 1 , ( - t X f ) ( b AX X U X X + - = - = X b X A I = + - - ) ( ) ( 1
•5 Image Warping X b X A X A b X b X A X b X A I X b AX X U X X = + = + - = - - = + - = - = - ) ( ) ( ) ( ) ( 1 Image at time t: X Image at time t-1: X’ X b X A = + - ) ( ) ( 1 Image Warping •How about values in are not integer. ) , ( y x X = •But image is sampled only at integer rows and columns • Instead of converting to and copying at we can convert integer values to and copy at X X ) 1 , ( - t X f ) 1 , ( - t X f X X ) 1 , ( - t X f ) 1 , ( - t X f

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•6 Image Warping • But how about the values in are not integer. X • Perform bilinear interpolation to compute

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lect831h - Anandan Affine Affine(0,0(0,0(x,y x x(x,y(1,1 u...

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