lecture-5 - Lecture-5 Other Optical Flow Methods 1...

This preview shows pages 1–13. Sign up to view the full content.

1 Lecture-5 Other Optical Flow Methods

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Important Issues • Local vs Global optical flow • What motion model? • What function to be minimized? • What minimization method? Minimization Methods • Least Squares fit • Weighted Least Squares fit • Newton-Raphson • Gradient Descent • Levenberg-Marquadet
3 Lucas & Kanade (Least Squares) • Optical flow eq t y x f v f u f - = + 9 9 9 1 1 1 t y x t y x f v f u f f v f u f - = + - = + M - - = 9 1 9 1 9 1 t t y y x x f f v u f f f f M M M t f Au = • Consider 3 by 3 window Lucas & Kanade t T T t T T t f A A A u f A A f 1 ) ( - = = = 2 2 2 2 2 ) ( min ti i j yi xi f v f u f + + ∑∑ - = - =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Lucas & Kanade 2 2 2 2 2 ) ( min ti i j yi xi f v f u f + + ∑∑ - = - = 0 ) ( 0 ) ( = + + = + + yi ti yi xi xi ti yi xi f f v f u f f f v f u f Lucas & Kanade - - = - ti yi ti xi yi yi xi yi xi xi f f f f f f f f f f v u 1 2 2
5 Lucas & Kanade 2 2 2 2 2 ) ( min ti i j yi xi i f v f u f w + + ∑∑ - = - = t Wf WAu = t T T A A = t T T Wf A WA A u 1 ) ( - = Lucas Kanade with Pyramids • Compute ‘simple’ LK at highest level • At level i • Take flow u i- 1 , v 1 from level i- 1 • bilinear interpolate it to create u i * i * matrices of twice resolution • multiply u i * , v i * by 2 • compute f t from a block displaced by u i * ( x,y ), v i * ( x,y ) • Apply LK to get u i ( x, y ), v i ( x, y ) (the correction in flow) • Add correction to u 1 1 to get u i i

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6 Lucas-Kanade without pyramids Fails in areas of large motion Lucas-Kanade with Pyramids
7

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
8 Global Flow
9 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 - =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
10 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 - = + [ ] t T T f X x X T f X a X f f X - = d ) )( ( Homework 2: Show this due 9/21 b Ax =
11 Basic Components • Pyramid construction • Motion estimation • Image warping • Coarse-to-fine refinement

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
12 Image Warping warp ) , ( t X f ) 1 , ( - t X f ) 1 , ( - t X f ) ( b AX X U X X + - = - = X b X A X b X A I = +
This is the end of the preview. Sign up to access the rest of the document.

lecture-5 - Lecture-5 Other Optical Flow Methods 1...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online