Region-Based Methods Accurate numerical differentiation may be impractical because of noise, a small number of frames, aliasing Region-based approaches Define v as the shift d=(dx, dy )that yields the best fit between image regions at different times Best match> maximizing a similarity measure
Region-Based Methods • Accurate numerical differentiation may be impractical because of noise, a small number of frames, aliasing • Region-based approaches – Define v as the shift that yields the best fit between image regions at different times – Best match → maximizing a similarity measure
Region-Based Matching Sum-of-squared difference SSD) SD2(x;d)=∑∑W()[1(x+(,)-1(x+4+(i, =-7 (x*[1(x)-2(x+d)2, Discrete 2D window Integer values dx, dy) Cross-correlation ncc
Region-Based Matching • Sum-of-squared difference (SSD) • Cross-correlation, NCC… Discrete 2D window Integer values (dx, dy)
Anandan Based on Laplacian pyramid Allows the computation of large displacement between frames Help enhance image structure( edges.) Coarse-to-fine SSD-based matching strategy Coarsest level displacement be 1p/for less SSD minima in 3x 3 search space using 5x5 gaussian of W(x Subpixel displacement are computed by finding the minimum of a quadratic surface parameters
Anandan • Based on Laplacian pyramid – Allows the computation of large displacement between frames – Help enhance image structure (edges.. ) • Coarse-to-fine SSD-based matching strategy – Coarsest level: displacement be 1p/f or less – SSD minima in 3x3 search space using 5x5 Gaussian of W(x) – Subpixel displacement are computed by finding the minimum of a quadratic surface parameters
Anandan Confidence measures of the ssd surface at the minimum nin.: nln I+ ko Smin + Cmam cmin h'1tk2sminth3C Cmin and Cmaz principle curvatures s min Ssd value at the minima k1=150,k2=1,k3=0
Anandan • Confidence measures of the SSD surface at the minimum – – S_min: SSD value at the minima – k_1 = 150, k_2=1, k_3 =0 Principle curvatures
Anandan Additional smoothness constraint Minimize (u2+u+u2+ux)+Cmaa(vemaa -Vo emaz)+cmin(v. emin-Vo emin) 'min, emax the direction of min and max curvature on the ssd surface at the minima The displacement from the higher level Gauss-Seidal iterations k+1 k )· maze+ L
Anandan • Additional smoothness constraint • Minimize • Gauss-Seidal iterations min max e e, The direction of min and max curvature on the SSD surface at the minima 0 v The displacement from the higher level