Anandan Matching and Smoothing are performed at each level of the Laplacian pyramid · Confidence measure Try to use c min and c max suggested by Anandan but not reliable
Anandan • Matching and Smoothing are performed at each level of the Laplacian pyramid • Confidence measure – Try to use c_min and c_max suggested by Anandan, but not reliable
Singh Two-stage matching method First, SSD with 3 adjacent band-pass filtered image SSDo(x, d)=SDo. 1(x, d )+SSDo -1(x,-d Average out spurious Ssd minima due to noise or periodic texture Converts ssdo into a probability distribution R(d)=e-k sSDo h=-ln(0.95)/(min( S Do)
Singh • Two-stage matching method – First, SSD with 3 adjacent band-pass filtered image • Converts SSD0 into a probability distribution Average out spurious SSD minima due to noise or periodic texture
Singh Subpixel velocity mean of the distribution Averaged over the integer displacement d ∑Rdl ∑B(dd ∑Ra(d) ∑Rad) Coarse-to-fine strategy Confidence measures: eigenvalues of the inverse covariant matrix ∑R(d)(d2-u)2∑Rd(d2-e)(d-c) ER(d)(2R(d)(d -ue)(dy -ve) 2R.(d)(dy -)2
Singh • Subpixel velocity: mean of the distribution – Averaged over the integer displacement d • Coarse-to-fine strategy • Confidence measures: eigenvalues of the inverse covariant matrix
Singh Barrons implementation Step1, computed SSD for a wide range of integer displacement N=4 2N< <2N (4N+1)x(4N+1 SSD surface to(2N+1)x (2N+1 subregions Step2: propagate velocity using neighborhood constraints ∑;B2n(v:) ∑;B2n(v;) ∑:Bn(v:) ∑:B2n(v) Gauss function of distance better results with w=2 than w=1
Singh • Step1, computed SSD for a wide range of integer displacement, N=4 – (4N+1)x(4N+1) SSD surface to (2N+1)x(2N+1) subregions • Step2: propagate velocity using neighborhood constraints Barron’s implementation Gauss function of distance, better results with w=2 than w=1
Singh Barron' s implementation Covariance matrix ∑:Bn(V)(u2-un)2∑:Bn(v)(u;-un)(c R,(v:)(E: R,(v (u;-un)(c:-Un,) 2: R,(v)(1-Um)2 Final velocity (v-vn)+(v-ve)s-(v-ve sc,v c are derived from intensity data in step 1 sn +( + Matrix inverse: replace singular values less than 0. 1 by 0. 1 to avoid singular systems
Singh • Covariance matrix • Final velocity – S_c, v_c are derived from intensity data in step1 – S_n, v_n Barron’s implementation Matrix inverse: replace singular values less than 0.1 by 0.1 to avoid singular systems