1、 TV-L1 .TV-L 1( L 1 Total variation-L 1 ) , TV-L 1 , . , G- -Letnikov) TV-L 1 , G-L TV-L 1 , . G-L , , , . , G-L , . , 12 . , , , TV-L 1 . ; -Letnikov; TV-L1 ; ; ; ; . , .E-mail: . .E-mail: . . .E-mail: . .E-mail: (61462065, 61661036) Research on TV-L1 Optical Flow Model for Image Registration Based
2、 on Fractional-order Differentiation ZHANG Gui-Mei SUN Xiao-Xu LIU Jian-Xin CHU Jun Key Laboratory of Jiangxi Province for Image Processing and Pattern Recognition, Nanchang Hangkong University; School of Mechanical Engineering, Xihua University; Abstract In computer vision and medical image analysi
3、s, non-rigid image registration is a challenging task.TV-L 1(Total variation-L 1 ) optical flow model has been proved to be an effective method in the field of non-rigid image registration.It can solve the problem of fuzzy edge caused by smooth displacement fields of Horn-Schunck, but its first-orde
4、r derivative in regularization term leads to fuzzy texture information with weak derivative property.Aiming at the problem, this paper introduces G-L -Letnikov) fractional differentiation to TV-L 1optical flow model, and proposes a new TV-L 1optical flow model based on fractional differentiation, an
5、d then finds the solution of the model using primal- -Letnikov fractional order differential instead of the first-order derivative in the regularization term for its better ability of detail description than first-order s.Then we purposefully control to retain or inhibit the texture information with
6、 weak derivative nature, thus improving the registration accuracy.Experimental results show that the proposed method has a better registration accuracy in registration of texture information with weak derivative, and that it can be considered an important extension and generalization of TV-L 1optica
7、l flow modes. Keyword Fractional differential; -Letnikov; TV-L1 (Total variation-L1) model; optical flow; weak texture; non-rigid registration; , , . 1 , , . 2 (0, 1) , , , , , . 3 , , . 4 , . 5 , , , , . 6 , , , , . , , . , , , , . , , . . , , , , , 7-9. Demons 7-9. , , . 10 Demons , , 11 Demons De
8、mons , , , , . 12 Horn-Schunck (H-S) , Horn-Schunck , , , , , , . , Horn-Schunck . , Pock 13 TV-L (Total variation-L) , , , L . 14 13 . 15 Demons . 13-15 . TV-L H-S , , , , , , . , , , , , , . , , , , G-L TV-L , , . 1 1.1 Horn-Schunck (H-S) 16 (x, y) t I (x, y, t) , t (x+x, y+y) , I (x+ x, y+y, t+ t
9、) , 16 , t , U= (u, v) , , , , x y u v, . . Horn , , , , 0, : , , , , , . H-S , , , , . 1.2 TV-L Horn-Schunck , Pock13 TV-L , , , , , , Pock w , w : x (u-u0) +Iy (v-v0) +It , u0 v0 , |u|+|v| H-S , L w) | H-S (Ixu+Iyv+It) . H-S , . , , ROF (Rudin Osher Fatemi) 17 , ROF , . , L H-S . TV-L H-S , , , ,
10、, |u|, , . TV-L , 18 TV-L . 2 G-L TV-L 17 , 19 , , R-L (Riemann-Liouville) G-L -Letnikov) Caputo . G-L R-L , , Caputo , . G-L R-L , G-L , TV-L , . 2.1 -Letnikov 19 , f (x) , cm= (-1) cm , Gamma , m , m , 0. , cm=0, (4) , . , , X R, X , X : Y : Y p= (p, p) , Y : (5) (9) : , G-L , . (7) (12) , (12) -L
11、etnikov . , (10) (13) . 1 Fig.1 Differential template 2.2 TV-L G-L TV-L , , TV-L (Fractional TV-L, FTV-L) : : , , TV-L 13 TV-L , TV-L TV-L . 2.3 TV-L 18 , O (1/N) . 18 FTV-L . 18 TV-L : : , , : , F F . 1. . 2. x, y TV-L TV-L : (12) , (25) , P, Q, Z p, q, z , : P, Q, Z L , (26) P (p) Q (q) Z (z) P, Q
12、, Z , : (21) (22) , F) G) . (26) (20) P Q Z (z) , 1, (15) , TV-L . : 1. 1) (21) : 2) (21) F) , F (p, q, z) P, Q, Z , P, Q, Z L : 2. 1) (22) (x- Ky) : 2) (22) G) , 1 L , L , , ai, j= , - i, j i, j , - i, j i, j . 3. . 1. FTV-L , , , , . : 2, , FTV-L ( (15) ) , . , . . , (u, v) 0, w 0, (p, q, z) 0. , . 4 , (u, v, w) (p, q, z) : (33) . 2.4 50 , , 50 , 50 , (Mean square error, MSE) (Peak singnal to noise ratio, PSNR) , 50. 2 (a) 2 (b) Lena MSE PSNR , 42 , . , 50 . , , , , , , 0.01.
