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INTEGRATION OF INTENSITY EDGE INFORMATION INTO THE REACTION-DIFFUSION STEREO ALGORITHM

INTEGRATION OF INTENSITY EDGE INFORMATION INTO THE REACTION-DIFFUSION STEREO ALGORITHM. Atsushi Nomura 1) Makoto Ichikawa 2) Koichi Okada 1) Hidetoshi Miike 1) 1) Yamaguchi University, Japan 2) Chiba University, Japan. In this talk,.

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INTEGRATION OF INTENSITY EDGE INFORMATION INTO THE REACTION-DIFFUSION STEREO ALGORITHM

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  1. INTEGRATION OF INTENSITY EDGE INFORMATION INTOTHE REACTION-DIFFUSION STEREO ALGORITHM Atsushi Nomura1) Makoto Ichikawa2) Koichi Okada1) Hidetoshi Miike1) 1)Yamaguchi University, Japan 2)Chiba University, Japan

  2. In this talk, • We integrate intensity edge information into a reaction-diffusion stereo algorithm. • Depth discontinuity => error of disparity detection. • Anisotropic diffusion.

  3. Outline of this talk • Stereo vision, stereo algorithm & related topics • Reaction-diffusion equations & reaction-diffusion algorithm • Proposed stereo algorithm integrating intensity edge information • Experimental results • Conclusion & future work

  4. Binocular Stereo Vision Object Object Optical axis Object Depth Disparity d=xL-xR Cross-correlation IL(x,y) IR(x,y) . . . Object (xL,y) (xR,y) Focul length Left eye Right eye stereo correspondence problem => segmentation problem dN-1 . . . d0 for possible disparity levels

  5. Previous Stereo Algorithms • Marr & Poggio, Proc. Roy. Soc. Lond., 1979 • original cooperative algorithm • continuity & uniqueness constraints • Zitnick & Kanade, IEEE-PAMI, 2000 • modern cooperative algorithm + occlusion detection • Sun et al., IEEE-PAMI, 2003 • belief-propagation algorithm • Deng et al., IEEE-PAMI, 2007 • graph-cuts algorithm

  6. Previous Edge Detection Algorithm • Marr & Hildreth, Proc. Roy. Soc. Lond., 1980 • LoG filter & DOG filter • Canny, IEEE-PAMI, 1986 • Standard algorithm • Heath et al., IEEE-PAMI, 1997 • Review of edge detection algorithms • Standard images

  7. Diffusion Equation & PDE Approach inImage Processing & Computer Vision Research • Koenderink, Biol. Cybern., 1984 • Diffusion equation =Gaussian filter • Perona & Malik, IEEE-PAMI, 1990 • Anisotropic diffusion • Black et al., IEEE-IP, 1998 • Anisotropic diffusion • Mrázek & Navara, IJCV, 2003 • Stopping time for non-linear diffusion filtering • Galié et al., J. Math. Imaging Vis., 2008 • Image compression using anisotropic diffusion

  8. Integration of Visual Cuesin Human Vision System • Landy et al., Vis. Res., 1995 • Fusion of multiple visual cues in depth perception • Linear fusion vs. weak fusion • Ichikawa et al., Vis. Res., 2003 • Non-linear integration model of disparity & other visual cues.

  9. Reaction-Diffusion Algorithm • Adamatzky et al., Reaction-Diffusion Computers, 2005 • proposing novel computer architecture, by utilizing reaction-diffusion equations. • Suzuki et al., Trans. IEICE, 2005 • image restoration + LSI implementation • Asai et al., Int. J. Bifurcation & Chaos, 2005 • Voronoi diagram + LSI implementation • Solving partial differential equations needs much computation power. Hardware (LSI) implementation has been introduced.

  10. Reaction-Diffusion Equations • A set of partial differential equations having diffusion terms and reaction terms. u(x,y,t), v(x,y,t): variables Du, Dv: diffusion coefficients f(u,v), g(u,v): reaction terms • FitzHugh-Nagumo type reaction terms Constants: 0<e<<1 a, b FitzHugh, Biophysical J., 1961 Nagumo et al., Proc. IRE, 1962

  11. Ordinary Differential Equation (ODE) System (Du=Dv=0) • Mono-stable system & bi-stable system Mono-stable a=0.25,b=1.0 e=1/100 a: threshold value Bi-stable a=0.25,b=10.0 e=1/100

  12. Reaction-Diffusion Equations inOne-Dimensional Case • FitzHugh-Nagumo equations: bi-stable system Parameter setting: Du=1.0, Dv=3.0 a=0.05, b=10.0, e=1/100 Propagation speed depends on the diffusion coefficients of Duand Dv.

  13. Discrete System of Reaction-Diffusion Equations in One-Dimensional Space • FitzHugh-Nagumo equations (discrete system) Du<<Dv (Du=1.0, Dv=5.0), D=1/4, a=0.25, e=1/1000, i: index of spatial position Mono-stable system (b=1.0) Bi-stable system (b=10.0) i i Initial conditions: ui(t): step function and vi(t=0)=0.0 (uniform)

  14. Reaction-Diffusion Stereo Algorithm • Nomura et al., Mach. Vis. Appl., (in press) The diffusion term Du2un drives the propagation of region of the disparity level dn. m: constant N: total number of possible disparity levels C: similarity measure dn: disparity level Disparity map:

  15. Reaction-Diffusion Stereo Algorithm (cont.) The uniqueness constraint is realized by, This term realizes the uniqueness constraint. Other set having umax increases this threshold level. Wi: inhibition area

  16. Flow Chart of Reaction-Diffusion Stereo Algorithm edge detection result ve integration edge detection result ue C(x,y,d0) u0(x,y,t) v0(x,y,t) self-inhibition due to Du<<Dv Left image: IL(x,y) dn (pixel) . . . . . . . . . Mutual inhibition through f(,,) Right image: IR(x,y) C(x,y,dn) un(x,y,t) vn(x,y,t) M(x,y,t) . . . . . . . . . Stereo disparity map C(x,y,dN-1) uN-1(x,y,t) vN-1(x,y,t) Stereo images Correlation maps Reaction-diffusion systems Computation of similarity measure at each disparity level dn

  17. Edge Detection Algorithm withReaction-Diffusion Equations • Nomura et al., J. Phys. Soc. Jpn., 2003 • Edge detection & Segmentation • Discrete version of reaction-diffusion equations • Thresholding • Nomura et al., Patt. Recog. Image Anal., 2008 • Edge detection utilizing reaction-diffusion equations • Adaptive threshold level

  18. Integration of Edge Information into Reaction-Diffusion Stereo Algorithm ue(x,y), ve(x,y): spatial distributions of u(x,y,t) and v(x,y,t) at a convergence state The diffusion coefficients (1-ue) and (1-ve) suppress propagation of region of the disparity leveldn.

  19. Experimental Results • The Middlebury stereo vision page provides • stereo image pairs, • ground-truth data of disparity maps, • definition of areas (occlusion area & depth discontinuity), • scores of other stereo algorithms • Example of stereo image pairs TSUKUBA 384X288 pixels 15 disparity levels CONES 450X375 pixels 60 disparity levels TEDDY 450X375 pixels 60 disparity levels VENUS 434X383 pixels 30 disparity levels

  20. Edge Detection Result withReaction-Diffusion Algorithm ue Edges detected by a reaction-diffusion algorithm ve

  21. Example: CONES RD (Previous Reaction-Diffusion Algoriothm) RD+IE (Proposed Reaction-Diffusion Algorithm with Intensity Edge)

  22. Experimental Results on the Middlebury Stereo Data Tested algorithms: Table of scores: RD: Nomura et al., Mach. Vis. Appl. (in press) RD+IE: Proposed in this presentation. ABP: Klaus et al., Proc. 18th ICPR, 2006. Adaptive back propagation algorithm + Color segmentation Error measure: Bad-Match-Percentage (%) threshold level = 1.0 (pixel)

  23. Disparity Error Maps and Intensity Edges RD RD+IE Definition of areas Intensity edges

  24. Conclusion & Future Work • Conclusion: • We proposed integration of intensity edge information into the reaction-diffusion stereo algorithm. • We confirmed performance of the proposed algorithm. • Future work: • dynamic integration • other visual cues Acknowledgments: The present study was supported in part bythe Grant-in-Aid for Scientific Research (C)(No. 20500206) from the Japan Society for thePromotion of Science.

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