Geometric attraction-driven flow for image segmentation and boundary detection

Novel forces in image segmentation based on active contours models are proposed for capturing objects in the image. Contemplating the common functionality of forces in previous active contours models, we propose the geometric attraction-driven flow (GADF), the binary edge function, and the binary balloon forces to detect objects in difficult cases such as varying illumination and complex shapes. The orientation of GADF is orthogonally aligned with the boundary of object and has the opposite direction across the boundary. It prevents the leakage through weak edges of objects, which occur due to illumination. To reduce the interference from other forces, we design the binary edge function using the property of the orientation in the GADF. We also design the binary balloon force based on the four-color theorem. Combining with initial dual level set functions, the proposed model captures holes in objects and multiple junctions from different colors. The result does not depend on positions of initial contours.

[1]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[2]  Rachid Deriche,et al.  Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation , 2002, International Journal of Computer Vision.

[3]  Vladimir Kolmogorov,et al.  "GrabCut": interactive foreground extraction using iterated graph cuts , 2004, ACM Trans. Graph..

[4]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[5]  Alan L. Yuille,et al.  Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[8]  Minju Lee,et al.  An Error Estimate of Upwind Method for Generalized Black-Scholes Equation , 2007 .

[9]  Kaleem Siddiqi,et al.  Flux Maximizing Geometric Flows , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Petia Radeva,et al.  Curvature Vector Flow to Assure Convergent Deformable Models for Shape Modelling , 2003, EMMCVPR.

[11]  K. Appel,et al.  Every Planar Map Is Four Colorable , 2019, Mathematical Solitaires & Games.

[12]  Xue-Cheng Tai,et al.  A binary level set model and some applications to Mumford-Shah image segmentation , 2006, IEEE Transactions on Image Processing.

[13]  Jian Sun,et al.  Lazy snapping , 2004, SIGGRAPH 2004.

[14]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[15]  Rachid Deriche,et al.  Active unsupervised texture segmentation on a diffusion based feature space , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[16]  Zeyun Yu,et al.  Normalized Gradient Vector Diffusion and Image Segmentation , 2002, ECCV.

[17]  K. Appel,et al.  Every planar map is four colorable. Part I: Discharging , 1977 .

[18]  James S. Duncan,et al.  Deformable boundary finding in medical images by integrating gradient and region information , 1996, IEEE Trans. Medical Imaging.

[19]  Xuecheng Tai,et al.  A parallel splitting up method and its application to Navier-Stokes equations , 1991 .

[20]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[21]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Xianghua Xie,et al.  RAGS: region-aided geometric snake , 2004, IEEE Transactions on Image Processing.

[23]  Guillermo Sapiro,et al.  Geodesic Active Contours , 1995, International Journal of Computer Vision.

[24]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[25]  Jerry L. Prince,et al.  Generalized gradient vector flow external forces for active contours , 1998, Signal Process..

[26]  Mila Nikolova,et al.  Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models , 2006, SIAM J. Appl. Math..

[27]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[28]  Olga Veksler,et al.  Graph Cuts in Vision and Graphics: Theories and Applications , 2006, Handbook of Mathematical Models in Computer Vision.

[29]  Daniel Cremers,et al.  An Experimental Comparison of Discrete and Continuous Shape Optimization Methods , 2008, ECCV.

[30]  Max A. Viergever,et al.  Efficient and reliable schemes for nonlinear diffusion filtering , 1998, IEEE Trans. Image Process..

[31]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[32]  Robin Thomas,et al.  The Four-Colour Theorem , 1997, J. Comb. Theory, Ser. B.

[33]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[34]  Rachid Deriche,et al.  Geodesic Active Regions: A New Framework to Deal with Frame Partition Problems in Computer Vision , 2002, J. Vis. Commun. Image Represent..

[35]  Gareth Funka-Lea,et al.  Graph Cuts and Efficient N-D Image Segmentation , 2006, International Journal of Computer Vision.

[36]  Anthony J. Yezzi,et al.  A Fully Global Approach to Image Segmentation via Coupled Curve Evolution Equations , 2002, J. Vis. Commun. Image Represent..

[37]  J. Thomas.  The four color theorem , 1977 .

[38]  Jorge S. Marques,et al.  A class of constrained clustering algorithms for object boundary extraction , 1996, IEEE Trans. Image Process..

[39]  J. Craggs.  Applied Mathematical Sciences , 1973 .

[40]  Chunming Li,et al.  Minimization of Region-Scalable Fitting Energy for Image Segmentation , 2008, IEEE Transactions on Image Processing.

[41]  Xianghua Xie,et al.  MAC: Magnetostatic Active Contour Model , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[42]  Junaed Sattar.  Snakes , Shapes and Gradient Vector Flow , 2022 .

[43]  Thomas Brox,et al.  Nonlinear structure tensors , 2006, Image Vis. Comput..

[44]  Kaleem Siddiqi,et al.  Area and length minimizing flows for shape segmentation , 1998, IEEE Trans. Image Process..

[45]  Xue-Cheng Tai,et al.  A variant of the level set method and applications to image segmentation , 2006, Math. Comput..

[46]  T. Chan,et al.  A Variational Level Set Approach to Multiphase Motion , 1996 .

[47]  Erlend Hodneland,et al.  Four-Color Theorem and Level Set Methods for Watershed Segmentation , 2009, International Journal of Computer Vision.

[48]  Nikos Paragios,et al.  Gradient vector flow fast geometric active contours , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  A. Yezzi,et al.  On the relationship between parametric and geometric active contours , 2000, Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154).