Integrating local distribution information with level set for boundary extraction

This paper presents a general object boundary extraction model for piecewise smooth images, which incorporates local intensity distribution information into an edge-based implicit active contour. Unlike traditional edge-based active contours that use gradient to detect edges, our model derives the neighborhood distribution and edge information with two different region-based operators: a Gaussian mixture model (GMM)-based intensity distribution estimator and the Hueckel operator. We propose the local distribution fitting model for more accurate segmentation, which incorporates the operator outcomes into the recent local binary fitting (LBF) model. The GMM and the Hueckel model parameters are estimated before contour evolution, which enables the use of the proposed model without the need for initial contour selection, i.e., the level set function is initialized with a random constant instead of a distance map. Thus our model essentially alleviates the initialization sensitivity problem of most active contours. Experiments on synthetic and real images show the improved performance of our approach over the LBF model.

[1]  Luigi Ambrosio,et al.  ON THE APPROXIMATION OF FREE DISCONTINUITY PROBLEMS , 1992 .

[2]  Théodore Papadopoulo,et al.  Efficient Segmentation of Piecewise Smooth Images , 2007, SSVM.

[3]  Jean-Philippe Thiran,et al.  Variational Segmentation using Fuzzy Region Competition and Local Non-Parametric Probability Density Functions , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[4]  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..

[5]  Chunming Li,et al.  Distance Regularized Level Set Evolution and Its Application to Image Segmentation , 2010, IEEE Transactions on Image Processing.

[6]  Xun Wang,et al.  Deformable Contour Method: A Constrained Optimization Approach , 2004, International Journal of Computer Vision.

[7]  Anthony J. Yezzi,et al.  Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification , 2001, IEEE Trans. Image Process..

[8]  Yehoshua Y. Zeevi,et al.  Integrated active contours for texture segmentation , 2006, IEEE Transactions on Image Processing.

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

[10]  James S. Duncan,et al.  Game-Theoretic Integration for Image Segmentation , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[12]  Daniel Cremers,et al.  An algorithm for minimizing the Mumford-Shah functional , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[13]  Nikolas P. Galatsanos,et al.  Edge preserving spatially varying mixtures for image segmentation , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[14]  Christopher V. Alvino,et al.  The Piecewise Smooth Mumford–Shah Functional on an Arbitrary Graph , 2009, IEEE Transactions on Image Processing.

[15]  Xun Wang,et al.  A comparative study of deformable contour methods on medical image segmentation , 2008, Image Vis. Comput..

[16]  Nikolas P. Galatsanos,et al.  A spatially constrained mixture model for image segmentation , 2005, IEEE Transactions on Neural Networks.

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

[18]  Daniel Cremers,et al.  TVSeg - Interactive Total Variation Based Image Segmentation , 2008, BMVC.

[19]  Chunming Li,et al.  Level set evolution without re-initialization: a new variational formulation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[20]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[21]  Allen R. Tannenbaum,et al.  Localizing Region-Based Active Contours , 2008, IEEE Transactions on Image Processing.

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

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

[24]  L. Ambrosio,et al.  Approximation of functional depending on jumps by elliptic functional via t-convergence , 1990 .

[25]  Andrew Blake,et al.  Sparse Finite Elements for Geodesic Contours with Level-Sets , 2004, ECCV.

[26]  Manfred H. Hueckel An Operator Which Locates Edges in Digitized Pictures , 1971, J. ACM.

[27]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[28]  Rachid Deriche,et al.  A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape , 2007, International Journal of Computer Vision.

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

[30]  K. Sum Vessel Extraction Under Non-Uniform Illumination : A Level Set Approach , 2009 .

[31]  Xavier Bresson,et al.  Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction , 2010, J. Sci. Comput..

[32]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Olivier Faugeras,et al.  Reconciling Distance Functions and Level Sets , 2000, J. Vis. Commun. Image Represent..

[34]  Xavier Bresson,et al.  Fast Global Minimization of the Active Contour/Snake Model , 2007, Journal of Mathematical Imaging and Vision.

[35]  Haim H. Permuter,et al.  A study of Gaussian mixture models of color and texture features for image classification and segmentation , 2006, Pattern Recognit..

[36]  Daniel Cremers,et al.  On the Statistical Interpretation of the Piecewise Smooth Mumford-Shah Functional , 2007, SSVM.

[37]  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.

[38]  Michael I. Jordan,et al.  On Convergence Properties of the EM Algorithm for Gaussian Mixtures , 1996, Neural Computation.