An active contour model and its algorithms with local and global Gaussian distribution fitting energies

In this paper, we propose an active contour model and its corresponding algorithms with detailed implementation for image segmentation. In the proposed model, the local and global region fitting energies are described by the combination of the local and global Gaussian distributions with different means and variances, respectively. In this combination, we increase a weighting coefficient by which we can adjust the ratio between the local and global region fitting energies. Then we present an algorithm for implementing the proposed model directly. Considering that, in practice, the selection of the weighting coefficient is troublesome, we present a modified algorithm in order to overcome this problem and increase the flexibility. By adaptively updating the weighting coefficient and the time step with the contour evolution, this algorithm is less sensitive to the initialization of the contour and can speed up the convergence rate. Besides, it is robust to the noise and can be used to extract the desired objects. Experiment results demonstrate that the proposed model and its algorithms are effective with application to both the synthetic and real-world images.

[1]  Roman Goldenberg,et al.  Fast Geodesic Active Contours , 1999, Scale-Space.

[2]  Chunming Li,et al.  Computerized Medical Imaging and Graphics Active Contours Driven by Local and Global Intensity Fitting Energy with Application to Brain Mr Image Segmentation , 2022 .

[3]  Lei Zhang,et al.  Active contours with selective local or global segmentation: A new formulation and level set method , 2010, Image Vis. Comput..

[4]  Yang Xiang,et al.  An active contour model for image segmentation based on elastic interaction , 2006, J. Comput. Phys..

[5]  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).

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

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

[8]  Reza Ghaderi,et al.  A novel fuzzy Dempster-Shafer inference system for brain MRI segmentation , 2013, Inf. Sci..

[9]  Amar Mitiche,et al.  Unsupervised Variational Image Segmentation/Classification Using a Weibull Observation Model , 2006, IEEE Transactions on Image Processing.

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

[11]  Chunming Li,et al.  Implicit Active Contours Driven by Local Binary Fitting Energy , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[12]  Xavier Bresson,et al.  Efficient Algorithm for Level Set Method Preserving Distance Function , 2012, IEEE Transactions on Image Processing.

[13]  John W. Fisher,et al.  Submitted to Ieee Transactions on Image Processing a Nonparametric Statistical Method for Image Segmentation Using Information Theory and Curve Evolution , 2022 .

[14]  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.

[15]  James M. Keller,et al.  Snakes on the Watershed , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Sankar K. Pal,et al.  Improving feature space based image segmentation via density modification , 2012, Inf. Sci..

[17]  Xiaoping Yang,et al.  A fast algorithm for global minimization of maximum likelihood based on ultrasound image segmentation , 2011 .

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

[19]  Fuchun Sun,et al.  Efficient visual tracking using particle filter with incremental likelihood calculation , 2012, Information Sciences.

[20]  Xavier Bresson,et al.  Completely Convex Formulation of the Chan-Vese Image Segmentation Model , 2012, International Journal of Computer Vision.

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

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

[23]  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..

[24]  Lavdie Rada,et al.  A New Variational Model with Dual Level Set Functions for Selective Segmentation , 2012 .

[25]  Yunmei Chen,et al.  A new stochastic variational PDE model for soft Mumford–Shah segmentation , 2011 .

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

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

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

[29]  Ke Chen,et al.  Image selective segmentation under geometrical constraints using an active contour approach , 2009 .

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

[31]  N. Zhang,et al.  Multiscale roughness measure for color image segmentation , 2012, Inf. Sci..

[32]  C. Lamberti,et al.  Maximum likelihood segmentation of ultrasound images with Rayleigh distribution , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[33]  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..

[34]  Chunming Li,et al.  Active contours driven by local Gaussian distribution fitting energy , 2009, Signal Process..

[35]  Tony F. Chan,et al.  Active Contours without Edges for Vector-Valued Images , 2000, J. Vis. Commun. Image Represent..

[36]  Olivier Basset,et al.  Segmentation of ultrasound images--multiresolution 2D and 3D algorithm based on global and local statistics , 2003, Pattern Recognit. Lett..

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

[38]  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.

[39]  Ridha Touzi,et al.  Segmentation of textured polarimetric SAR scenes by likelihood approximation , 2004, IEEE Transactions on Geoscience and Remote Sensing.

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

[41]  Amar Mitiche,et al.  Multiregion level-set partitioning of synthetic aperture radar images , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[42]  Amar Mitiche,et al.  Variational and Level Set Methods in Image Segmentation , 2010 .

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

[44]  Kaleem Siddiqi,et al.  Flux maximizing geometric flows , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[45]  Sun Zheng,et al.  An intensive restraint topology adaptive snake model and its application in tracking dynamic image sequence , 2010, Inf. Sci..

[46]  Lei Zhang,et al.  Active contours driven by local image fitting energy , 2010, Pattern Recognit..

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

[48]  Josiane Zerubia,et al.  A Level Set Model for Image Classification , 1999, International Journal of Computer Vision.