Image segmentation based on an active contour model of partial image restoration with local cosine fitting energy

Abstract In this paper, we use the cosine function to express the data energy fitting of a traditional active contours model and propose a model based on sectional image recovery local cosine-fitting energy active contours, which is used to segment medical and synthetic images. The algorithm is a single level image segmentation method. It can process synthetic images with intensity inhomogeneity. Moreover, our model for the images with noise and the fuzzy ones is more efficient and robust, and the computational speed was similar or faster, compared with Convex Variant of the Mumford–Shah Model and Thresholding (CVMST) model, a local binary fitting (LBF) model and L 0 Regularized Mumford–Shah (L0MS) model. In addition, we describe the model in a discrete form, which is more convenient to add a regular term to control the segmentation. Therefore the massive calculation is reduced by re-initializing the level set curve. At the end of the paper, the modified algorithm has been utilized to segment medical images and three-dimensional visualization results are obtained. The experimental results indicate that the segmentation results are accurate and efficient when applied to different kinds of images.

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

[2]  Ting-Zhu Huang,et al.  Region-based object and background extraction via active contours , 2013 .

[3]  Chunming Li,et al.  A Level Set Method for Image Segmentation in the Presence of Intensity Inhomogeneities With Application to MRI , 2011, IEEE Transactions on Image Processing.

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

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

[6]  Ting-Zhu Huang,et al.  An adaptive weighting parameter estimation between local and global intensity fitting energy for image segmentation , 2014, Commun. Nonlinear Sci. Numer. Simul..

[7]  Hui Wang,et al.  An active contour model and its algorithms with local and global Gaussian distribution fitting energies , 2014, Inf. Sci..

[8]  Geoffrey D. Rubin,et al.  Adaptive border marching algorithm: Automatic lung segmentation on chest CT images , 2008, Comput. Medical Imaging Graph..

[9]  Farrokh Marvasti,et al.  Fast restoration of natural images corrupted by high-density impulse noise , 2013, EURASIP Journal on Image and Video Processing.

[10]  Zhi Xu,et al.  Variant of the region-scalable fitting energy for image segmentation. , 2015, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Weimin Huang,et al.  The $L_{0}$ Regularized Mumford–Shah Model for Bias Correction and Segmentation of Medical Images , 2015, IEEE Transactions on Image Processing.

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

[13]  Hui Wang,et al.  A global minimization hybrid active contour model with applications to oil spill images , 2014, Comput. Math. Appl..

[14]  Jerry L. Prince,et al.  Snakes, shapes, and gradient vector flow , 1998, IEEE Trans. Image Process..

[15]  Robert D. Nowak,et al.  Majorization–Minimization Algorithms for Wavelet-Based Image Restoration , 2007, IEEE Transactions on Image Processing.

[16]  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..

[17]  Raymond H. Chan,et al.  Constrained Total Variation Deblurring Models and Fast Algorithms Based on Alternating Direction Method of Multipliers , 2013, SIAM J. Imaging Sci..

[18]  L O Hall,et al.  Review of MR image segmentation techniques using pattern recognition. , 1993, Medical physics.

[19]  Yu-Fei Yang,et al.  A projected gradient algorithm based on the augmented Lagrangian strategy for image restoration and texture extraction , 2011, Image Vis. Comput..

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

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

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

[23]  Ting-Zhu Huang,et al.  Region-based active contours with cosine fitting energy for image segmentation. , 2015, Journal of the Optical Society of America. A, Optics, image science, and vision.

[24]  Chuan Chen,et al.  Alternating Direction Method of Multipliers for Nonlinear Image Restoration Problems , 2015, IEEE Transactions on Image Processing.

[25]  Alfred M. Bruckstein,et al.  Finding Shortest Paths on Surfaces Using Level Sets Propagation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Ting-Zhu Huang,et al.  Image restoration using total variation with overlapping group sparsity , 2013, Inf. Sci..

[27]  Michael K. Ng,et al.  A New Convex Optimization Model for Multiplicative Noise and Blur Removal , 2014, SIAM J. Imaging Sci..

[28]  Zhi Xu,et al.  A two-stage image segmentation via global and local region active contours , 2016, Neurocomputing.

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

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

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

[32]  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.

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

[34]  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).

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

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

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

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

[39]  Ming Yan,et al.  Restoration of Images Corrupted by Impulse Noise and Mixed Gaussian Impulse Noise using Blind Inpainting , 2013, SIAM J. Imaging Sci..

[40]  Raymond H. Chan,et al.  A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford-Shah Model and Thresholding , 2013, SIAM J. Imaging Sci..