Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification

©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/83.935033In this work, we first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford–Shah paradigm from a curve evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Each gradient step involves solving an optimal estimation problem for the data within each region, connecting curve evolution and the Mumford–Shah functional with the theory of boundary-value stochastic processes. The resulting active contour model offers a tractable implementation of the original Mumford–Shah model (i.e., without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation) to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner. Various implementations of this algorithm are introduced to increase its speed of convergence.We also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions. Next, by generalizing the data fidelity term of the original Mumford– Shah functional to incorporate a spatially varying penalty, we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing. This more general model leads us to a novel PDE-based approach for simultaneous image magnification, segmentation, and smoothing, thereby extending the traditional applications of the Mumford–Shah functional which only considers simultaneous segmentation and smoothing

Fast Mumford-Shah Segmentation using Image Scale Space Bases

©2007 SPIE - Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic electronic or print reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.Presented at Computational Imaging V, January 28, 2007, San Jose, CA, USA.http://dx.doi.org/10.1117/12.715201Image segmentation using the piecewise smooth variational model proposed by Mumford and Shah is both robust and computationally expensive. Fortunately, both the intermediate segmentations computed in the process of the evolution, and the final segmentation itself have a common structure. They typically resemble a linear combination of blurred versions of the original image. In this paper, we present methods for fast approximations to Mumford-Shah segmentation using reduced image bases. We show that the majority of the robustness of Mumford-Shah segmentation can be obtained without allowing each pixel to vary independently in the implementation. We illustrate segmentations of real images that show how the proposed segmentation method is both computationally inexpensive, and has comparable performance to Mumford-Shah segmentations where each pixel is allowed to vary freely

A Survey of Image Segmentation Based On Multi Region Level Set Method

Abstract−Image segmentation has a long tradition as one of the fundamental problems in computer vision. Level Sets are an important category of modern image segmentation techniques are based on partial differential equations (PDE), i.e. progressive evaluation of the differences among neighboring pixels to find object boundaries. Earlier method used novel level set method (LSM) for image segmentation. This method used edges and region information for segmentation of objects with weak boundaries. This method designed a nonlinear adaptive velocity and a probability-weighted stopping force by using Bayesian rule. However the difficulty of image segmentation methods based on the popular level set framework to handle an arbitrary number of regions. To address this problem the present work proposes Multi Region Level Set Segmentation which handles an arbitrary number of regions. This can be explored with addition of shape prior's considerations. In addition apriori information of these can be incorporated by using Bayesian scheme. While segmenting both known and unknown objects, it allows the evolution of enormous invariant shape priors. The image structures are considered as separate regions, when they are unknown. Then region splitting is used to obtain the number of regions and the initialization of the required level set functions. In the next step, the energy requirement of level set functions is robustly minimized and similar regions are merged in a last step. Experimental result achieves better result when compare with existing system

Convex Image Segmentation Model Based on Local and Global Intensity Fitting Energy and Split Bregman Method

We propose a convex image segmentation model in a variational level set formulation. Both the local information and the global information are taken into consideration to get better segmentation results. We first propose a globally convex energy functional to combine the local and global intensity fitting terms. The proposed energy functional is then modified by adding an edge detector to force the active contour to the boundary more easily. We then apply the split Bregman method to minimize the proposed energy functional efficiently. By using a weight function that varies with location of the image, the proposed model can balance the weights between the local and global fitting terms dynamically. We have applied the proposed model to synthetic and real images with desirable results. Comparison with other models also demonstrates the accuracy and superiority of the proposed model

Image Segmentation using PDE, Variational, Morphological and Probabilistic Methods

The research in this dissertation has focused upon image segmentation and its related areas, using the techniques of partial differential equations, variational methods, mathematical morphological methods and probabilistic methods. An integrated segmentation method using both curve evolution and anisotropic diffusion is presented that utilizes both gradient and region information in images. A bottom-up image segmentation method is proposed to minimize the Mumford-Shah functional. Preferential image segmentation methods are presented that are based on the tree of shapes in mathematical morphologies and the Kullback-Leibler distance in information theory. A thorough evaluation of the morphological preferential image segmentation method is provided, and a web interface is described. A probabilistic model is presented that is based on particle filters for image segmentation. These methods may be incorporated as components of an integrated image processed system. The system utilizes Internet Protocol (IP) cameras for data acquisition. It utilizes image databases to provide prior information and store image processing results. Image preprocessing, image segmentation and object recognition are integrated in one stage in the system, using various methods developed in several areas. Interactions between data acquisition, integrated image processing and image databases are handled smoothly. A framework of the integrated system is implemented using Perl, C++, MySQL and CGI. The integrated system works for various applications such as video tracking, medical image processing and facial image processing. Experimental results on this applications are provided in the dissertation. Efficient computations such as multi-scale computing and parallel computing using graphic processors are also presented