Fast Constrained Surface Extraction by Minimal Paths

In this paper we consider a new approach for single object segmentation in 3D images. Our method improves the classical geodesic active surface model. It greatly simplifies the model initialization and naturally avoids local minima by incorporating user extra information into the segmentation process. The initialization procedure is reduced to introducing 3D curves into the image. These curves are supposed to belong to the surface to extract and thus, also constitute user given information. Hence, our model finds a surface that has these curves as boundary conditions and that minimizes the integral of a potential function that corresponds to the image features. Our goal is achieved by using globally minimal paths. We approximate the surface to extract by a discrete network of paths. Furthermore, an interpolation method is used to build a mesh or an implicit representation based on the information retrieved from the network of paths. Our paper describes a fast construction obtained by exploiting the Fast Marching algorithm and a fast analytical interpolation method. Moreover, a Level set method can be used to refine the segmentation when higher accuracy is required. The algorithm has been successfully applied to 3D medical images and synthetic images.     

Fast Surface Segmentation Guided by User Input Using Implicit Extension of Minimal Paths

We introduce a novel implicit approach for single object segmentation in 3D images. The boundary surface of this object is assumed to contain two or more known curves (the constraining curves), given by an expert. The aim of our method is to find the desired surface by exploiting the information given in the supplied curves as much as possible. We use a cost potential which penalizes image regions of low interest (for example areas of low gradient). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. These paths globally minimize an energy which is defined from the cost potential. Our approach, although conceptually different, can be seen as an implicit extension to 3D of the minimal path framework already known for 2D image segmentation. As for this previous approach, and unlike other variational methods, our method is not prone to local minima traps of the energy. We present a fast implementation which has been successfully applied to 3D medical and synthetic images. Roberto Ardon graduated from the Ecole Centrale Paris in 2001 with a major in applied mathematics, obtained his master degree in image processing from the Ecole Normale Supérieure de Cachan in the same year and his Ph.D. degree in applied mathematics from the University Paris-Dauphine in 2005. Currently he is a research scientist in Philips Medical Systems Research Paris. His research interests include calculus of variations mainlly focused on medical image processing. Laurent D. Cohen was at Ecole Normale Superieure Ulm in Paris from 1981 to 1985. He received Master's and Ph.D. degrees in Applied Mathematics from Paris 6 in 1983 and 1986. From 1985 to 1987, he was member at the Computer Graphics and Image Processing group at Schlumberger Palo Alto Research, California and Schlumberger Montrouge Research, and remained consultant there for a few years afterwards. He began working with INRIA, France in 1988, mainly with the medical image understanding group Epidaure. Since 1990, he is Research Scholar (Charge then Directeur de Recherche) with CNRS in the Applied Mathematics and Image Processing group at CEREMADE, University Paris-Dauphine. His research interests and teaching at the university are applications of variational methods and Partial Differential Equations to Image Processing and Computer Vision, like deformable models, minimal paths, surface reconstruction, Image registration, Image segmentation and restoration. He obtained CS 2002 Prize for Image and Signal Processing. He has been member in program committees for boards for about 20 international conferences. Anthony Yezzi obtained his Ph.D. in 1997 through the Department of Electrical Engineering at the University of Minnesota. After completing a postdoctoral research position in the Laboratory for Information and Decision Systems (LIDS) at Massacusetts Institute of Technology, he joined the faculty of the School of Electrical and Computer Engineering at Georgia Institute of Technology in 1999 where he currently holds the position of Associate Professor. Prof. Yezzi has also consulted for a number of medical imaging companies including GE, Picker, and VTI, and has been an IEEE member since 1999. His research lies primarily within the fields of image processing and computer vision. He has worked on a variety of problems including image denoising, edge-detection, segmentation and grouping, shape analysis, multi-frame stereo reconstruction, tracking, and registration. Some central themes of his research include curve and surface evolution theory, differential geometry, and partial differential equations.     

拓扑梯度耦合多重最小修补路径的连续边缘图像修复算法

当前的图像修复算法都是利用非连续边缘的已知块信息来完成损坏区域的填充,造成图像模糊与视觉不连通;且修复路径都是随机确定,使其成本较高.对此,提出了拓扑梯度耦合多重最小路径快速行军的连续轮廓图像修复优化算法.引入拓扑梯度,检测出缺失区域的边缘轮廓;定义关键点择取规则,提取图像损坏区域的关键点,嵌入权重因子,建立权重距离函数,计算最小修补路径成本,并设计多重最小路径快速行军机制,提取出连续边缘,完成损坏区域填充.仿真结果显示,与其他图像修复算法相比,本文算法可检测出损坏区域的连续边缘轮廓;且该算法具有更好的修复视觉与效率.     

Global Minimum for Active Contour Models: A Minimal Path Approach

A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour models energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the snake energy by including the internal regularization term in the external potential term. Our method is based on finding a path of minimal length in a Riemannian metric. We then make use of a new efficient numerical method to find this shortest path.It is shown that the proposed energy, though based only on a potential integrated along the curve, imposes a regularization effect like snakes. We explore the relation between the maximum curvature along the resulting contour and the potential generated from the image.The method is capable to close contours, given only one point on the objects' boundary by using a topology-based saddle search routine.We show examples of our method applied to real aerial and medical images.     

A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model

We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141–151) and T. Chan and L. Vese (2001. IEEE-IP, 10(2):266–277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap; it needs only log n level set functions for n phases in the piecewise constant case; it can represent boundaries with complex topologies, including triple junctions; in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.     

DREAM2S: Deformable Regions Driven by an Eulerian Accurate Minimization Method for Image and Video Segmentation

This paper deals with image and video segmentation using active contours. We propose a general form for the energy functional related to region-based active contours. We compute the associated evolution equation using shape derivation tools and accounting for the evolving region-based terms. Then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented. Experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions. As an example, it has been successfully applied to face segmentation in real video sequences.