Fast Object Segmentation by Growing Minimal Paths from a Single Point on 2D or 3D Images

In this paper, we present a new method for segmenting closed contours and surfaces. Our work builds on a variant of the minimal path approach. First, an initial point on the desired contour is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. We assume that the desired object has a closed boundary. This a-priori knowledge on the topology is used to devise a relevant criterion for stopping the keypoint detection and front propagation. The final domain visited by the front will yield a band surrounding the object of interest. Linking pairs of neighboring keypoints with minimal paths allows us to extract a closed contour from a 2D image. This approach can also be used for finding an open curve giving extra information as stopping criteria. Detection of a variety of objects on real images is demonstrated. Using a similar idea, we can extract networks of minimal paths from a 3D image called Geodesic Meshing. The proposed method is applied to 3D data with promising results.

Multiple paths extraction in images using a constrained expanded trellis

Single shortest path extraction algorithms have been used in a number of areas such as network flow and image analysis. In image analysis, shortest path techniques can be used for object boundary detection, crack detection, or stereo disparity estimation. Sometimes one needs to find multiple paths as opposed to a single path in a network or an image where the paths must satisfy certain constraints. In this paper, we propose a new algorithm to extract multiple paths simultaneously within an image using a constrained expanded trellis (CET) for feature extraction and object segmentation. We also give a number of application examples for our multiple paths extraction algorithm.     

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.     

一种新的基于切线的路径规划方法

提出了一种崭新的基于切线的路径规划方法.它在二维离散姿态空间中,用障碍物的边界线建立环境模型,用凸壳和切线构造局部最短路径,复杂地形能被主干线结构有效地分解.跳跃式扫描技术和按需扩展搜索图的策略使它优于切线图法.它能非常有效地利用稀疏环境和处理较大的规划空间,并且能适应未知和动态的环境, 这使它成为远距离漫游的理想导航方法. 仿真表明,本文算法通常都能得到全局最优路径,并且规划速度快、内存需求小，非常适合于实时应用.􀁱     

Membrane boundary extraction using circular multiple paths

Membrane proteins represent over 50% of known drug targets. Accordingly, several widely used assays in the high content analysis area rely on quantitative measures of the translocation of proteins between intracellular organelles and the cell surface. In order to increase the sensitivity of these assays, one needs to measure the signal specifically along the membrane, requiring a precise segmentation of this compartment. Manual tracing of membrane boundary is very time-consuming and confronts us with issues of objectivity and reproducibility. In this paper, we present an approach based on a circular multiple paths technique on transformed images that enables us to segment the membrane compartment accurately and rapidly. We have presented three approaches for image transformation. The circular property of the multiple paths ensures that we are obtaining closed contours for the membrane boundary. The position of the multiple paths provides the edges of the membrane boundary. The effectiveness of our algorithm is illustrated using cells expressing epitope-tagged membrane proteins.     

Forward/Backward contour tracing with feedback

This correspondence describes a contour extraction algorithm which can gradually improve its results until the extracted contours are closed. This is achieved by an architecture with a feedback path for local smoothing. The feedback path is activated only when one or more contours obtained are not closed in order to initiate smoothing in noisy areas of the image to remove local irregularities that cause the problems. A forward/backward boundary tracing mechanism is employed to facilitate locating any troubled areas. A smoothing method appropriate for reducing local irregularities is discussed. The proposed algorithm is very suitable for those applications that demand closed contours, such as character recognition and blob detection.     

Shortest polygonal paths in space

A classical problem of geometry is the following: given a convex polygon in the plane, find an inscribed polygon of shortest circumference. In this paper we generalize this problem to arbitrary polygonal paths in space and consider two cases: in the “open” case the wanted path of shortest length can have different start and end point, whereas in the “closed” case these two points must coincide. We show that finding such shortest paths can be reduced to finding a shortest path in a planar “channel”. The latter problem can be solved by an algorithm of linear-time complexity in the open as well in the closed case. Finally, we deal with constrained problems where the wanted path has to fulfill additional properties; in particular, if it has to pass straight through a further point, we show that the length of such a constrained polygonal path is a strictly convex function of some angle α, and we derive an algorithm for determining such constrained polygonal paths efficiently.     

Exact, scaled image rotations in finite Radon transform space

The Finite Radon Transform (FRT) is a discrete analogue of classical tomography. The FRT permits exact reconstruction of a discrete object from its discrete projections. The set of projection angles for the FRT is intrinsic to each image array size. It is shown here that the set of FRT angles is closed under a rotation by any of its members. A periodic re-ordering of the elements of the 1D FRT projections is then equivalent to an exact 2D image rotation. FRT-based rotations require minimal interpolation and preserve all of the original image pixel intensities. This approach has applications in image feature matching, multi-scale data representation and data encryption.     

Multiple Contour Finding and Perceptual Grouping using Minimal Paths

We address the problem of finding a set of contour curves in an image. We consider the problem of perceptual grouping and contour completion, where the data is a set of points in the image. A new method to find complete curves from a set of contours or edge points is presented. Our approach is based on a previous work on finding contours as minimal paths between two end points using the fast marching algorithm (L. D Cohen and R. Kimmel, International Journal of Computer Vision, Vol. 24, No. 1, pp. 57–78, 1997). Given a set of key points, we find the pairs of points that have to be linked and the paths that join them. We use the saddle points of the minimal action map. The paths are obtained by backpropagation from the saddle points to both points of each pair.In a second part, we propose a scheme that does not need key points for initialization. A set of key points is automatically selected from a larger set of admissible points. At the same time, saddle points between pairs of key points are extracted. Next, paths are drawn on the image and give the minimal paths between selected pairs of points. The set of minimal paths completes the initial set of contours and allows to close them. We illustrate the capability of our approach to close contours with examples on various images of sets of edge points of shapes with missing contours.     

Iso-scallop tool path planning for triangular mesh surfaces in multi-axis machining

Triangular mesh enables the flexible construction of complex surface geometry and has become a general representation of 3D objects in computer graphics. However, the creation of a tool path with constant residual scallop height on triangular mesh surfaces in multi-axis machining is not a convenient task for current algorithms. In this study, an isoscallop tool path planning method for triangular mesh surfaces, in which the tool path is derived directly from the contours of a normalized geodesic distance field (GDF), without any post-processing is proposed. First, the GDF is built to determine the shortest geodesic distance from each vertex to the mesh boundary. Then, the normalizing process is performed on the GDF to ensure that its first contour meets the isoscallop height requirement considering the mesh curvature and effective cutter radius. To improve the computational efficiency, the GDF is only built in the mesh area related to the first contour by specifying a stop distance. Moreover, an adaptive refinement process is conducted on the mesh to improve the smoothness and accuracy of the tool path. Finally, the triangular mesh is trimmed along this first contour for a new round of tool path planning. The proposed method is organized recursively and terminated when no new paths are generated. Simulations and experiments are conducted to verify the effectiveness and superiority of the proposed tool path planning method.     

一种基于离散变权网络的动态最短路径快速算法

在离散变权动态网络中,求解最短路径的最优化算法的计算复杂性通常远大于O(n2),不适用于实时的动态交通信息导航系统。提出的动态最短路径快速算法,是在所有的当前点与下一个待选点之间以及待选点与目标点之间的动态弧的权值之和中选择一个最小值,然后把该待选点作为当前点继续选择下一个待选点,如此反复,直到达到目标点为止。该算法所得到的路径是一个次优解,但其执行时间却比寻找最优解算法要小得多,并且所得到的解要优于选择最短距离路径的动态解。实验结果证明这是一种适用于动态交通导航的有效算法。     

Globally minimal surfaces by continuous maximal flows

In this paper, we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction. We present a solution, simulating a continuous maximal flow by a novel system of partial differential equations. Existing methods are either grid-biased (graph-based methods) or suboptimal (active contours and surfaces). The solution simulates the flow of an ideal fluid with isotropic velocity constraints. Velocity constraints are defined by a metric derived from image data. An auxiliary potential function is introduced to create a system of partial differential equations. It is proven that the algorithm produces a globally maximal continuous flow at convergence, and that the globally minimal surface may be obtained trivially from the auxiliary potential. The bias of minimal surface methods toward small objects is also addressed. An efficient implementation is given for the flow simulation. The globally minimal surface algorithm is applied to segmentation in 2D and 3D as well as to stereo matching. Results in 2D agree with an existing minimal contour algorithm for planar images. Results in 3D segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias.     

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.     

Geodesic Active Contours

A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical snakes based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. The scheme was implemented using an efficient algorithm for curve evolution. Experimental results of applying the scheme to real images including objects with holes and medical data imagery demonstrate its power. The results may be extended to 3D object segmentation as well.     

Reduce the stretch in surface flattening by finding cutting paths to the surface boundary

This paper presents a method for finding cutting paths on a 3D triangular mesh surface to reduce the stretch in the flattened surface. The cutting paths link the surface boundary and the nodes where the Gaussian curvature is high, and their total length is minimized. First, a linear algorithm for computing an approximate boundary geodesic distance map is introduced; the map encapsulates the undirected geodesic distance from every triangular node to the surface boundary approximately. This is followed by determining the undirected shortest paths passing through all the nodes where the Gaussian curvature is larger than a threshold. The cutting paths walk along the triangular edges of the given surface. Compared with other similar approaches, our method reaches a faster speed, and can deal with surfaces with widely distributed curvatures.     

3维牙颌模型牙齿分割的路径规划方法

目的 从3维牙颌模型上分割出单颗牙齿是计算机辅助正畸系统的重要步骤。由于3维测量分辨率和网格重建精度的有限性,三角网格牙颌模型上牙龈和牙缝边界往往融合在一起,使得单颗牙齿的自动分割变得极为困难。传统方法容易导致分割线断裂、分支干扰等问题,且手工交互较多,为此提出一种新颖的基于路径规划技术的单颗牙齿自动分割方法。方法 为避免在探测边界时牙龈和牙缝相互干扰,采用牙龈路径和牙缝路径分开规划策略。首先基于离散曲率分析和一种双重路径规划法搜索牙龈分割路径,并基于搜索到的牙龈路径利用图像形态学和B样条拟合技术构建牙弓曲线;然后综合牙龈路径和牙弓曲线的形态特征探测牙龈路径上的牙缝凹点以划界每颗牙齿的牙龈边界轮廓,并通过匹配和搜索牙龈边界轮廓上颊舌侧凹点间的最优路径确定齿间牙缝边界路径;最后细化整个路径以获取每颗牙齿精确的封闭分割轮廓。结果 对不同畸形程度的患者牙颌模型进行分割实验,结果表明,本文方法对于严重畸形的牙齿能够产生正确的分割结果,而且简单快速,整个分割过程基本能够控制在20 s以内。和现有方法相比,本文方法具有较少的人工干预和参数调整,除了在个别牙齿边界较为模糊的位置需要手动调整外,大部分情况都是自动的。结论 提出的路径规划方法具有强大的抗干扰能力,能够有效克服牙缝牙沟等分支干扰以及分割线断裂等问题,最大程度地减少人工干预,适用于各类畸形牙患者模型的牙齿分割。     

三维重构中轮廓线间的连接和光滑问题的处理

在使用面绘制算法重构三维实体模型时，由于原始数据稀疏，需要通过一定的方法对填充在相邻轮廓线间的三角形或多边形进行拟和，以达到光滑的效果。本文先按照最小内角最大准则进行Delaunay三角剖分，当可选三角形的最小内角相等时再运用最短路径法在相邻轮廓线间构造三角形，然后再在三角格网上构造Bezier三角曲面，不仅使构造出来的格网具有较好形状，又提高了表面的光滑程度和重构的精度。     

Interactive segmentation of non-star-shaped contours by dynamic programming

In this paper we present the Rack algorithm for the detection of optimal non-star-shaped contours in images. It is based on the combination of a user-driven image transformation and dynamic programming. The fundamental idea is to interactively specify and edit the general shape of the desired object by using a rack. This rack is used to model the image as a directed acyclic weighted graph that contains a path corresponding to the expected contour. In this graph, the shortest path with respect to an adequate cost function can be calculated efficiently via dynamic programming. The experimental results indicate the algorithm's ability of combining an acceptable amount of user interaction with generally good segmentation results.     

Active Rays: Polar-transformed Active Contours for Real-Time Contour Tracking

In this paper we describe a new approach to contour extraction and tracking, which is based on the principles of active contour models and overcomes its shortcomings. We formally introduce active rays, describe the contour extraction as an energy minimization problem and discuss what active contours and active rays have in common.The main difference is that for active rays a unique ordering of the contour elements in the 2D image plane is given, which cannot be found for active contours. This is advantageous for predicting the contour elements' position and prevents crossings in the contour. Further, another advantage is that instead of an energy minimization in the 2D image plane the minimization is reduced to a 1D search problem. The approach also shows any-time behavior, which is important with respect to real-time applications. Finally, the method allows for the management of multiple hypotheses of the object's boundary. This is an important aspect if concave contours are to be tracked.Results on real image sequences (tracking a toy train in a laboratory scene, tracking pedestrians in an outdoor scene) show the suitability of this approach for real-time object tracking in a closed loop between image acquisition and camera movement. The contour tracking can be done within the image frame rate (25 fps) on standard Unix workstations (HP 735) without any specialized hardware.     

基于侧影轮廓的图像三维重建方法

针对自标定单幅图像的三维重建问题,提出一种基于侧影轮廓的图像三维重建方法。使用成角度平面镜装置拍摄目标物体,对所得图像进行边缘跟踪,得到闭合的轮廓曲线,利用满足平面镜成像原理的2对侧影轮廓计算灭点,根据灭点间的约束关系计算相机参数,在此基础上重建得到物体的三维模型。实验结果表明,该方法能快速重建逼真的三维模型。