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.

In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford--Shah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We will give a numerical algorithm using finite differences. Finally, we will present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

This article surveys deformable models, a promising and vigorously researched computer-assisted medical image analysis technique. Among model-based techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottom-up) constraints derived from the image data together with (top-down) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the model-based image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.

Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. It differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation. Using several two-dimensional (2-D) examples and one three-dimensional (3-D) example, we show that GVF has a large capture range and is able to move snakes into boundary concavities.

The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds. 1 Introduction Sethian`s Fast Marching Method [8], is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M ) steps, where M is the total number of grid points in the domain. The technique hinges on producing numerically consistent approximations to the operators in the Eikonal equation that select the correct viscosity solution; this is done through the use of upwind nite dierence operators. The structure of this upwinding is then used to systematically construct the solution to the Eik...

We have been developing a theory for the generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Keywords: shape representation; shape matching; shock graph; shock graph grammar; subgraph isomorphism. 1 I...

In this note, we analyze the geometric active contour models proposed in [10, 31] from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and efficiently to the desired feature. Moreover, we consider some 3-D active surface models based on these ideas. Key words: Active vision, shape and object representation, object recognition, active contours, snakes, visual tracking, edge detection, segmentation, gradient flows, Riemannian metrics, geometric heat equations, curve and surface evolution. Gradient Flows and Geometric Active Contour Models Abstract In this note, we analyze the geometric active contour models proposed in [10, 31] from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new m...

This paper presents a topologically adaptable snakes model for image segmentation and object representation. The model is embedded in the framework of domain subdivision using simplicial decomposition. This framework extends the geometric and topological adaptability of snakes while retaining all of the features of traditionalsnakes, such as user interaction, and overcoming many of the limitations of traditionalsnakes. By superposing a simplicial grid over the image domain and using this grid to iteratively reparameterize the deforming snakes model, the model is able to flow into complex shapes, even shapes with significant protrusions or branches, and to dynamically change topology as necessitated by the data. Snakes can be created and can split into multiple parts or seamlessly merge into other snakes. The model can also be easily converted to and from the traditional parametric snakes model representation. We apply a 2D model to various synthetic and real images in order to segment ...

This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and region-based segmentation modules under a curve-based optimization objective function. The task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework. The textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters, and analyzing their responses as multi-component conditional probability density functions. The texture segmentation is obtained by unifying region and boundary-based information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradient-descent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution is guided by boundary and region-based segmentation forces, and is constrained by a regularity force. The level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled. The performance of our method is demonstrated on a variety of synthetic and real textured frames.

8.997> 1INTRODUCTION T HE problem of detecting and tracking moving objects has a wide variety of applications in computer vision such as coding, video surveillance, monitoring, augmented reality, and robotics. Additionally, it provides input to higher level vision tasks, such as 3D reconstruction and 3D representation. This paper addresses the problem using boundary-based information to detect and track several nonrigid moving objects over a sequence of frames acquired by a static observer. During the last decade, a large variety of motion detection algorithms have been proposed. Early approaches for motion detection rely on the detection of temporal changes. Such methods [1] employ a thresholding technique over the interframe difference, where pixelwise differences or block differences (to increase robustness) have been considered. The difference map is usually binarized using a predefined threshold value to obtain the motion/nomotion classi