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.

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.

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 concave boundaries, howevel; have limited their utility. This paper develops 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 dijhsion of the gradient vectors of a gray-level or binary edge map derived from the image. The resultant field has a large capture range and forces active contours into concave regions. Examples on simulated images and one real image are presented. 1

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The system achieves much of its power by transferring parts of previously learned solutions rather than a single complete solution. The system exploits strong features in the multi-dimensional function produced by reinforcement learning in solving a particular task. These features are stable and easy to recognize early in the learning process. They generate a partitioning of the state space and thus the function. The partition is represented as a graph. This is used to index and compose functions stored in a case base to form a close approximation to the solution of the new task. Experiments demonstrate that function composition often produces more 1.

A novel, physically motivated deformable model for shape recovery and segmentation is presented. The model, referred to as the charged-particle model (CPM), is inspired by classical electrodynamics and is based on a simulation of charged particles moving in an electrostatic field. The charges are attracted towards the contours of the objects of interest by an electrostatic field, whose sources are computed based on the gradient-magnitude image. The electric field plays the same role as the potential forces in the snake model, while internal interactions are modeled by repulsive Coulomb forces. We demonstrate the flexibility and potential of the model in a wide variety of settings: shape recovery using manual initialization, automatic segmentation, and skeleton computation. We perform a comparative analysis of the proposed model with the active contour model and show that specific problems of the latter are surmounted by our model. The model is easily extendable to 3D and copes well with noisy images.

Active Contour (or Snake) Model is recognized as one of the efficient tools for 2D/3D image segmentation. However, traditional snake models prove to be limited in several aspects. The present paper describes a set of diffusion equations applied to image gradient vectors, yielding a vector field over the image domain. The obtained vector field provides the Snake Model an external force as well as an automatic way to generate the initial contours. Finally a region merging technique is employed to further improve the segmentation results.

In this paper, we present an approach for image segmentation, based on the existing Active Snake Model and Watershed-based Region Merging. Our algorithm includes initial segmentation using Normalized Gradient Vector Diffusion ( NG VD) and region merging based on Region Adjacency Graph (RAG). We use a set of heat diffusion equations to generate a vector field over the image domain, which provides us with a natural way to define seeds as well as an external force to attract the active snakes. Then an initial segmentation of the original image can be obtained by a similar idea as seen in active snake model. Finally an RAG-based region merging technique is used to find the true segmentation as desired. The experimental results show that our NGVD-based region merging algorithm overcomes some problems as seen in classic active snake model. We will also see that our NGVD has several advantages over the traditional gradient vector diffusion.

Deformable models are used extensively in image processing, computer vision, and medical imaging applications, particularly to delineate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This chapter presents an external force for deformable models, 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 deformable model external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding deformable model is formulated directly from a dynamic force equation rather than a energy minimization formulation. Using several two-dimensional examples and two three-dimensional examples, we show that GVF has a large capture range and is able to move deformable models into ...

We present a new five-dimensional (5-D) space representation of diffusion magnetic resonance imaging (dMRI) of high angular resolution. This 5-D space is basically a non-Euclidean space of position and orientation in which crossing fiber tracts can be clearly disentangled, that cannot be separated in three-dimensional position space. This new representation provides many possibilities for processing and analysis since classical methods for scalar images can be extended to higher dimensions even if the spaces are not Euclidean. In this paper, we show examples of how regularization and segmentation of dMRI is simplified with this new representation. The regularization is used with the purpose of denoising and but also to facilitate the segmentation task by using several scales, each scale representing a different level of resolution. We implement in five dimensions the Chan–Vese method combined with active contours without edges for the segmentation and the total variation functional for the regularization. The purpose of this paper is to explore the possibility of segmenting white matter structures directly as entirely separated bundles in this 5-D space. We will present results from a synthetic model and results on real data of a human brain acquired with diffusion spectrum magnetic resonance imaging (MRI), one of the dMRI of high angular resolution available. These results will lead us to the conclusion that this new high-dimensional representation indeed simplifies the problem of segmentation and regularization.

Abstract. We propose a new multiscale image segmentation model, based on the active contour/snake model and the Polyakov action. The concept of scale, general issue in physics and signal processing, is introduced in the active contour model, which is a well-known image segmentation model that consists of evolving a contour in images toward the boundaries of objects. The Polyakov action, introduced in image processing by Sochen-Kimmel-Malladi in Sochen et al. (1998), provides an efficient mathematical framework to define a multiscale segmentation model because it generalizes the concept of harmonic maps embedded in higher-dimensional Riemannian manifolds such as multiscale images. Our multiscale segmentation model, unlike classical multiscale segmentations which work scale by scale to speed up the segmentation process, uses all scales simultaneously, i.e. the whole scale space, to introduce the geometry of multiscale images in the segmentation process. The extracted multiscale structures will be useful to efficiently improve the robustness and the performance of standard shape analysis techniques such as shape recognition and shape registration. Another advantage of our method is to use not only the Gaussian scale space but also many other multiscale spaces such as the Perona-Malik scale space, the curvature scale space or the Beltrami scale space. Finally, this multiscale segmentation technique is coupled with a multiscale edge detecting function based on the gradient vector flow model, which is able to extract convex and concave object boundaries independent of the initial condition. We apply our multiscale segmentation model on a synthetic image and a medical image.