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.

Abstract. This paper presents a new method for determining the minimal non-rigid deformation between two 3-D surfaces, such as those which describe anatomical structures in 3-D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3-D surfaces. 1.

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

Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented here, with two novel features. First, explicit prevention of self-intersecting surface geometries is provided, unlike conventional deformable models, which use regularization constraints to discourage but not necessarily prevent such behavior. Second, deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model-based constraints such as expected thickness of an anatomic surface. These two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human MR images, accurately locating the depths of the sulci, even where noise and partial volume artifacts in the image obscure the visibility of sulci. The extracted surfaces are enforced to be simple two-dimensional manifolds (having the topology of a sphere), even though the data may have topological holes. This automatic 3-D cortex segmentation technique has been applied to 150 normal subjects, simultaneously extracting both the gray/white and gray/cerebrospinal fluid interface from each individual. The collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter. Three alternative criteria for defining cortical thickness at each cortical location were developed and compared. These results are shown to corroborate published postmortem and in vivo measurements of cortical thickness. © 2000 Academic Press 1.

In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surface-like model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly non-uniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.

This paper presents a volumetric formulation for the multi-view stereo problem which is amenable to a computationally tractable global optimisation using Graph-cuts. Our approach is to seek the optimal partitioning of 3D space into two regions labelled as ‘object’ and ‘empty’ under a cost functional consisting of the following two terms: (1) A term that forces the boundary between the two regions to pass through photo-consistent locations and (2) a ballooning term that inflates the ‘object ’ region. To take account of the effect of occlusion on the first term we use an occlusion robust photo-consistency metric based on Normalised Cross Correlation, which does not assume any geometric knowledge about the reconstructed object. The globally optimal 3D partitioning can be obtained as the minimum cut solution of a weighted graph.

We present a novel method to extract iso-surfaces from distance volumes. It generates high quality semi-regular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multi-scale force-based solver refines the initial mesh into a semi-regular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. A set of discrete iso-distance ribbons are rapidly built and connected while respecting the topology of the iso-surface implied by the data. Subsequent multi-scale refinement is driven by a simple force-based solver designed to combine good iso-surface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the iso-surface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples.

Abstract-This paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images. We propose a global contour model based on a stable and regenerative shape matrix, which is invariant and unique under rigid motions. Combined with Markov random field to model local deformations, this yields prior distribution that exerts influence over a global model while allowing for deformations. We then cast the problem of extraction into posterior estimation and show its equivalence to energy minimization of a generalized active contour model. We discuss pertinent issues in shape training, energy minimization, line search strategies, minimax regularization and initialization by generalized Hough transform. Finally, we present experimental results and compare its performance to rigid template matching. Index Terms-Deformable model, rigid template, snake, active contour, boundary extraction. I.

Active contours, or snakes, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. A new type of external force for active contours, called gradient vector flow (GVF) was introduced recently to address problems associated with initialization and poor convergence to boundary concavities. GVF is computed as a di#usion of the gradient vectors of a gray-level or binary edge map derived from the image. In this paper, we generalize the GVF formulation to include two spatially varying weighting functions. This improves active contour convergence to long, thin boundary indentations, while maintaining other desirable properties of GVF, such as an extended capture range. The original GVF is a special case of this new generalized GVF (GGVF) model. An error analysis for active contour results on simulated test images is also presented. # 1998 Elsevier Science B.V. All rights reserved. Zusammenfassung Aktive Umrisse, oder Schlangen, we...

In this paper we present a new approach for automatically segmentation and tracking of faces in color images. Segmentation of faces is performed by evaluating color and shape information. First, skin-like regions are determined based on the color attributes hue and saturation. Then regions with elliptical shape are selected as face hypotheses. They are verified by searching for facial features in their interior. After a face is reliably detected, it is tracked over time. Tracking is realized by using an active contour model. The exterior forces of the snake are defined based on color features. They push or pull snaxels perpendicular to the snake. Results for tracking are shown for an image sequence consisting of 150 frames.