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17
An Active Contour Model For Mapping The Cortex
 IEEE TRANS. ON MEDICAL IMAGING
, 1995
"... A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approac ..."
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Cited by 64 (13 self)
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A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approach are proposed to achieve this goal. The primary difference between this formulation and that of snakes is in the specification of the external force acting on the active contour. A study of the uniqueness and fidelity of solutions is made through convexity and frequency domain analyses, and a criterion for selection of the regularization coefficient is developed. Examples demonstrating the performance of this method on simulated and real data are provided.
Shape and Topology Constraints on Parametric Active Contours
 Computer Vision and Image Understanding
, 2000
"... In recent years, the field of active contour based image segmentation has seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parmetric) manner corresponding to the Lagrangian formulation. The second approach represents active c ..."
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Cited by 30 (2 self)
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In recent years, the field of active contour based image segmentation has seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parmetric) manner corresponding to the Lagrangian formulation. The second approach represents active contours in an implicit manner corresponding to the Eulerian framework. After comparing these two approaches, we describe several new topological and physical constraints applied to parametric active contours in order to combine the advantages of these two contour representations. This paper proposes a framework for handling parametric active contours shape and topology in a more intuitive manner. More precisely, the following three algorithms are introduced: 1. Metric and Shape Control: a new internal force expression Mlows to regularize both vertex spacing and vertex smoothness. The smoothness constraint is enforced without producing any shrinkage.
Deformable Contours: Modeling, Extraction, Detection And Classification
, 1994
"... This thesis presents an integrated approach in modeling, extracting, detecting and classifying deformable contours directly from noisy images. We begin by conducting a case study on regularization, formulation and initialization of the active contour models (snakes). Using minimax principle, we deri ..."
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Cited by 16 (0 self)
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This thesis presents an integrated approach in modeling, extracting, detecting and classifying deformable contours directly from noisy images. We begin by conducting a case study on regularization, formulation and initialization of the active contour models (snakes). Using minimax principle, we derive a regularization criterion whereby the values can be automatically and implicitly determined along the contour. Furthermore, we formulate a set of energy functionals which yield snakes that contain Hough transform as a special case. Subsequently, we consider the problem of modeling and extracting arbitrary deformable contours from noisy images. We combine a stable, invariant and unique contour model with Markov random field to yield prior distribution that exerts influence over an arbitrary global model while allowing for deformation. Under the Bayesian framework, contour extraction turns into posterior estimation, which is in turn equivalent to energy minimization in a generalized active...
On Regularization, Formulation and Initialization of the Active Contour Models (Snakes)
"... In snake formulation, large regularization enhances the robustness against noise and incomplete data, while small values increase the accuracy in capturing boundary variations. We present a local minimax criterion which automatically determines the optimal regularization at every locations along the ..."
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Cited by 14 (3 self)
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In snake formulation, large regularization enhances the robustness against noise and incomplete data, while small values increase the accuracy in capturing boundary variations. We present a local minimax criterion which automatically determines the optimal regularization at every locations along the boundary with no added computation cost. We also modify existing energy formulations to repair deficiencies in internal energy and improve performance in external energy. This yields snakes that contain Hough transform as a special case. We can therefore initialize the snake efficiently and reliably using Hough transform. 1 Introduction The active contour models (snakes) [1] turn boundary detection into an optimization problem. Given a snake v = fv i = (x i ; y i ) : i = 1; 2; : : :; ng one seeks to minimize its energy: e(v) = n X i=1 i E int (v i ) + (1 \Gamma i )E ext (v i ) (1) where the internal energy E int imposes continuity and smoothness constraints; and the external energy E...
Ziplock Snakes
, 1997
"... We propose a snakebased approach that allows a user to specify only the distant end points of the curve he wishes to delineate without having to supply an almost complete polygonal approximation. This greatly simplifies the initialization process and yields excellent convergence properties. This is ..."
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Cited by 9 (0 self)
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We propose a snakebased approach that allows a user to specify only the distant end points of the curve he wishes to delineate without having to supply an almost complete polygonal approximation. This greatly simplifies the initialization process and yields excellent convergence properties. This is achieved by using the image information around the end points to provide boundary conditions and by introducing an optimization schedule that allows a snake to take image information into account first only near its extremities and then, progressively, toward its center. In effect, the snakes are clamped onto the image contour in a manner reminiscent of a ziplock being closed. These snakes can be used to alleviate the often repetitive task practitioners face when segmenting images by eliminating the need to sketch a feature of interest in its entirety, that is, to perform a painstaking, almost complete, manual segmentation. Keywords : Snakes, Deformable models, Interactive initialization, B...
On Deformable Models for Visual Pattern Recognition
, 2002
"... This paper reviews modelbased methods fornonrig# shape recogLj#If8 These methods model, match andclassif nonrigg shapes, which aregefIxq#x problematic for conventationalalgentati using rigg models. ..."
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Cited by 8 (2 self)
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This paper reviews modelbased methods fornonrig# shape recogLj#If8 These methods model, match andclassif nonrigg shapes, which aregefIxq#x problematic for conventationalalgentati using rigg models.
ShockBased ReactionDiffusion Bubbles for Image Segmentation
, 1994
"... FigureGround segmentation is a fundamental problem in computer vision. The main difficulty is the integration of lowlevel, pixelbased local image features to obtain global objectbased descriptions. Active contours in the form of snakes, balloons, and levelset modeling techniques have been propos ..."
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Cited by 8 (2 self)
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FigureGround segmentation is a fundamental problem in computer vision. The main difficulty is the integration of lowlevel, pixelbased local image features to obtain global objectbased descriptions. Active contours in the form of snakes, balloons, and levelset modeling techniques have been proposed that satisfactorily address this question for certain applications. However, these methods require manual initialization, do not always perform well near sharp protrusions or indentations, or often cross gaps. We propose an approach inspired by these methods and a shockbased representation of shape in terms of parts, protrusions, and bends. In this representation parts are related to fourth order shocks. Since initially it is not clear where the objects or their parts are, parts are hypothesized in the form of fourth order shocks randomly initialized in homogeneous areas of images. These shocks then form evolving contours, or bubbles, which grow, shrink, merge, split and disappear to cap...
Topology and Shape Constraints on Parametric Active Contours
, 2000
"... In recent years, the field of active contour based image segmentation has seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parametric) manner corresponding to the Lagrangian formulation. The second approach represents active ..."
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Cited by 7 (1 self)
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In recent years, the field of active contour based image segmentation has seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parametric) manner corresponding to the Lagrangian formulation. The second approach represents active contours in an implicit manner corresponding to the Eulerian framework. After comparing these two approaches, we describe several new topological and geometrical constraints applied to parametric active contours in order to combine the advantages of these two contour representations. This paper proposes a framework for handling parametric active contours shape and topology in a more intuitive manner. More precisely, the following three algorithms are introduced: 1. Metric and Shape Control: a new internal force expression allows to regularize both vertex spacing and vertex smoothness. The smoothness constraint is enforced without producing any shrinkage. 2. Contour Resolution Control: the to...
Contour Motion Estimation from Image Sequences Using Curvature Information
"... This paper presents a novel method of velocity field estimation for the points on moving contours in a 2D image sequence. The method determines the corresponding point in a next image frame by considering the curvature change of a given point on the contour. In traditional methods, there are errors ..."
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Cited by 7 (1 self)
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This paper presents a novel method of velocity field estimation for the points on moving contours in a 2D image sequence. The method determines the corresponding point in a next image frame by considering the curvature change of a given point on the contour. In traditional methods, there are errors in optical flow estimation for the points which have low curvature variations since those methods compute solutions by approximating normal optical flow. The proposed method computes optical flow vectors of contour points minimizing the curvature changes. As a first step, snakes are used to locate smooth curves in 2D imagery. Thereafter, the extracted curves are tracked continuously. Each point on a contour has a unique corresponding point on the contour in the next frame whenever the curvature distribution of the contour varies smoothly. The experimental results showed that the proposed method computes accurate optical flow vectors for various moving contours. Keywords  Contour motion, ...
Convexity Analysis of Active Contour Problems
 Image Visual Computing J
, 1996
"... A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analys ..."
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Cited by 4 (0 self)
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A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics of their convexity, and suggesting that external potentials involving center of mass computations may be better behaved than the ususal potentials based on image gradients. Most importantly, our analysis provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries. I. Introduction Active contours, originally described by Kass, Witkin, and Terzopoulos [1], have been successfully used in a wide variety of applications. Their main advantage is that they are topologically isomorphic to the feature...