Last update: August 1, 2004.

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Publications on interactive curve extraction from images (snakes or active contour/surface models) used in Computer Vision :

• Pascal Fua et al. :
  • Imposing Hard Constraints on Deformable Models Through Optimization in Orthogonal Subspaces, 1997.
  • Ziplock Snakes, 1994.
• Frederic Leymarie et al. :
  • Tracking Deformable Objects in the Plane Using an Active Contour Model, 1993.
• Demetri Terzopoulos et al. :
  • T-Snakes: Topology adaptive snakes, 2000.
  • Dynamic 3D models with local and global deformations: Deformable superquadrics, 1990 & 1991.
  • Symmetry-Seeking Models for 3D Object Reconstruction, 1987.
  • Snakes: Active Contour Models, 1987 & 1988.

BibTeX references.

Abstract:

An approach is presented for imposing generic hard constraints on deformable models at a low computational cost, while preserving the good convergence properties of snake-like models. We believe this capability to be essential not only for the accurate modeling of individual objects that obey known geometric and semantic constraints but also for the consistent modeling of sets of objects. Examples in 2D (linear features) and 3D (linear features and surfaces) are presented.

Summary :

Given a deformable model, the state vector that defines its shape, an objective function to be minimized and a set of constraints to be satisfied, each iteration of the optimization performs 2 steps:

1. Orhtogonally project the current state toward the constraint surface, i.e., the set of all states that satisfy the constraints.
2. Minimize the objective function in the subspace that is tangent to the constraint surface.

Abstract:

We propose a snake-based approach that lets a user specify only the distant endpoints of the curve he wishes to delineate without having to supply an almost complete polygonal approximation. We greatly simplify the initialization process and achieve much better convergence properties than those of traditional snakes by using the image information around these endpoints 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 abolishing the need to sketch a feature of interest in its entirety, that is, to perform a painstaking, almost complete, manual segmentation.

The problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed. In evaluating these problems, a technique based on an active contour model commonly called a snake is examined. The technique is applied to cell locomotion and tracking studies. The snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases. A detailed analysis of the snake model, emphasizing its limitations and shortcomings, is presented, and improvements to the original description of the model are proposed. Problems of convergence of the optimization scheme are considered. In particular, an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed. Hierarchical filtering methods, as well as a continuation method based on a discrete sale-space representation, are discussed. Results for both segmentation and tracking are presented. Possible failures of the method are discussed.

Index Term: image segmentation; hierarchical filtering; deformable objects; active contour model; noisy intensity image; tracking; nonrigid object; snake; cell locomotion; segmentation; convergence; optimization; terminating criterion; topographic features; continuation method; discrete sale-space representation; convergence; filtering and prediction theory; graph theory; image segmentation; optimisation; tracking

We present a new class of deformable contours (snakes) and apply them to the segmentation of medical images. Our snakes are defined in terms of an affine cell image decomposition (ACID). The "snakes in ACID" framework significantly extends conventional snakes, enabling topological flexibility among other features. The resulting topology adaptive snakes, or "T-snakes," can be used to segment some of the most complex-shaped biological structures from medical images in an efficient and highly automated manner.

The authors present a physically based approach to fitting complex three-dimensional shapes using a novel class of dynamic models that can deform both locally and globally. They formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The model's six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. The local deformation parameters reconstruct the details of complex shapes that the global abstraction misses. The equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces. The authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational, rotational, and deformational degrees of freedom of the models. Model fitting experiments involving 2D monocular image data and 3D range data are presented.

Page created & maintained by Frederic Leymarie, 1998-2004.
Comments, suggestions, etc., mail to: leymarie@lems.brown.edu