Demetri Terzopoulos

Snakes: Active Contour Models

A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scale-space continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest.

Deformable models in medical image analysis: a survey.

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, including segmentation, shape representation, matching and motion tracking.

Elastically deformable models

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.

Dynamic 3D models with local and global deformations: deformable superquadrics

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 models 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. >

Realistic modeling for facial animation

A major unsolved problem in computer graphics is the construction and animation of realistic human facial models. Traditionally, facial models have been built painstakingly by manual digitization and animated by ad hoc parametrically controlled facial mesh deformations or kinematic approximation of muscle actions. Fortunately, animators are now able to digitize facial geometries through the use of scanning range sensors and animate them through the dynamic simulation of facial tissues and muscles. However, these techniques require considerable user input to construct facial models of individuals suitable for animation. In this paper, we present a methodology for automating this challenging task. Starting with a structured facial mesh, we develop algorithms that automatically construct functional models of the heads of human subjects from laser-scanned range and reflectance data. These algorithms automatically insert contractile muscles at anatomically correct positions within a dynamic skin model and root them in an estimated skull structure with a hinged jaw. They also synthesize functional eyes, eyelids, teeth, and a neck and fit them to the final model. The constructed face may be animated via muscle actuations. In this way, we create the most authentic and functional facial models of individuals available to date and demonstrate their use in facial animation.

Constraints on deformable models: recovering 3D shape and nongrid motion

Abstract Inferring the 3D structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision. Our approach makes use of dynamic, elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real-world visual constraints. We specialize these models to include intrinsic forces inducing a preference for axisymmetry. Image-based constraints are applied as extrinsic forces that mold the symmetry-seeking model into shapes consistent with image data. We describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects. We generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data. For time-varying images, the force becomes dynamic and the model is able to infer not only depth, but nonrigid motion as well. We demonstrate the recovery of 3D shape and nonrigid motion from natural imagery.

Regularization of Inverse Visual Problems Involving Discontinuities

Inverse problems, such as the reconstruction problems that arise in early vision, tend to be mathematically ill-posed. Through regularization, they may be reformulated as well-posed variational principles whose solutions are computable. Standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions. Discontinuities present serious difficulties to standard regularization, however, since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers. This paper proposes a general class of controlled-continuity stabilizers which provide the necessary control over smoothness. These nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with (noncontinuous) continuity control functions. In the context of computational vision, they may be thought of as controlled-continuity constraints. These generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities, for which global smoothness constraints fail.

Artificial fishes: physics, locomotion, perception, behavior

This paper proposes a framework for animation that can achieve the intricacy of motion evident in certain natural ecosystems with minimal input from the animator. The realistic appearance, movement, and behavior of individual animals, as well as the patterns of behavior evident in groups of animals fall within the scope of the framework. Our approach to emulating this level of natural complexity is to model each animal holistically as an autonomous agent situated in its physical world. To demonstrate the approach, we develop a physics-based, virtual marine world. The world is inhabited by artificial fishes that can swim hydrodynamically in simulated water through the motor control of internal muscles that motivates fins. Their repertoire of behaviors relies on their perception of the dynamic environment. As in nature, the detailed motions of artificial fishes in their virtual habitat are not entirely predictable because they are not scripted.

Analysis and synthesis of facial image sequences using physical and anatomical models

An approach to the analysis of dynamic facial images for the purposes of estimating and resynthesizing dynamic facial expressions is presented. The approach exploits a sophisticated generative model of the human face originally developed for realistic facial animation. The face model which may be simulated and rendered at interactive rates on a graphics workstation, incorporates a physics-based synthetic facial tissue and a set of anatomically motivated facial muscle actuators. The estimation of dynamical facial muscle contractions from video sequences of expressive human faces is considered. An estimation technique that uses deformable contour models (snakes) to track the nonrigid motions of facial features in video images is developed. The technique estimates muscle actuator controls with sufficient accuracy to permit the face model to resynthesize transient expressions. >

The computation of visible-surface representations

A computational theory of visible-surface representations is developed. The visible-surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of: (1) integrating multiscale constraints on surface depth and orientation from multiple-visual sources; (2) interpolating dense, piecewise-smooth surfaces from these constraints; (3) detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation; and (4) structuring large-scale, distributed-surface representations to achieve computational efficiency. Visible-surface reconstruction is an inverse problem. A well-posed variational formulation results from the use of a controlled-continuity surface model. Discontinuity detection amounts to the identification of this generic models distributed parameters from the data. Finite-element shape primitives yield a local discretization of the variational principle. The result is an efficient algorithm for visible-surface reconstruction. >