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.

In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/image generation - display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling - curve, surface, solid, and object representations;J.6[Com- puter Applications]: Computer-Aided Engineering - computeraided design General Terms: Algorithms, Graphics. 1

The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software.

The bottle-neck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particles with an implicit integration method. The simulator models cloth as a triangular mesh, with internal cloth forces derived using a simple continuum formulation that supports modeling operations such as local anisotropic stretch or compression; a unified treatment of damping forces is included as well. The implicit integration method generates a large, unbanded sparse linear system at each time step which is solved using a modified conjugate gradient method that simultaneously enforces particles ’ constraints. The constraints are always maintained exactly, independent of the number of conjugate gradient iterations, which is typically small. The resulting simulation system is significantly faster than previous accounts of cloth simulation systems in the literature. Keywords—Cloth, simulation, constraints, implicit integration, physically-based modeling. 1

Several properties of the cerebral cortex, including its columnar and laminar organization, as well as the topographic organization of cortical areas, can only be properly understood in the context of the intrinsic two-dimensional structure of the cortical surface. In order to study such cortical properties in humans, it is necessary to obtain an accurate and explicit representation of the cortical surface in individual subjects. Here we describe a set of automated procedures for obtaining accurate reconstructions of the cortical surface, which have been applied to data from more than 100 subjects, requiring little or no manual intervention. Automated routines for unfolding and flattening the cortical surface are described in a companion paper. These procedures allow for the routine use of cortical surface-based analysis and visualization methods in functional brain imaging.

Spacetime constraints are a new method for creating character animation. The animator specifies what the character has to do, for instance, "jump from here to there, clearing a hurdle in between;" how the motion should be performed, for instance "don't waste energy," or "come down hard enough to splatter whatever you land on;" the character's physical structure---the geometry, mass, connectivity, etc. of the parts; and the physical resources available to the character to accomplish the motion, for instance the character 's muscles, a floor to push off from, etc. The requirements contained in this description, together with Newton 's laws, comprise a problem of constrained optimization. The solution to this problem is a physically valid motion satisfying the "what" constraints and optimizing the "how" criteria. We present as examples a Luxo lamp performing a variety of coordinated motions. These realistic motions conform to such principles of traditional animation as anticipation, squas...

We present an algorithm to efficiently and robustly process collisions, contact and friction in cloth simulation. It works with any technique for simulating the internal dynamics of the cloth, and allows true modeling of cloth thickness. We also show how our simulation data can be post-processed with a collision-aware subdivision scheme to produce smooth and interference free data for rendering.

The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the severe topological re-strictions that NURBS impose. In order to move beyond these re-strictions, we have recently introduced subdivision surfaces into our production environment. Subdivision surfaces are not new, but their use in high-end CG production has been limited. Here we describe a series of developments that were required in order for subdivision surfaces to meet the demands of high-end production. First, we devised a practical technique for construct-ing provably smooth variable-radius fillets and blends. Second, we developed methods for using subdivision surfaces in clothing sim-ulation including a new algorithm for efficient collision detection. Third, we developed a method for constructing smooth scalar fields on subdivision surfaces, thereby enabling the use of a wider class of programmable shaders. These developments, which were used extensively in our recently completed short film Geri’s game, have become a highly valued feature of our production environment.

This paper presents a robust, adaptive method for animating dynamic visco-elastic deformable objects that provides a guaranteed frame rate. Our approach uses a novel automatic space and time adaptive level of detail technique, in combination with a largedisplacement (Green) strain tensor formulation. The body is partitioned in a non-nested multiresolution hierarchy of tetrahedral meshes. The local resolution is determined by a quality condition that indicates where and when the resolution is too coarse. As the object moves and deforms, the sampling is refined to concentrate the computational load into the regions that deform the most. Our model consists of a continuous differential equation that is solved using a local explicit finite element method. We demonstrate that our adaptive Green strain tensor formulation suppresses unwanted artifacts in the dynamic behavior, compared to adaptive mass-spring and other adaptive approaches. In particular, damped elastic vibration modes are shown to be nearly unchanged for several levels of refinement. Results are presented in the context of a virtual reality system. The user interacts in real-time with the dynamic object through the control of a rigid tool, attached to a haptic device driven with forces derived from the method.

this paper, we introduce a method for recovery of compact volumetric models for single part objects. To solve the shape recovery problem in isolation from segmentation, we assume that only a single object is present in the scene at a time. Although we made this simplification to break up the problem, this assumption is still valid for some restricted environments [30]. We show that the shape of those objects can be recovered subject to the model's internal constraints. In this work we use a partic- ular example of compact volumetric models--superquad- ric primitives with parametric deformations. We introduce a least-squares minimization method to recover model and deformation parameters using range data as the input. Range data enables us to study shape recovery independent of different passive techniques of obtaining depth data, such as depth from stereo, depth from focus, or depth from motion. The fitting function which we min- imize is a cost or energy function whose value depends on the distance of points from the model's surface and on the overall size of the model. We show that the solution space, which can have more than one "deep" minimum or acceptable solution and many shallow local minima, can be searched efficiently with a gradient descent method. By using a stochastic technique, the procedure can escape from shallow local minima, and a particular solution among several acceptable solutions can be reached by searching in a constrained parameter subspace. The paper is organized as follows. Section II is on parametric models in computer vision, focusing on comparison of generalized cylinders and superquadrics. Section III explains superquadric models in detail. Section IV is about recovery of nondeformed superquadric models, and Section V is on recovery of defo...