This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.

The surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds. As such, it is a difficult domain for computational as well as visualization purposes. We have therefore designed a set of procedures for modifying the representation of the cortical surface to (i) inflate it so that activity buried inside sulci may be visualized, (ii) cut and flatten an entire hemisphere, and (iii) transform a hemisphere into a simple parameterizable surface such as a sphere for the purpose of establishing a surface-based coordinate system. � 1999 Academic Press

In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented straightforwardly. We demonstrate performance that compares favorably to other polygonal methods and is faster than reported results for other methods on sculptured surfaces. 1 Introduction We introduce a framework for minimum distance calculations that applies well to both polygonal and parametric model representations (Figure 1). The resulting methods scale well with problem size, have time-critical properties, and are interactive for large polygonal models and sculptured surfaces. In robotics, minimum distance queries have been used in path planning [2], path modification [25], and collision avoidance [15]. In computer graphics, minimum distance computations have played roles in physical...

A new tracing algorithm is described that supports haptic rendering of NURBS surfaces without the use of any intermediate representation. By using this tracing algorithm in conjunction with algorithms for surface proximity testing and surface transitions, a complete haptic rendering system for sculptured models has been developed. The system links an advanced CAD modeling system with a Sarcos force-reflecting exo-skeleton arm. A method for measuring the quality of the tracking component of the haptic rendering separately from the haptic device and force computation is also described.

dag is a pic or POSTSCRIPT preprocessor that draws directed graphs. It works well on acyclic graphs and other graphs that can be drawn as hierarchies. Graph descriptions contain nodes, edges, and optional control statements. Here is a drawing of a graph from Forrester's book, World Dynamics (Wright-Allen, Cambridge, MA, 1971). It took 2.1 CPU seconds on a VAX-8650 to make this drawing. S8 9 S24 25 27 S1 2 10 S35 43 36 S30 31 33 42 T1 26 T24 3 16 17 18 11 14 13 12 32 T30 34 4 15 19 29 37 39 41 38 40 23 5 21 20 28 6 T35 22 7 T8 I. Introduction Directed graphs have many applications in computing, such as describing data structures, finite automata, data flow, procedure calls, and software configuration dependencies. A picture is a good way to represent a directed graph. It is seldom easy to understand much about a graph from a list of edges, but with a picture one can quickly find individual nodes, groups of related nodes, and trace paths in the graph. The main obstacle is that it can be...

This paper presents a method for planning the motions of autonomous vehicles moving on general terrains. The method obtains the geometric path and vehicle speeds that minimize motion time consid- ering vehicle dynamics, terrain topography, obstacles, and surface mobility. The terrain is represented by a smooth cubic B patch, and the geometric path consists of a B spline curve mapped to the surface. The time optimal motions are computed by first obtaining the best ohstacle- free path from all paths represented by a uniform grid. This path is further optimized with a local optimization, using the optimal motion time along the path as the cost function and the control points of a B spline as the optimizing parameters. Examples are presented that demonstrate the method for a simple dynamic model of a vehicle moving on a mountainous terrain. I. INTRODUCTION T HE problem of motion planning of autonomous vehicles consistsof selecting the geometric path and vehicle speeds so as to avoi...

Modeling two-dimensional and three-dimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometry representations, which model a complex object, surface and interior together, as a boolean combination of simpler objects. Because neither representation is good for all applications, conversion between the two is often necessary. We consider the problem of converting boundary representations of polyhedral objects into constructive solid geometry (CSG) representations. The CSG representations for a polyhedron P are based on the half-spaces supporting the faces of P . For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone...

Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression, and simplification of 3D shapes. Different features, such as flats, limbs, tips, pits, and various blending shapes that transition between them may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in the surface smoothness and to quantization effects when they operate on triangulated surfaces.

To date, MRI-SPAMM data from different image slices have been analyzed independently. In this paper, we propose an approach for 3D tag localization and tracking of SPAMM data by a novel deformable B-solid. The solid is defined in terms of a 3D tensor product B-spline. The iso-parametric curves of the B-spline solid have special importance. These are termed implicit snakes as they deform under image forces from tag lines in different image slices. The localization and tracking of tag lines is performed under constraints of continuity and smoothness of the B-solid. To track motion from boundaries and restrict image forces to the myocardium, a volumetric model is employed as a pair of coupled endocardial and epicardial B-spline surfaces. To recover deformations of the Left Ventricle (LV) an energy-minimization problem is posed where both tag and LV boundary data are used. The framework has been implemented on tag data from Short Axis (SA) cardiac images, as well as SA LV boundaries, and i...

We develop a dynamic, free-form surface model which is useful for representing a broad class of objects with symmetries and topological variability. The new model is based upon swung NURBS surfaces, and it inherits their desirable cross-sectional design properties. It melds these geometric features with the demonstrated conveniences of surface design within a physics-based framework. We demonstrate several applications of dynamic NURBS swung surfaces, including interactive sculpting through the imposition of forces and the adjustment ofphysical parameters such as mass, damping, and elasticity. Additional applications include surface design with geometric and physical constraints, by rounding solids, and through the tting of unstructured data. We derive the equations of motion for the dynamic NURBS swung surface model using Lagrangian mechanics of an elastic surface and the nite element method. We also show that these surfaces are a special case of D-NURBS surfaces, a recently proposed physicsbased generalization of standard geometric NURBS. Our free-form, rational model not only provides a systematic and uni ed approach for a variety ofCAGD problems such as constraint-based optimization, variational design, automatic weight selection, shape approximation, etc., but it also supports interactive sculpting using physics-based manipulation tools.