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

A popular technique for rendition of isosurfaces in sampled data is to consider cells with sample points as corners and approximate the isosurface in each cell by one or more polygons whose vertices are obtained by interpolation of the sample data. That is, each polygon vertex is a point on a cell edge, between two adjacent sample points, where the function is estimated to equal the desired threshold value. The two sample points have values on opposite sides of the threshold, and the interpolated point is called an intersection point. When one cell face has an intersection point ineach of its four edges, then the correct connection among intersection points becomes ambiguous. An incorrect connection can lead to erroneous topology in the rendered surface, and possible discontinuities. We show that disambiguation methods, to be at all accurate, need to consider sample values in the neighborhood outside the cell. This paper studies the problems of disambiguation, reports on some solutions, and presents some statistics on the occurrence of such ambiguities. A natural way to incorporate neighborhood information is through the use of calculated gradients at cell corners. They provide insight into the behavior of a function in well-understood ways. We introduce two gradient-consistency heuristics that use calculated gradients at the corners of ambiguous faces, as well as the function values at those corners, to disambiguate at a reasonable computational cost. These methods give the correct topology on several examples that caused problems for other methods we examined.

In recent years, numerous techniques have been developed for the polygonization of implicit surfaces. This article reviews the principal algorithms and provides a framework for identifying their conceptual similarities as well as their practical differences. Particular attention is devoted to the much discussed problem of topological ambiguity, with solutions analyzed according to their consistency and correctness. Included in this evaluation are implementation suggestions for various application requirements.

Human motions generate characteristic spatiotemporal patterns. We have developed a set of techniques for analyzing the patterns generated by people walking across the field of view. After change detection, the XYT pattern can be fit with a smooth spatiotemporal surface. This surface is approximately periodic, reflecting the periodicity of the gait. The surface can be expressed as a combination of a standard parameterized surface -- the canonical walk -- and a deviation surface that is specific to the individual walk.

The previous implementations of our Epipolar-Plane Image Analysis mapping technique demonstrated the feasibility and benefits of the approach, but were carried out for restricted camera geometries. The question of more general geometries made the technique's utility for autonomous navigation uncertain. We have developed a generalization of our analysis that (a) enables varying view direction, including variation over time (b) provides three-dimensional connectivity information for building coherent spatial descriptions of observed objects; and (c) operates sequentially, allowing initiation and refinement of scene feature estimates while the sensor is in motion. To implement this generalization it was necessary to develop an explicit description of the evolution of images over time. We have achieved this by building a process that creates a set of two-dimensional manifolds defined at the zeros of a three-dimensional spatiotemporal Laplacian. These manifolds represent explicitly both the spatial and temporal structure of the temporally evolving imagery, and we term them spatiotemporal surfaces. The surfaces are constructed incrementally, as the images are acquired. We describe a tracking mechanism that operates locally on these evolving surfaces in carrying out three-dimensional scene reconstruction.

Recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent. For three or more views, shape recovery is possible, and several algorithms have recently been developed for this purpose. We present a new approach to the multiframe stereo problem which does not depend on differential measurements in the image, which may be noise sensitive. Instead, we use a linear smoother to optimally combine all of the measurements available at the contours (and other edges) in all of the images. This allows us to extract a robust and dense estimate of surface shape, and to integrate shape information from both surface markings and occluding contours. Keywords: Computer vision, image sequence analysis, motion analysis and multiframe stereo, shape and object representation, occluding contours (profiles). c flDigital Equipment Corporation 1993. All rights reserved. 1 Computer and Information Science Department, University...

Two paradigms for visual analysis are top-down, starting from high-level models or information about the image, and bottom-up, where little is assumed about the image or objects in it. We explore a local, bottom-up approach to image analysis. We develop operators to identify and classify image junctions, whichcontain important visual cues for identifying occlusion, transparency, and surface bends. Like the human visual system, we begin with the application of linear filters which are oriented in all possible directions. Wedevelop an efficientway to create an oriented filter of arbitrary orientation by describing it as a linear combination of basis filters. This approach to oriented filtering, which we call steerable filters, offers advantages for analysis as well as computation. We design a variety of steerable filters, including steerable quadrature pairs, which measure local energy. We show applications of these filters in orientation and texture analysis, and image representation and enhanc...

Recovering a hierarchical motion description of a long image sequence is one way to recognize objects and their motions. Intermediate-level and high-level motion analysis, i.e., recognizing a coordinated sequence of events such as walking and throwing, has been formulated previously as a process that follows high-level object recognition. This thesis develops an alternative approach to intermediate-level and high-level motion analysis. It does not depend on complex object descriptions and can therefore be computed prior to object recognition. Toward this end, a new computational framework for low and intermediate-level processing of long sequences of images is presented. Our new computational framework uses spatiotemporal (ST) surface flow and ST flow curves. As contours move, their projections into the image also move. Over time, these projections sweep out ST surfaces. Thus, these surfaces are direct representations of object motion. ST surface flow is defined as the natural extensio...

Scalar functions of three variables, w = f(x; y; z), are common in many types of scienti c and medical applications. Such 3D scalar elds can be understood as elevation maps in four dimensions, with three independent variables (x; y; z) and a fourth, dependent, variable w that corresponds to the elevations. We show how techniques developed originally for the display of 3-manifolds in 4D Euclidean space can be adapted to visualize 3D scalar elds in a variety of ways. 1

A method for extracting intersection-free iso-surfaces from volumetric data with an octree structure is presented. Unlike contouring techniques designed for uniform grids (such as Marching Cubes), adaptive contouring methods (such as Dual Contouring) can and do often generate intersecting polygons. Our main contribution is a polygon generation algorithm that produces triangles enclosed in nonoverlapping volumes, which guarantees an intersection-free mesh. Like other adaptive contouring methods, this new method generates crack-free and feature-preserving surfaces on both uniform and octree grids. We demonstrate the method on both scanned objects and industrial models. 1.