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21
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 559 (14 self)
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In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fairing, to lowpass filtering. We describe a very simple surface signal lowpass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimizationbased 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]: ComputerAided Engineering  computeraided design General Terms: Algorithms, Graphics. 1
Topological Considerations in Isosurface Generation
 ACM Transactions on Graphics
, 1994
"... 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 e ..."
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Cited by 96 (0 self)
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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 wellunderstood ways. We introduce two gradientconsistency 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.
Analyzing Gait With Spatiotemporal Surfaces
 In IEEE Workshop on Motion of NonRigid and Articulated Objects
, 1994
"... 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 ..."
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Cited by 66 (1 self)
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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.
Generalizing epipolarplane image analysis on the spatiotemporal surface
 In IJCV
, 1989
"... The previous implementations of our EpipolarPlane 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 un ..."
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Cited by 54 (0 self)
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The previous implementations of our EpipolarPlane 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 threedimensional 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 twodimensional manifolds defined at the zeros of a threedimensional 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 threedimensional scene reconstruction.
Robust Shape Recovery from Occluding Contours Using a Linear Smoother
, 1993
"... 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 ..."
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Cited by 46 (9 self)
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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...
Steerable Filters and Local Analysis of Image Structure
, 1992
"... Two paradigms for visual analysis are topdown, starting from highlevel models or information about the image, and bottomup, where little is assumed about the image or objects in it. We explore a local, bottomup approach to image analysis. We develop operators to identify and classify image junct ..."
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Cited by 30 (0 self)
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Two paradigms for visual analysis are topdown, starting from highlevel models or information about the image, and bottomup, where little is assumed about the image or objects in it. We explore a local, bottomup 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...
Fourdimensional views of 3D scalar fields
 In Proceedings of IEEE Visualization
, 1992
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Image Sequence Description Using Spatiotemporal Flow Curves: Toward MotionBased Recognition
, 1991
"... Recovering a hierarchical motion description of a long image sequence is one way to recognize objects and their motions. Intermediatelevel and highlevel motion analysis, i.e., recognizing a coordinated sequence of events such as walking and throwing, has been formulated previously as a process tha ..."
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Cited by 11 (1 self)
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Recovering a hierarchical motion description of a long image sequence is one way to recognize objects and their motions. Intermediatelevel and highlevel motion analysis, i.e., recognizing a coordinated sequence of events such as walking and throwing, has been formulated previously as a process that follows highlevel object recognition. This thesis develops an alternative approach to intermediatelevel and highlevel 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 intermediatelevel 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...