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136
Surface reconstruction from unorganized points
 COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS)
, 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
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Cited by 645 (8 self)
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We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from twodimensional slices, and interactive surface sketching.
ReTiling Polygonal Surfaces
 Computer Graphics
, 1992
"... This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speed ..."
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Cited by 402 (2 self)
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This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speedingup the offline rendering of complex scenes. Unfortunately, generating these levels of detail is a timeconsuming task usually left to a human modeler. This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one another to create a retiling of a surface that is faithful to both the geometry and the topology of the original surface. Themain contributions of this paper are: 1) a robust method of connecting together new vertices over a surface, 2) a way of using an estimate of surface curvature to distribute more new vertices at regions of higher curvature and 3) a method of smoothly interpolating between models that represent the same object at different levels of detail. The key notion in the retiling procedure is the creation of an intermediate model called the mutual tessellation of a surface that contains both the vertices from the original model and the new points that are to become vertices in the retiled surface. The new model is then created by removing each original vertex and locally retriangulating the surface in a way that matches the local connectedness of the initial surface. This technique for surface retessellation has been successfully applied to isosurface models derived from volume data, Connolly surface molecular models and a tessellation of a minimal surface of interest to mathematicians. CRCategoriesandSubjectDescriptors: I.3.3 [ComputerGraph ics]: Picture/Image Generation  Display algorithms
Simplifying Surfaces with Color and Texture using Quadric Error Metrics
, 1998
"... There are a variety of application areas in which there is a need for simplifying complex polygonal surface models. These models often have material properties such as colors, textures, and surface normals. Our surface simplification algorithm, based on iterative edge contraction and quadric error m ..."
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Cited by 167 (2 self)
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There are a variety of application areas in which there is a need for simplifying complex polygonal surface models. These models often have material properties such as colors, textures, and surface normals. Our surface simplification algorithm, based on iterative edge contraction and quadric error metrics, can rapidly produce high quality approximations of such models. We present a natural extension of our original error metric that can account for a wide range of vertex attributes. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modelingsurface and object representations Keywords: surface simplification, multiresolution modeling, level of detail, quadric error metric, edge contraction, surface properties, discontinuity preservation 1 INTRODUCTION Many applications in computer graphics and visualization can benefit from automatic simplification of complex polygonal models. Such models are usually not only geometrically complex, but they may also have ...
FreeForm Shape Design Using Triangulated Surfaces
, 1994
"... We present an approach to modeling with truly mutable yet completely controllable freeform surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a ..."
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Cited by 153 (0 self)
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We present an approach to modeling with truly mutable yet completely controllable freeform surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a constrained shape optimization, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying many patchbased approaches. Triangulated point sets are used to approximate these smooth variational surfaces, bridging the gap between patchbased and particlebased representations. Automatic refinement, mesh smoothing, and retriangulation maintain a good computational mesh as the surface shape evolves, and give sample points and surface features much of the freedom to slide around in the surface that oriented particles enjoy. The resulting surface triangulations are constructed and maintained in real time. 1 Introduction ...
Extended gaussian images
 Proceedings of the IEEE
, 1984
"... This is a primer on extended Gaussian Images. Extended Gaussian Images are useful for representing the shapes of surfaces. They can be computed easily from: 1. Needle maps obtained using photometric stereo, or 2. Depth maps generated by ranging devices or stereo. Importantly, they can also be determ ..."
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Cited by 148 (3 self)
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This is a primer on extended Gaussian Images. Extended Gaussian Images are useful for representing the shapes of surfaces. They can be computed easily from: 1. Needle maps obtained using photometric stereo, or 2. Depth maps generated by ranging devices or stereo. Importantly, they can also be determined simply from geometric models of the objects. Extended Gaussian images can be of use in at least two of the tasks facing a machine vision system.
(MIT AI Memo 740)
Computing Local Surface Orientation and Shape from Texture for Curved Surfaces
, 1997
"... Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the `texture distortion' from the image, and (b) Interpreting the `texture distortion' to infer the orientation and shape of the surface in the scene. We model the texture distortion f ..."
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Cited by 87 (4 self)
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Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the `texture distortion' from the image, and (b) Interpreting the `texture distortion' to infer the orientation and shape of the surface in the scene. We model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters. We have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis. One need not explicitly identify texels or make restrictive assumptions about the nature of the texture such as isotropy. We use nonlinear minimization of a least squares error criterion to recover the surface orientation (slant and tilt) and shape (principal curvatures and directions) based on the estimated affine transforms in a number of different directions. A simple linear algorithm based on singular value decomposition of the linear parts of the affine transforms provides the initial guess for the minimization procedure. Experimental results on both planar and curved surfaces under perspective projection demonstrate good estimates for both orientation and shape. A sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture.
Dynamics of TCP/RED and a Scalable Control
 IN PROCEEDINGS OF IEEE INFOCOM 2002
, 2002
"... We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise traffic. We develop a general multilink multisource model for TCP/RED and derive a local stability condition in the case of a single link with ..."
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Cited by 76 (11 self)
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We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise traffic. We develop a general multilink multisource model for TCP/RED and derive a local stability condition in the case of a single link with heterogeneous sources. We validate our model with simulations and illustrate the stability region of TCP/RED. These results suggest that TCP/RED becomes unstable when delay increases, or more strikingly, when link capacity increases. The analysis illustrates the difficulty of setting RED parameters to stabilize TCP: they can be tuned to improve stability, but only at the cost of large queues even when they are dynamically adjusted. Finally, we present a simple distributed congestion control algorithm that maintains stability for arbitrary network delay, capacity, load and topology.
Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation
, 2000
"... We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P #R 3 . Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The spe ..."
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Cited by 73 (5 self)
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We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P #R 3 . Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The speed of our algorithm is derived from a projectionbased approach we use to determine the incident faces on a point. We define our sampling criteria to sample the surface and guarantee a topologically correct mesh after surface reconstruction for such a sampled surface. We also present a new algorithm to find the normal at a vertex, when the surface is sampled according our given criteria. We also present results of our surface reconstruction using our algorithm on unorganized point clouds of various models. 1. Introduction The problem of surface reconstruction from unorganized point clouds has been, and continues to be, an important topic of research. The problem can be loosely stated ...
Computing Minimum Length Paths of a Given Homotopy Class
 Comput. Geom. Theory Appl
, 1991
"... In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides reveal ..."
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Cited by 73 (7 self)
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In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides revealing connections between the minimum paths under these three distance functions, the framework provided by the universal cover leads to simplified lineartime algorithms for shortest path trees, for minimumlink paths in simple polygons, and for paths restricted to c given orientations. 1 Introduction If a wire, a pipe, or a robot must traverse a path among obstacles in the plane, then one might ask what is the best route to take. For the wire, perhaps the shortest distance is best; for the pipe, perhaps the fewest straightline segments. For the robot, either might be best depending on the relative costs of turning and moving. In this paper, we find shortest paths and shortest closed curve...
Shape From Texture for Smooth Curved Surfaces in Perspective Projection
 Journal of Mathematical Imaging and Vision
, 1992
"... Projective distortion of surface texture observed in a perspective image can provide direct information about the shape of the underlying surface. Previous theories have generally concerned planar surfaces; in this paper we present a systematic analysis of first and secondorder texture distortion ..."
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Cited by 48 (6 self)
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Projective distortion of surface texture observed in a perspective image can provide direct information about the shape of the underlying surface. Previous theories have generally concerned planar surfaces; in this paper we present a systematic analysis of first and secondorder texture distortion cues for the case of a smooth curved surface. In particular, we analyze several kinds of texture gradients and relate them to surface orientation and surface curvature. The local estimates obtained from these cues can be integrated to obtain a global surface shape, and we show that the two surfaces resulting from the wellknown tilt ambiguity in the local foreshortening cue typically have qualitatively different shapes. As an example of a practical application of the analysis, a shape from texture algorithm based on local orientationselective filtering is described, and some experimental results are shown. i Figure 1: This image of a slanting plane covered with circles illustrates several...