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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 ..."
Abstract

Cited by 651 (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.
Shape modeling with front propagation: A level set approach
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods ..."
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Cited by 631 (17 self)
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Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and overcomes some of their limitations. Our techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object’s topology is made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian to model propagating solidhiquid interfaces with curvaturedependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a “HamiltonJacob? ’ type equation written for a function in which the interface is a particular level set. A speed term synthesizpd from the image is used to stop the interface in the vicinity of object boundaries. The resulting equation of motion is solved by employing entropysatisfying upwind finite difference schemes. We present a variety of ways of computing evolving front, including narrow bands, reinitializations, and different stopping criteria. The efficacy of the scheme is demonstrated with numerical experiments on some synthesized images and some low contrast medical images. Index Terms Shape modeling, shape recovery, interface motion, level sets, hyperbolic conservation laws, HamiltonJacobi
Mesh optimization
, 1993
"... We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy f ..."
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Cited by 355 (9 self)
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We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).
Piecewise smooth surface reconstruction
, 1994
"... We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of t ..."
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Cited by 270 (13 self)
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We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.
Robust parameter estimation in computer vision
 SIAM Reviews
, 1999
"... Abstract. Estimation techniques in computer vision applications must estimate accurate model parameters despite smallscale noise in the data, occasional largescale measurement errors (outliers), and measurements from multiple populations in the same data set. Increasingly, robust estimation techni ..."
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Cited by 129 (10 self)
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Abstract. Estimation techniques in computer vision applications must estimate accurate model parameters despite smallscale noise in the data, occasional largescale measurement errors (outliers), and measurements from multiple populations in the same data set. Increasingly, robust estimation techniques, some borrowed from the statistics literature and others described in the computer vision literature, have been used in solving these parameter estimation problems. Ideally, these techniques should effectively ignore the outliers and measurements from other populations, treating them as outliers, when estimating the parameters of a single population. Two frequently used techniques are leastmedian of
On Reliable Surface Reconstruction from Multiple Range Images
, 1996
"... This paper addresses the problem of integrating multiple registered 2.5D range images into a single 3D surface model which has topology and geometry consistent with the measurements. Reconstruction of a model of the correct surface topology is the primary goal. Extraction of the correct surface topo ..."
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Cited by 97 (11 self)
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This paper addresses the problem of integrating multiple registered 2.5D range images into a single 3D surface model which has topology and geometry consistent with the measurements. Reconstruction of a model of the correct surface topology is the primary goal. Extraction of the correct surface topology is recognised as a fundamental step in building 3D models. Model optimization can then be performed to fit the data to the desired accuracy with an efficient representation. A novel integration algorithm is presented that is based on local reconstruction of surface topology using operations in 3D space. A new continuous implicit surface function is proposed which merges the connectivity information inherent in the individual sampled range images. This enables the construction of a single triangulated model using a standard method. The algorithm is guaranteed to reconstruct the correct topology of surface features larger than the range image sampling resolution. Reconstruction of triangu...
Representation and Recognition of FreeForm Surfaces
, 1992
"... We introduce a new surface representation for recognizing curved objects. Our approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ..."
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Cited by 52 (6 self)
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We introduce a new surface representation for recognizing curved objects. Our approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ellipsoid, until it fits the surface of the object. We define local regularity constraints that the mesh must satisfy. We then define a canonical mapping between the mesh describing the object and a standard spherical mesh. A surface curvature index that is poseinvariant is stored at every node of the mesh. We use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene. We show how the similarity between reference model and observed data can be evaluated and we show how the pose of the reference object in the observed scene can be easily computed using this representation. We present results on real range images which show that this approach to modelling and recognizing threedimensional objects has three main advantages: First, it is applicable to complex curved surfaces that cannot be handled by conventional techniques. Second, it reduces the recognition problem to the computation of similarity between spherical distributions; in particular, the recognition algorithm does not require any combinatorial search. Finally, even though it is based on a spherical mapping, the approach can handle occlusions and partial views.
Algorithms for reverse engineering boundary representation models
 ComputerAided Design
, 2001
"... Aprocedure for reconstructing solid models of conventional engineering objects from a multipleview, 3D point cloud is described. (Conventional means bounded by simple analytical surfaces, swept surfaces and blends.) Emphasis is put on producing accurate and topologically consistent boundary represe ..."
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Cited by 45 (8 self)
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Aprocedure for reconstructing solid models of conventional engineering objects from a multipleview, 3D point cloud is described. (Conventional means bounded by simple analytical surfaces, swept surfaces and blends.) Emphasis is put on producing accurate and topologically consistent boundary representation models, ready to be used in computer aided design and manufacture. The basic phases of our approach to reverse engineering are summarised, and related computational difficulties are analysed. Four key algorithmic components are presented in more detail: efficiently segmenting point data into regions; creating translational and rotational surfaces with smooth, constrained profiles; creating the topology of Brep models; and finally adding blends. The application of these algorithms in an integrated system is illustrated by means of various examples, including a wellknown reverse engineering benchmark. 1.
Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy
 IEEE TRANS. PATTERN ANAL. MACH. INTELL
, 2001
"... This paper presents methods for the leastsquares fitting of spheres, cylinders, cones, and tori to 3D point data, and their application within a segmentation framework. Leastsquares fitting of surfaces other than planes, even of simple geometric type, has been rarely studied. Our main application ..."
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Cited by 40 (0 self)
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This paper presents methods for the leastsquares fitting of spheres, cylinders, cones, and tori to 3D point data, and their application within a segmentation framework. Leastsquares fitting of surfaces other than planes, even of simple geometric type, has been rarely studied. Our main application areas of this research are reverse engineering of solid models from depthmaps and automated 3D inspection where reliable extraction of these surfaces is essential. Our fitting method has the particular advantage of being robust in the presence of geometric degeneracy, i.e., as the principal curvatures of the surfaces being fitted decrease (or become more equal), the results returned naturally become closer and closer to those surfaces of simpler type, i.e., planes, cylinders, cones, or spheres, which best describe the data. Many other methods diverge because, in such cases, various parameters or their combination become infinite.
A Cognitive Architecture for Artificial Vision
, 1999
"... A new cognitive architecture for artificial vision is proposed. The architecture, aimed at an autonomous intelligent system, is cognitive in the sense that several cognitive hypotheses have been postulated as guidelines for its design. The first one is the existence of a conceptual representation le ..."
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Cited by 40 (17 self)
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A new cognitive architecture for artificial vision is proposed. The architecture, aimed at an autonomous intelligent system, is cognitive in the sense that several cognitive hypotheses have been postulated as guidelines for its design. The first one is the existence of a conceptual representation level between the subsymbolic level, that processes sensory data, and the linguistic level, that describes scenes by means of a highlevel language. The conceptual level plays the role of the interpretation domain for the symbols at the linguistic levels. A second cognitive hypothesis concerns the active role of a focus of attention mechanism in the link between the conceptual and the linguistic level: the exploration process of the perceived scene is driven by linguistic and associative expectations. This link is modeled as a timedelay attractor neural network. Results are reported obtained by an experimental implementation of the architecture.