Results 1  10
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14
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
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Cited by 480 (6 self)
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A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subsetsubset matching. A leastsquares technique is used to estimate 3D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
Hierarchical Face Clustering on Polygonal Surfaces
, 2001
"... Many graphics applications, and interactive systems in particular, rely on hierarchical surface representations to efficiently process very complex models. Considerable attention has been focused on hierarchies of surface approximations and their construction via automatic surface simpliﬁcati ..."
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Cited by 125 (1 self)
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Many graphics applications, and interactive systems in particular, rely on hierarchical surface representations to efficiently process very complex models. Considerable attention has been focused on hierarchies of surface approximations and their construction via automatic surface simpliﬁcation. Such representations have proven effective for adapting the level of detail used in real time display systems. However, other applications such as raytracing, collision detection, and radiosity benefit from an alternative multiresolution framework: hierarchical partitions of the original surface geometry. We present a new method for representing a hierarchy of regions on a polygonal surface which partition that surface into a set of face clusters. These clusters, which are connected sets of faces, represent the aggregate properties of the original surface a different scales rather than providing geometric approximations of varying complexity. We also describe the combination of an effective error metric and a novel algorithm for constructing these hierarchies.
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.
Faithful LeastSquares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation
 PROC. 5TH EUROPEAN CONF. COMPUTER VISION
, 1998
"... This paper addresses a problem arising in the reverse engineering of solid models from depthmaps. We wish to identify and fit surfaces of known type wherever these are a good fit. This paper presents a set of methods for the leastsquares fitting of spheres, cylinders, cones and tori to threed ..."
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Cited by 37 (7 self)
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This paper addresses a problem arising in the reverse engineering of solid models from depthmaps. We wish to identify and fit surfaces of known type wherever these are a good fit. This paper presents a set of methods for the leastsquares fitting of spheres, cylinders, cones and tori to threedimensional point data. Leastsquares fitting of surfaces other planes, even of simple geometric type, has been little studied. Our method
A Comparison of Local Surface Geometry Estimation Methods
, 1997
"... . The performance of several methods for estimating local surface geometry (the principal frame plus the principal quadric) are examined by applying them to a suite of synthetic and real test data which have been corrupted by various amounts of additive Gaussian noise. Methods considered include fin ..."
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Cited by 24 (3 self)
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. The performance of several methods for estimating local surface geometry (the principal frame plus the principal quadric) are examined by applying them to a suite of synthetic and real test data which have been corrupted by various amounts of additive Gaussian noise. Methods considered include finite differences, a facet based approach, and quadric surface fitting. The nonlinear quadric fitting method considered was found to perform the best but has the greatest computational cost. The facet based approach works as well as the other quadric fitting methods and has a much smaller computational cost. Hence it is the recommended method to use in practice. Key words: Principal quadric  Geometry  Estimation  Evaluation 1 Introduction This paper presents a comparative analysis of several techniques for determining the local surface geometry of smooth surfaces from 3D scanner data. That is, techniques for determining the principal frame and principal quadric at a point on a smooth s...
Geometric leastsquares fitting of spheres, cylinders, cones and tori
, 1997
"... This paper considers a problem arising in the reverse engineering of boundary representation solid models from threedimensional depth maps of scanned objects. In particular, we wish to identify and fit surfaces of known type wherever these are a good fit, and we briefly outline a segmentation strat ..."
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Cited by 9 (0 self)
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This paper considers a problem arising in the reverse engineering of boundary representation solid models from threedimensional depth maps of scanned objects. In particular, we wish to identify and fit surfaces of known type wherever these are a good fit, and we briefly outline a segmentation strategy for deciding to which surface type the depth points should be assigned. The particular contributions of this paper are methods for the leastsquares fitting of spheres, cylinders, cones and tori to threedimensional data. While plane fitting is well understood, leastsquares fitting of other surfaces, even of such simple geometric type, has been much less studied; we review previous approaches to the fitting of such surfaces. Our method has the particular advantage of being robust in the sense that as the principal curvatures of the surfaces being fitted decrease (or become more equal), the results which are returned naturally become closer and closer to the surfaces of “simpler type”, i.e. planes, cylinders, or cones (or spheres) which best describe the data, unlike other methods which may diverge as various parameters or their combination become infinite. Keywords. Nonlinear least squares. Geometric distance. Cylinder, cone, sphere, torus, surface fitting. 1
3D Reconstruction of the Human Jaw from A Sequence of Images
, 1997
"... A novel approach is proposed to obtain a record of the patient's occlusion using computer vision. Data acquisition is obtained using intraoral video cameras. The technique utilizes shape from shading to extract 3D information from 2D views of the jaw, and a novel technique for 3D data registration ..."
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Cited by 8 (7 self)
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A novel approach is proposed to obtain a record of the patient's occlusion using computer vision. Data acquisition is obtained using intraoral video cameras. The technique utilizes shape from shading to extract 3D information from 2D views of the jaw, and a novel technique for 3D data registration using genetic algorithms. The resulting 3D model can be used for diagnosis, treatment planning, and implant purposes. The overall purpose of this research is to develop a modelbased vision system for orthodontics to replace traditional approaches. This system will be flexible, accurate, and will reduce the cost of orthodontic treatments. KeywordsImage Sequence Analysis, Shape Representation, Registration. I. Introduction O RTHODONTIC treatment involves the application of force systems to teeth over time to correct malocclusions. In order to evaluate tooth movement progress, the orthodontist monitors this movement by means of visual inspection, intraoral measurements, fabrication of p...
An mrf and gaussian curvature based shape representation for shapematching
 In CVPR
, 2007
"... Matching and registration of shapes is a key issue in Computer Vision, Pattern Recognition, and Medical Image Analysis. This paper presents a shape representation framework based on Gaussian curvature and Markov random fields (MRFs) for the purpose of shape matching. The method is based on a surface ..."
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Cited by 5 (0 self)
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Matching and registration of shapes is a key issue in Computer Vision, Pattern Recognition, and Medical Image Analysis. This paper presents a shape representation framework based on Gaussian curvature and Markov random fields (MRFs) for the purpose of shape matching. The method is based on a surface mesh model in R3, which is projected into a twodimensional space and there modeled as an extended boundary closed Markov random field. The surface is homeomorphic to S2. The MRF encodes in the nodes entropy features of the corresponding similarities based on Gaussian curvature, and in the edges the spatial consistency of the meshes. Correspondence between two surface meshes is then established by performing probabilistic inference on the MRF via Gibbs sampling. The technique combines both geometric, topological, and probabilistic information, which can be used to represent shapes in three dimensional space, and can be generalized to higher dimensional spaces. As a result, the representation can be used for shape matching, registration, and statistical shape analysis.
Least Squares Fitting of Parametric Surfaces to Measured Data
, 2000
"... The problem is considered of tting surfaces to measured data using the least squares norm, where it is assumed that a parameterization of the surface is available. Examples of practical applications include the product design and quality assurance of manufactured parts. There has been much recen ..."
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Cited by 4 (2 self)
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The problem is considered of tting surfaces to measured data using the least squares norm, where it is assumed that a parameterization of the surface is available. Examples of practical applications include the product design and quality assurance of manufactured parts. There has been much recent algorithmic development based on conventional tting ideas, mainly orthogonal distance regression. A dierent approach is taken here which explicitly takes account of the measurement process, and this is illustrated by some examples. 1 Introduction Let m points x i ; i = 1; : : : ; m in IR 3 be obtained by sampling the surface of a manufactured part. Then the problem considered here is that of determining a model part (or equivalently a set of parameters dening the model part) which best ts those data. This kind of problem is a fundamental problem in metrology, where it is required to assess a manufactured part using data gathered by a coordinate measuring system. 1 Let a point...
Estimation of error in curvature computation on multiscale freeform surfaces
 Int. J. Comput. Vision
"... Abstract. A novel technique for multiscale curvature computation on a freeform 3D surface is presented. This is achieved by convolving local parametrisations of the surface with 2D Gaussian filters iteratively. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh ..."
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Cited by 3 (0 self)
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Abstract. A novel technique for multiscale curvature computation on a freeform 3D surface is presented. This is achieved by convolving local parametrisations of the surface with 2D Gaussian filters iteratively. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh. Smoothing results are shown for 3D surfaces with different shapes indicating that surface noise is eliminated and surface details are removed gradually. A number of evolution properties of 3D surfaces are described. Next, the surface Gaussian and mean curvature values are estimated accurately at multiple scales which are then mapped to colours and displayed directly on the surface. The performance of the technique when selecting different directions as an arbitrary direction for the geodesic at each vertex are also presented. The results indicate that the error observed for the estimation of Gaussian and mean curvatures is quite low after only one iteration. Furthermore, as the surface is smoothed iteratively, the error is further reduced. The results also show that the estimation error of Gaussian curvature is less than that of mean curvature. Our experiments demonstrate that estimation of smoothed surface curvatures are very accurate and not affected by the arbitrary direction of the first geodesic line when constructing semigeodesic coordinates. Our technique is independent of the underlying triangulation and is also more efficient than volumetric diffusion techniques since 2D rather than 3D convolutions are employed. Finally, the method presented here is a generalisation of the Curvature Scale Space method for 2D contours. The CSS method has outperformed comparable techniques