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148
Skeleton Based Shape Matching and Retrieval
, 2003
"... In this paper, we describe a novel method for searching and comparing 3D objects. The method encodes the geometric and topological information in the form of a skeletal graph and uses graph matching techniques to match the skeletons and to compare them. The skeletal graphs can be manually annotated ..."
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Cited by 98 (1 self)
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In this paper, we describe a novel method for searching and comparing 3D objects. The method encodes the geometric and topological information in the form of a skeletal graph and uses graph matching techniques to match the skeletons and to compare them. The skeletal graphs can be manually annotated to refine or restructure the search. This helps in choosing between a topological similarity and a geometric (shape) similarity. A feature of skeletal matching is the ability to perform partmatching, and its inherent intuitiveness, which helps in defining the search and in visualizing the results. Also, the matching results, which are presented in a pernode basis can be used for driving a number of registration algorithms, most of which require a good initial guess to perform registration. In this paper, we also describe a visualization tool to aid in the selection and specification of the matched objects.
An autonomous mobile robot with a 3D laser range finder for 3D exploration and digitalization of indoor environments
, 2003
"... Digital 3D models of the environment are needed in rescue and inspection robotics, facility managements and architecture. This paper presents an automatic system for gaging and digitalization of 3D indoor environments. It consists of an autonomous mobile robot, a reliable 3D laser range finder and t ..."
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Cited by 86 (22 self)
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Digital 3D models of the environment are needed in rescue and inspection robotics, facility managements and architecture. This paper presents an automatic system for gaging and digitalization of 3D indoor environments. It consists of an autonomous mobile robot, a reliable 3D laser range finder and three elaborated software modules. The first module, a fast variant of the Iterative Closest Points algorithm, registers the 3D scans in a common coordinate system and relocalizes the robot. The second module, a next best view planner, computes the next nominal pose based on the acquired 3D data while avoiding complicated obstacles. The third module, a closedloop and globally stable motor controller, navigates the mobile robot to a nominal pose on the base of odometry and avoids collisions with dynamical obstacles. The 3D laser range finder acquires a 3D scan at this pose. The proposed method allows one to digitalize large indoor environments fast and reliably without any intervention and solves the SLAM problem. The results of two 3D digitalization experiments are presented using a fast octreebased visualization method.
Curveskeleton properties, applications, and algorithms
 IEEE Transactions on Visualization and Computer Graphics
, 2007
"... Curveskeletons are thinned 1D representations of 3D objects useful for many visualization tasks including virtual navigation, reducedmodel formulation, visualization improvement, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applicati ..."
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Cited by 66 (3 self)
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Curveskeletons are thinned 1D representations of 3D objects useful for many visualization tasks including virtual navigation, reducedmodel formulation, visualization improvement, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are. In this paper, we provide an overview of many curveskeleton applications and compile a set of desired properties of such representations. We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms.
Poseoblivious shape signature
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 13
, 2007
"... A 3D shape signature is a compact representation for some essence of a shape. Shape signatures are commonly utilized as a fast indexing mechanism for shape retrieval. Effective shape signatures capture some global geometric properties which are scale, translation, and rotation invariant. In this pa ..."
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Cited by 62 (3 self)
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A 3D shape signature is a compact representation for some essence of a shape. Shape signatures are commonly utilized as a fast indexing mechanism for shape retrieval. Effective shape signatures capture some global geometric properties which are scale, translation, and rotation invariant. In this paper, we introduce an effective shape signature which is also poseoblivious. This means that the signature is also insensitive to transformations which change the pose of a 3D shape such as skeletal articulations. Although some topologybased matching methods can be considered poseoblivious as well, our new signature retains the simplicity and speed of signature indexing. Moreover, contrary to topologybased methods, the new signature is also insensitive to the topology change of the shape, allowing us to match similar shapes with different genus. Our shape signature is a 2D histogram which is a combination of the distribution of two scalar functions defined on the boundary surface of the 3D shape. The first is a definition of a novel function called the localdiameter function. This function measures the diameter of the 3D shape in the neighborhood of each vertex. The histogram of this function is an informative measure of the shape which is insensitive to pose changes. The second is the centricity function that measures the average geodesic distance from one vertex to all other vertices on the mesh. We evaluate and compare a number of methods for measuring the similarity between two signatures, and demonstrate the effectiveness of our poseoblivious shape signature within a 3D search engine application for different databases containing hundreds of models.
Feature Extraction from Point Clouds
 In Proceedings of the 10 th International Meshing Roundtable
, 2001
"... This paper describes a new method to extract feature lines directly from a surface point cloud. No surface reconstruction is needed in advance, only the inexpensive computation of a neighbor graph connecting nearby points. ..."
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Cited by 55 (0 self)
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This paper describes a new method to extract feature lines directly from a surface point cloud. No surface reconstruction is needed in advance, only the inexpensive computation of a neighbor graph connecting nearby points.
Delaunay triangulation based surface reconstruction: Ideas and algorithms
 EFFECTIVE COMPUTATIONAL GEOMETRY FOR CURVES AND SURFACES
, 2006
"... ..."
A Globally Optimal Algorithm for Robust TVL 1 Range Image Integration
"... Robust integration of range images is an important task for building highquality 3D models. Since range images, and in particular range maps from stereo vision, may have a substantial amount of outliers, any integration approach aiming at highquality models needs an increased level of robustness. ..."
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Cited by 47 (8 self)
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Robust integration of range images is an important task for building highquality 3D models. Since range images, and in particular range maps from stereo vision, may have a substantial amount of outliers, any integration approach aiming at highquality models needs an increased level of robustness. Additionally, a certain level of regularization is required to obtain smooth surfaces. Computational efficiency and global convergence are further preferable properties. The contribution of this paper is a unified framework to solve all these issues. Our method is based on minimizing an energy functional consisting of a total variation (TV) regularization force and an L 1 data fidelity term. We present a novel and efficient numerical scheme, which combines the duality principle for the TV term with a pointwise optimization step. We demonstrate the superior performance of our algorithm on the wellknown Middlebury multiview database and additionally on realworld multiview images. 1.
Efficient computation of a simplified medial axis
 Proc. of ACM Solid Modeling
, 2003
"... Applications of of the medial axis have been limited because of its instability and algebraic complexity. In this paper, we use a simplification of the medial axis, the θSMA, that is parameterized by a separation angle (θ) formed by the vectors connecting a point on the medial axis to the closest p ..."
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Cited by 44 (3 self)
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Applications of of the medial axis have been limited because of its instability and algebraic complexity. In this paper, we use a simplification of the medial axis, the θSMA, that is parameterized by a separation angle (θ) formed by the vectors connecting a point on the medial axis to the closest points on the boundary. We present a formal characterization of the degree of simplification of the θSMA as a function of θ, and we quantify the degree to which the simplified medial axis retains the features of the original polyhedron. We present a fast algorithm to compute an approximation of the θSMA. It is based on a spatial subdivision scheme, and uses fast computation of a distance field and its gradient using graphics hardware. The complexity of the algorithm varies based on the error threshold that is used, and is a linear function of the input size. We have applied this algorithm to approximate the SMA of models with tens or hundreds of thousands of triangles. Its running time varies from a few seconds, for a model consisting of hundreds of triangles, to minutes for highly complex models.
SmoothSurface Reconstruction in Near Linear Time
, 2001
"... A surface reconstruction algorithm takes as input a set of sample points from an unknown closed and smooth surface in 3d space, and produces a piecewise linear approximation of the surface that contains the sample points. Variants of this problem have received considerable attention in computer ..."
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Cited by 42 (6 self)
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A surface reconstruction algorithm takes as input a set of sample points from an unknown closed and smooth surface in 3d space, and produces a piecewise linear approximation of the surface that contains the sample points. Variants of this problem have received considerable attention in computer vision and computer graphics and more recently in computational geometry. In the latter area, three different algorithms (Amenta and Bern `98, and refined in Amenta, Choi, Dey and Leekha `00; Amenta, Choi and Kolluri `00; Boissonnat and Cazals `00) have been proposed. These algorithms have a correctness guarantee: if the sample is sufficiently dense then the output is a good approximation to the original surface. They have unfortunately a worstcase running time that is quadratic in the size of the input. This is so because they are based on the construction of 3d Voronoi diagrams or Delaunay tetrahedrizations, which can have quadratic size. Even worse, according to recent work (Erickson `01), there are surfaces for which this is the case even when the sample set is "locally uniform" on the surface. In this paper, we describe a new algorithm that also has a correctness guarantee but whose worstcase running time is almost linear. In fact, O(n log n) where n is the input size. As in some of the previous algorithms, the piecewise linear approximation produced by the new algorithm is a subset of the 3d Delaunay tetrahedrization; however, this is obtained by computing only the relevant parts of the 3d Delaunay structure. The algorithm first estimates for each sample point the surface normal and a parameter that is then used to "decimate" the set of samples. The resulting subset of sample points is locally uniform and so a reconstruction based on it can be compu...
Retrieving articulated 3D models using medial surfaces
, 2008
"... We consider the use of medial surfaces to represent symmetries of 3D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this ..."
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Cited by 38 (2 self)
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We consider the use of medial surfaces to represent symmetries of 3D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3D object model retrieval. Our formulation uses the geometric information