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126
Partial and approximate symmetry detection for 3D geometry
 ACM TRANSACTIONS ON GRAPHICS
, 2006
"... “Symmetry is a complexityreducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and manmade objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a com ..."
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Cited by 112 (17 self)
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“Symmetry is a complexityreducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and manmade objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries. These symmetries can be partial, approximate, or both. The method is based on matching simple local shape signatures in pairs and using these matches to accumulate evidence for symmetries in an appropriate transformation space. A clustering stage extracts potential significant symmetries of the object, followed by a verification step. Based on a statistical sampling analysis, we provide theoretical guarantees on the success rate of our algorithm. The extracted symmetry graph representation captures important highlevel information about the structure of a geometric model which in turn enables a large set of further processing operations, including shape compression, segmentation, consistent editing, symmetrization, indexing for retrieval, etc.
Salient geometric features for partial shape matching and similarity
 jTOG
"... This article introduces a method for partial matching of surfaces represented by triangular meshes. Our method matches surface regions that are numerically and topologically dissimilar, but approximately similar regions. We introduce novel local surface descriptors which efficiently represent the ge ..."
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Cited by 111 (4 self)
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This article introduces a method for partial matching of surfaces represented by triangular meshes. Our method matches surface regions that are numerically and topologically dissimilar, but approximately similar regions. We introduce novel local surface descriptors which efficiently represent the geometry of local regions of the surface. The descriptors are defined independently of the underlying triangulation, and form a compatible representation that allows matching of surfaces with different triangulations. To cope with the combinatorial complexity of partial matching of large meshes, we introduce the abstraction of salient geometric features and present a method to construct them. A salient geometric feature is a compound highlevel feature of nontrivial local shapes. We show that a relatively small number of such salient geometric features characterizes the surface well for various similarity applications. Matching salient geometric features is based on indexing rotationinvariant features and a voting scheme accelerated by geometric hashing. We demonstrate the effectiveness of our method with a number of applications, such as computing selfsimilarity, alignments, and subparts similarity.
Recent advances in compression of 3D meshes
 In Advances in Multiresolution for Geometric Modelling
, 2003
"... Summary. 3D meshes are widely used in graphic and simulation applications for approximating 3D objects. When representing complex shapes in a raw data format, meshes consume a large amount of space. Applications calling for compact storage and fast transmission of 3D meshes have motivated the multit ..."
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Cited by 70 (3 self)
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Summary. 3D meshes are widely used in graphic and simulation applications for approximating 3D objects. When representing complex shapes in a raw data format, meshes consume a large amount of space. Applications calling for compact storage and fast transmission of 3D meshes have motivated the multitude of algorithms developed to efficiently compress these datasets. In this paper we survey recent developments in compression of 3D surface meshes. We survey the main ideas and intuition behind techniques for singlerate and progressive mesh coding. Where possible, we discuss the theoretical results obtained for asymptotic behavior or optimality of the approach. We also list some open questions and directions for future research. 1
Hierarchical mesh segmentation based on fitting primitives
 THE VISUAL COMPUTER
, 2006
"... In this paper we describe a hierarchical face clustering algorithm for triangle meshes based on fitting primitives belonging to an arbitrary set. The method proposed is completely automatic, and generates a binary tree of clusters, each of which fitted by one of the primitives employed. Initially, e ..."
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Cited by 67 (9 self)
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In this paper we describe a hierarchical face clustering algorithm for triangle meshes based on fitting primitives belonging to an arbitrary set. The method proposed is completely automatic, and generates a binary tree of clusters, each of which fitted by one of the primitives employed. Initially, each triangle represents a single cluster; at every iteration, all the pairs of adjacent clusters are considered, and the one that can be better approximated by one of the primitives forms a new single cluster. The approximation error is evaluated using the same metric for all the primitives, so that it makes sense to choose which is the most suitable primitive to approximate the set of triangles in a cluster. Based on this approach, we implemented a prototype which uses planes, spheres and cylinders, and have experimented that for meshes made of 100k faces, the whole binary tree of clusters can be built in about 8 seconds on a standard PC. The framework here described has natural application in reverse engineering processes, but it has been also tested for surface denosing, feature recovery and character skinning.
Mixedinteger quadrangulation
 ACM Trans. Graph
, 2009
"... the input mesh by some simple heuristic or by the user. (b) In a global optimization procedure a cross field is generated on the mesh which interpolates the given constraints and is as smooth as possible elsewhere. The optimization includes the automatic generation and placement of singularities. (c ..."
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Cited by 50 (9 self)
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the input mesh by some simple heuristic or by the user. (b) In a global optimization procedure a cross field is generated on the mesh which interpolates the given constraints and is as smooth as possible elsewhere. The optimization includes the automatic generation and placement of singularities. (c) A globally smooth parametrization is computed on the surface whose isoparameter lines follow the cross field directions and singularities lie at integer locations. (d) Finally, a consistent, feature aligned quadmesh can be extracted. We present a novel method for quadrangulating a given triangle mesh. After constructing an as smooth as possible symmetric cross field satisfying a sparse set of directional constraints (to capture the geometric structure of the surface), the mesh is cut open in order to enable a low distortion unfolding. Then a seamless globally smooth parametrization is computed whose isoparameter lines follow the cross field directions. In contrast to previous methods, sparsely distributed directional constraints are sufficient to automatically determine the appropriate number, type and position of singularities in the quadrangulation. Both steps of the algorithm (cross field and parametrization) can be formulated as a mixedinteger problem which we solve very efficiently by an adaptive greedy solver. We show several complex examples where high quality quad meshes are generated in a fully automatic manner.
Vector Field Design on Surfaces
 ACM Transactions on Graphics
, 2006
"... Figure 1: This figure shows various vector fields created on surfaces using our vector field design system. The vector field shown at the right was used to guide texture synthesis shown in Figure 12 (right). Vector field design on surfaces is necessary for many graphics applications: examplebased t ..."
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Cited by 45 (15 self)
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Figure 1: This figure shows various vector fields created on surfaces using our vector field design system. The vector field shown at the right was used to guide texture synthesis shown in Figure 12 (right). Vector field design on surfaces is necessary for many graphics applications: examplebased texture synthesis, nonphotorealistic rendering, and fluid simulation. A vector field design system should allow a user to create a large variety of complex vector fields with relatively little effort. In this paper, we present a vector field design system for surfaces that allows the user to control the number of singularities in the vector field and their placement. Our system combines basis vector fields to make an initial vector field that meets the user’s specifications. The initial vector field often contains unwanted singularities. Such singularities cannot always be eliminated, due to the PoincaréHopf index theorem. To reduce the effect caused by these singularities, our system allows a user to move a singularity to a more favorable location or to cancel a pair of singularities. These operations provide topological guarantees for the vector field in that they only affect the userspecified singularities. Other editing operations are also provided so that the user may change the topological and geometric characteristics of the vector field. We demonstrate our vector field design system for several applications: examplebased texture synthesis, painterly rendering of images, and pencil sketch illustrations of smooth surfaces.
Isotropic remeshing of surfaces: A local parameterization approach
 In Proceedings of 12th International Meshing Roundtable
, 2003
"... We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the original mesh geometry. The algorithm has three stages. In the first s ..."
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Cited by 39 (4 self)
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We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the original mesh geometry. The algorithm has three stages. In the first stage the required number or vertices are generated by iterative simplification or refinement. The second stage performs an initial vertex partition using an areabased relaxation method. The third stage achieves precise isotropic vertex sampling prescribed by a given density function on the mesh. We use a modification of Lloyd’s relaxation method to construct a weighted centroidal Voronoi tessellation of the mesh. We apply these iterations locally on small patches of the mesh that are parameterized into the 2D plane. This allows us to handle arbitrary complex meshes with any genus and any number of boundaries. The efficiency and the accuracy of the remeshing process is achieved using a patchwise parameterization technique.
A Bayesian method for probable surface reconstruction and decimation
 ACM TRANS. GRAPH
, 2006
"... We present a Bayesian technique for the reconstruction and subsequent decimation of 3D surface models from noisy sensor data. The method uses oriented probabilistic models of the measurement noise, and combines them with featureenhancing prior probabilities over 3D surfaces. When applied to surface ..."
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Cited by 36 (5 self)
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We present a Bayesian technique for the reconstruction and subsequent decimation of 3D surface models from noisy sensor data. The method uses oriented probabilistic models of the measurement noise, and combines them with featureenhancing prior probabilities over 3D surfaces. When applied to surface reconstruction, the method simultaneously smooths noisy regions while enhancing features, such as corners. When applied to surface decimation, it finds models that closely approximate the original mesh when rendered. The method is applied in the context of computer animation, where it finds decimations that minimize the visual error even under nonrigid deformations.