Results 1  10
of
12
Discovering Structural Regularity in 3D Geometry
, 2008
"... We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point or meshbased models. Our method assumes no p ..."
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Cited by 81 (10 self)
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We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point or meshbased models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis.
Consistent Segmentation of 3D Models
 Computers 01/04/2010 81 K3D D1.4.1 & Graphics, IEEE SMI 2009 proceedings, (33)3
, 2009
"... This paper proposes a method to segment a set of models consistently. The method simultaneously segments models and creates correspondences between segments. First, a graph is constructed whose nodes represent the faces of every mesh, and whose edges connect adjacent faces within a mesh and correspo ..."
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Cited by 29 (4 self)
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This paper proposes a method to segment a set of models consistently. The method simultaneously segments models and creates correspondences between segments. First, a graph is constructed whose nodes represent the faces of every mesh, and whose edges connect adjacent faces within a mesh and corresponding faces in different meshes. Second, a consistent segmentation is created by clustering this graph, allowing for outlier segments that are not present in every mesh. The method is demonstrated for several classes of objects and used for two applications: symmetric segmentation and segmentation transfer. Key words: Mesh segmentation, Mesh analysis 1.
A Survey on Shape Correspondence
, 2011
"... We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in spacetime registration, where one seeks a correspondence between nonrigid and timevarying surfaces, an ..."
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Cited by 29 (6 self)
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We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in spacetime registration, where one seeks a correspondence between nonrigid and timevarying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult since it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function, and solution approach. We conclude the survey by discussing open problems and future perspectives.
Partial intrinsic reflectional symmetry of 3d shapes
 ACM Transactions on Graphics (TOG
"... Figure 1: Given a closed 2manifold mesh, we compute a scalar field (a), which accentuates the axes of prominent, partial intrinsic reflectional symmetries. The top few (closed) Voronoi boundaries (b) between symmetric point pairs, as induced by the scalar field, can be imperfect. We develop an iter ..."
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Cited by 22 (3 self)
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Figure 1: Given a closed 2manifold mesh, we compute a scalar field (a), which accentuates the axes of prominent, partial intrinsic reflectional symmetries. The top few (closed) Voronoi boundaries (b) between symmetric point pairs, as induced by the scalar field, can be imperfect. We develop an iterative refinement scheme to extract the final set of intrinsic reflectional symmetry axes or IRSAs (c), which can be open curves. Incorporating symmetry cues offered by IRSAs into a conventional mesh segmentation scheme leads to highly semantic results (d). While many 3D objects exhibit various forms of global symmetries, prominent intrinsic symmetries which exist only on parts of an object are also well recognized. Such partial symmetries are often seen as more natural than a global one, even when the symmetric parts are under complex pose. We introduce an algorithm to extract partial intrinsic reflectional symmetries (PIRS) of a 3D shape. Given a closed 2manifold mesh, we develop a voting scheme to obtain an intrinsic reflectional symmetry axis (IRSA) transform, which is a scalar field over the mesh that accentuates prominent IRSAs of the shape. We then extract a set of explicit IRSA curves on the shape based on a refined measure of local reflectional symmetry support along a curve. The iterative refinement procedure combines IRSAinduced region growing and regionconstrained symmetry support refinement to improve accuracy and address potential issues arising from rotational symmetries in the shape. We show how the extracted IRSA curves can be incorporated into a conventional mesh segmentation scheme so that the implied symmetry cues can be utilized to obtain more meaningful results. We also demonstrate the use of IRSA curves for symmetrydriven part repair. 1
Symmetry Hierarchy of ManMade Objects
"... We introduce symmetry hierarchy of manmade objects, a highlevel structural representation of a 3D model providing a symmetryinduced, hierarchical organization of the model’s constituent parts. Given an input mesh, we segment it into primitive parts and build an initial graph which encodes interp ..."
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Cited by 9 (3 self)
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We introduce symmetry hierarchy of manmade objects, a highlevel structural representation of a 3D model providing a symmetryinduced, hierarchical organization of the model’s constituent parts. Given an input mesh, we segment it into primitive parts and build an initial graph which encodes interpart symmetries and connectivity relations, as well as selfsymmetries in individual parts. The symmetry hierarchy is constructed from the initial graph via recursive graph contraction which either groups parts by symmetry or assembles connected sets of parts. The order of graph contraction is dictated by a set of precedence rules designed primarily to respect the law of symmetry in perceptual grouping and the principle of compactness of representation. We show that symmetry hierarchy naturally implies a hierarchical segmentation that is more meaningful than those produced by local geometric considerations. We also develop an application of symmetry hierarchies for structural shape editing. 1.
Prior Knowledge for Part Correspondence
"... Classical approaches to shape correspondence base their computation purely on the properties, in particular geometric similarity, of the shapes in question. Their performance still falls far short of that of humans in challenging cases where corresponding shape parts may differ significantly in geom ..."
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Cited by 8 (2 self)
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Classical approaches to shape correspondence base their computation purely on the properties, in particular geometric similarity, of the shapes in question. Their performance still falls far short of that of humans in challenging cases where corresponding shape parts may differ significantly in geometry or even topology. We stipulate that in these cases, shape correspondence by humans involves recognition of the shape parts where prior knowledge on the parts would play a more dominant role than geometric similarity. We introduce an approach to part correspondence which incorporates prior knowledge imparted by a training set of presegmented, labeled models and combines the knowledge with contentdriven analysis based on geometric similarity between the matched shapes. First, the prior knowledge is learned from the training set in the form of perlabel classifiers. Next, given two query shapes to be matched, we apply the classifiers to assign a probabilistic label to each shape face. Finally, by means of a joint labeling scheme, the probabilistic labels are used synergistically with pairwise assignments derived from geometric similarity to provide the resulting part correspondence. We show that the incorporation of knowledge is especially effective in dealing with shapes exhibiting large intraclass variations. We also show that combining knowledge and content analyses outperforms approaches guided by either attribute alone. 1.
Closedform Blending of Local Symmetries
, 2010
"... We present a closedform solution for the symmetrization problem, solving for the optimal deformation that reconciles aset of local bilateral symmetries.Given as input aset of pointpairs which should be symmetric,we first compute for each local neighborhood a transformation which wouldproduce anapp ..."
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Cited by 3 (0 self)
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We present a closedform solution for the symmetrization problem, solving for the optimal deformation that reconciles aset of local bilateral symmetries.Given as input aset of pointpairs which should be symmetric,we first compute for each local neighborhood a transformation which wouldproduce anapproximate bilateral symmetry. We then solve forasingle global symmetry whichincludes all of these local symmetries,while minimizingthe deformation within each local neighborhood. Our main motivation is the symmetrization of digitized fossils, which areoftendeformedbyacombinationofcompressionandbending. Inaddition, we use the technique tosymmetrize articulated models.
SymmetryGuided Texture Synthesis and Manipulation
"... This paper presents a framework for symmetryguided texture synthesis and processing. It is motivated by the longstanding problem of how to optimize, transfer, and control the spatial patterns in textures. The key idea is that symmetry representations that measure autocorrelations with respect to a ..."
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Cited by 3 (2 self)
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This paper presents a framework for symmetryguided texture synthesis and processing. It is motivated by the longstanding problem of how to optimize, transfer, and control the spatial patterns in textures. The key idea is that symmetry representations that measure autocorrelations with respect to all transformations of a group are a natural way to describe spatial patterns in many realworld textures. To leverage this idea, we provide methods to transfer symmetry representations from one texture to another, process the symmetries of a texture, and optimize textures with respect to properties of their symmetry representations. These methods are automatic and robust, as they don’t require explicit detection of discrete symmetries. Applications are investigated for optimizing, processing and transferring symmetries and textures.
M.: Case studies in costoptimized paneling of architectural freeform surfaces
 Advances in Architectural Geometry 2010
, 2010
"... Paneling an architectural freeform surface refers to an approximation of the design surface by a set of panels that can be manufactured using a selected technology at a reasonable cost, while respecting the design intent and achieving the desired aesthetic quality of panel layout and surface smoothn ..."
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Cited by 2 (1 self)
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Paneling an architectural freeform surface refers to an approximation of the design surface by a set of panels that can be manufactured using a selected technology at a reasonable cost, while respecting the design intent and achieving the desired aesthetic quality of panel layout and surface smoothness. Eigensatz and coworkers [Eigensatz et al. 2010] have recently introduced a computational solution to the paneling problem that allows handling largescale freeform surfaces involving complex arrangements of thousands of panels. We extend this paneling algorithm to facilitate effective design exploration, in particular for local control of tolerance margins and the handling of sharp crease lines. We focus on the practical aspects relevant for the realization of largescale freeform designs and evaluate the performance of the paneling algorithm with a number of case studies. Eigensatz et al. reference surface panelized surface plane cylinder paraboloid torus cubic mold types Figure 1: Given a reference surface (top row), the paneling algorithm produces a rationalization of the the input. The paneling solution (middle row) employs a small set of molds that can be reused for costeffective panel production (bottom row), while preserving surface smoothness and respecting the original design intent. The shown metal paneling solution is 40 % cheaper than the production alternative of using custom molds for each individual panel. Figure 11 presents a variety of solutions that achieve cost savings of up to 60%. Figure 4 lists the metal cost ratios used. Case Studies in CostOptimized Paneling of Architectural Freeform Surfaces 1
Symmetry in Scalar Field Topology
"... Fig. 1. Symmetric patterns identified using contour trees in electron microscopy data of RuBisCO molecule in complex with RuBisCO large subunit methyltransferase (EMDB 1734). (a) Volume rendering of the molecule highlighting repeating structures in the scalar field. (b) Four different types of regio ..."
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Cited by 2 (2 self)
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Fig. 1. Symmetric patterns identified using contour trees in electron microscopy data of RuBisCO molecule in complex with RuBisCO large subunit methyltransferase (EMDB 1734). (a) Volume rendering of the molecule highlighting repeating structures in the scalar field. (b) Four different types of regions, indicative of the different subunits in the molecule, identified by the symmetry detection algorithm shown in cyan, magenta, brown, and violet. Regions with the same color are symmetric with respect to the scalar field distribution. (c) Subtrees of the contour tree are classified into different groups based on similarity. Subtrees belonging to a common group are shown with the same color and the corresponding regions are identified to be symmetric. Abstract — Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetryaware transfer function design and symmetryaware isosurface extraction. Index Terms—Scalar field symmetry, contour tree, similarity measure, persistence, isosurface extraction, transfer function design. 1