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StructureAware Shape Processing
 EUROGRAPHICS ’13 / MATEU SBERT AND LÁSZLÓ SZIRMAYKALOS
, 2013
"... Shape structure is about the arrangement and relations between shape parts. Structureaware shape processing goes beyond local geometry and low level processing, and analyzes and processes shapes at a high level. It focuses more on the global inter and intra semantic relations among the parts of sha ..."
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Cited by 22 (9 self)
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Shape structure is about the arrangement and relations between shape parts. Structureaware shape processing goes beyond local geometry and low level processing, and analyzes and processes shapes at a high level. It focuses more on the global inter and intra semantic relations among the parts of shape rather than on their local geometry. With recent developments in easy shape acquisition, access to vast repositories of 3D models, and simpletouse desktop fabrication possibilities, the study of structure in shapes has become a central research topic in shape analysis, editing, and modeling. A whole new line of structureaware shape processing algorithms has emerged that base their operation on an attempt to understand such structure in shapes. The algorithms broadly consist of two key phases: an analysis phase, which extracts structural information from input data; and a (smart) processing phase, which utilizes the extracted information for exploration, editing, and synthesis of novel shapes. In this survey paper, we organize, summarize, and present the key concepts and methodological approaches towards efficient structureaware shape processing. We discuss common models of structure, their implementation in terms of mathematical formalism and algorithms, and explain the key principles in the context of a number of stateoftheart approaches. Further, we attempt to list the key open problems and challenges, both at the technical and at the conceptual level, to make it easier for new researchers to better explore and contribute to this topic. Our goal is to both give the practitioner an overview of available structureaware shape processing techniques, as well as identify future research questions in this important, emerging, and fascinating research area.
Pairwise Harmonics for Shape Analysis
"... This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis framework in which the descriptors are based on pairs of ..."
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Cited by 3 (0 self)
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This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis framework in which the descriptors are based on pairs of surface points. Such a pairwise analysis approach leads to a new class of shape descriptors that are more global, discriminative and can effectively capture the variations in the underlying geometry. Specifically, we introduce new shape descriptors based on the isocurves of harmonic functions whose global maximum and minimum occur at the point pair. We show that these shape descriptors can infer shape structures and consistently lead to simpler and more efficient algorithms than the stateoftheart methods for three applications: intrinsic reflectional symmetry axis computation, matching shape extremities, and simultaneous surface segmentation and skeletonization.
Multiscale Symmetry Detection in Scalar Fields by Clustering Contours
"... Fig. 1. Clustering based analysis detects symmetry at different scales in a 3D cryoelectron microscopy image of AMPactivated kinase (EMDB1897). (left) The threefold rotational symmetry is apparent from the volume rendering. (center) Contours are represented as points in a highdimensional shape ..."
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Cited by 2 (0 self)
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Fig. 1. Clustering based analysis detects symmetry at different scales in a 3D cryoelectron microscopy image of AMPactivated kinase (EMDB1897). (left) The threefold rotational symmetry is apparent from the volume rendering. (center) Contours are represented as points in a highdimensional shape descriptor space (illustrated in 2D). Symmetric contours form a cluster in the descriptor space and can be easily identified. Three such clusters are shown in gold, blue, and pink. (right) Three symmetric regions of different sizes, highlighted in gold, blue, and pink, detected by the method. Abstract—The complexity in visualizing volumetric data often limits the scope of direct exploration of scalar fields. Isocontour extraction is a popular method for exploring scalar fields because of its simplicity in presenting features in the data. In this paper, we present a novel representation of contours with the aim of studying the similarity relationship between the contours. The representation maps contours to points in a highdimensional transformationinvariant descriptor space. We leverage the power of this representation to design a clustering based algorithm for detecting symmetric regions in a scalar field. Symmetry detection is a challenging problem because it demands both segmentation of the data and identification of transformation invariant segments. While the former task can be addressed using topological analysis of scalar fields, the latter requires geometry based solutions. Our approach combines the two by utilizing the contour tree for segmenting the data and the descriptor space for determining transformation invariance. We discuss two applications, query driven exploration and asymmetry visualization, that demonstrate the effectiveness of the approach. Index Terms—Scalar field visualization, symmetry detection, contour tree, data exploration. 1
Structuureaware shape processing
"... Shape structure is about the arrangement and relations between shape parts. Structureaware shape processing goes beyond local geometry and low level processing, and analyzes and processes shapes at a high level. It focuses more on the global inter and intra semantic relations among the parts of sha ..."
Abstract
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Shape structure is about the arrangement and relations between shape parts. Structureaware shape processing goes beyond local geometry and low level processing, and analyzes and processes shapes at a high level. It focuses more on the global inter and intra semantic relations among the parts of shape rather than on their local geometry. With recent developments in easy shape acquisition, access to vast repositories of 3D models, and simpletouse desktop fabrication possibilities, the study of structure in shapes has become a central research topic in shape analysis, editing, and modeling. A whole new line of structureaware shape processing algorithms has emerged that base their operation on an attempt to understand such structure in shapes. The algorithms broadly consist of two key phases: an analysis phase, which extracts structural information from input data; and a (smart) processing phase, which utilizes the extracted information for exploration, editing, and synthesis of novel shapes. In this survey paper, we organize, summarize, and present the key concepts and methodological approaches towards efficient structureaware shape processing. We discuss common models of structure, their implementation in terms of mathematical formalism and algorithms, and explain the key principles in the context of a number of stateoftheart approaches. Further, we attempt to list the key open problems and challenges, both at the technical and at the conceptual level, to make it easier for new researchers to better explore and contribute to this topic. Our goal is to both give the practitioner an overview of available structureaware shape processing techniques, as well as identify future research questions in this important, emerging, and fascinating research area.
Characterization of Partial Intrinsic Symmetries
"... Abstract. We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry processing algorithms. Our goal is to compute all “significant ” symmetry information of the shape, ..."
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Abstract. We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry processing algorithms. Our goal is to compute all “significant ” symmetry information of the shape, which we define as rsymmetries, i.e., we report all isometric selfmaps within subsets of the shape that contain at least an intrinsic circle or radius r. By specifying r, the user has direct control over the scale at which symmetry should be detected. Unlike previous techniques, we do not rely on feature points, voting or probabilistic schemes. Rather than that, we bound computational efforts by splitting our algorithm into two phases. The first detects infinitesimal rsymmetries directly using a local differential analysis, and the second performs direct matching for the remaining discrete symmetries. We show that our algorithm can successfully characterize and extract intrinsic symmetries from a number of example shapes.
A LowDimensional Representation for Robust Partial Isometric Correspondences Computation
"... Intrinsic shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency. While global isometric matching is well understood, only a few heuristic solutions are known for partial matching. Pa ..."
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Intrinsic shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency. While global isometric matching is well understood, only a few heuristic solutions are known for partial matching. Partial matching is particularly important for robustness to topological noise, which is a common problem in realworld scanner data. We introduce a new approach to partial isometric matching based on the observation that isometries are fully determined by local information: a map of a single point and its tangent space fixes an isometry. We develop a new representation for partial isometric maps based on equivalence classes of correspondences between pairs of points and their tangentspaces. We apply our approach to register partial point clouds and compare it to the stateoftheart methods, where we obtain significant improvements over global methods for realworld data and stronger guarantees than previous partial matching algorithms. 1
Keywords: Symmetry detection Intrinsic symmetry Skeleton
, 2013
"... tonb e dat metry detection algorithms. In this paper, we leverage recent advances in curve skeleton extraction from point clouds for symmetry detection. Our method exploits the properties noise and missing data, which are typical results of acquisition via 3D capture/scanning devices. Intrinsic sy ..."
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tonb e dat metry detection algorithms. In this paper, we leverage recent advances in curve skeleton extraction from point clouds for symmetry detection. Our method exploits the properties noise and missing data, which are typical results of acquisition via 3D capture/scanning devices. Intrinsic symmetry is defined as a region over a shape that possesses a selfmap that preserves geodesic disto adapt e hes to w imperfect point clouds. The key idea in this paper is to take advantage of cent success on robust curve skeleton extractio imperfect point cloud data [8–12] and transform the symmetry detection problem from an input point cloud to its extracted curve skeleton. Given an imperfect point cloud, we expect curve skeleton extraction to be an easier problem than that of intrinsic symmetry detection since the
SkeletonIntrinsic Symmetrization of Shapes
"... Enhancing the selfsymmetry of a shape is of fundamental aesthetic virtue. In this paper, we are interested in recovering the aesthetics of intrinsic reflection symmetries, where an asymmetric shape is symmetrized while keeping its general pose and perceived dynamics. The key challenge to intrinsic ..."
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Enhancing the selfsymmetry of a shape is of fundamental aesthetic virtue. In this paper, we are interested in recovering the aesthetics of intrinsic reflection symmetries, where an asymmetric shape is symmetrized while keeping its general pose and perceived dynamics. The key challenge to intrinsic symmetrization is that the input shape has only approximate reflection symmetries, possibly far from perfect. The main premise of our work is that curve skeletons provide a concise and effective shape abstraction for analyzing approximate intrinsic symmetries as well as symmetrization. By measuring intrinsic distances over a curve skeleton for symmetry analysis, symmetrizing the skeleton, and then propagating the symmetrization from skeleton to shape, our approach to shape symmetrization is skeletonintrinsic. Specifically, given an input shape and an extracted curve skeleton, we introduce the notion of a backbone as the path in the skeleton graph about which a selfmatching of the input shape is optimal. We define an objective function for the reflective selfmatching and develop an algorithm based on genetic programming to solve the global search problem for the backbone. The extracted backbone then guides the symmetrization of the skeleton, which in turn, guides the symmetrization of the whole shape. We show numerous intrinsic symmetrization results of hand drawn sketches and artistmodeled or reconstructed 3D shapes, as well as several applications of skeletonintrinsic symmetrization of shapes. Beauty is bound up with symmetry Hermann Weyl [Wey83]. 1.
The Catholic University of America
"... Figure 1: Spectral Global Intrinsic Symmetry Invariant Functions (GISIFs) computed on a fivepoint star with rotational symmetries; fi j denotes a GISIF computed using eigenfunctions of the LaplaceBeltrami operator corresponding to repeated eigenvalues i through j (see Eq. 7). We introduce spectral ..."
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Figure 1: Spectral Global Intrinsic Symmetry Invariant Functions (GISIFs) computed on a fivepoint star with rotational symmetries; fi j denotes a GISIF computed using eigenfunctions of the LaplaceBeltrami operator corresponding to repeated eigenvalues i through j (see Eq. 7). We introduce spectral Global Intrinsic Symmetry Invariant Functions (GISIFs), a class of GISIFs obtained via eigendecomposition of the LaplaceBeltrami operator on compact Riemannian manifolds, and provide associated theoretical analysis. We also discretize the spectral GISIFs for 2D manifolds approximated either by triangle meshes or point clouds. In contrast to GISIFs obtained from geodesic distances, our spectral GISIFs are robust to topological changes. Additionally, for symmetry analysis, our spectral GISIFs represent a more expressive and versatile class of functions than the classical Heat Kernel Signatures (HKSs) and Wave Kernel Signatures (WKSs). Finally, using our defined GISIFs on 2D manifolds, we propose a class of symmetryfactored embeddings and distances and apply them to the computation of symmetry orbits and symmetryaware segmentations. 1
Understanding the structure of large, diverse collections of shapes
, 2013
"... Due to recent developments in modeling software and advances in acquisition techniques for 3D geometry, large numbers of shapes have been digitized. Existing datasets include millions of realworld objects, cultural heritage artifacts, scientific and engineering models, all of which capture the worl ..."
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Due to recent developments in modeling software and advances in acquisition techniques for 3D geometry, large numbers of shapes have been digitized. Existing datasets include millions of realworld objects, cultural heritage artifacts, scientific and engineering models, all of which capture the world around us at nano to planetary scales. As large repositories of 3D shape collections continue to grow, understanding the data, especially encoding the intermodel similarity and their variations, is of the utmost importance. In this dissertation we address the challenge of deriving structure from a large, unorganized, and diverse collection of 3D polygonal models. By structure we refer to how objects correspond to each other, how they are segmented into semantic parts, and how the parts deform and change across the models. While previous work has generally dealt with small and relatively homogeneous datasets, in this dissertation we concentrate on diverse and large collections. Our contribution is threefold. First, we present an algorithm for establishing correspondences between pairs of shapes related by a nonuniform deformation. Second, we develop a robust and efficient algorithm for computing perpoint similarities between all shapes in