Results 1  10
of
176
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 106 (18 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.
iWIRES: An analyzeandedit approach to shape manipulation
 ACM SIGGRAPH Trans. Graph
, 2009
"... Figure 1: A complex model (left) consisting of 108 components is analyzed and 250 intelligent wires (in green) are extracted. Editing a few wires induces a new wire configuration (in blue) and leads to the result on the right. Manmade objects are largely dominated by a few typical features that car ..."
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Cited by 88 (25 self)
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Figure 1: A complex model (left) consisting of 108 components is analyzed and 250 intelligent wires (in green) are extracted. Editing a few wires induces a new wire configuration (in blue) and leads to the result on the right. Manmade objects are largely dominated by a few typical features that carry special characteristics and engineered meanings. Stateoftheart deformation tools fall short at preserving such characteristic features and global structure. We introduce iWIRES, a novel approach based on the argument that manmade models can be distilled using a few special 1D wires and their mutual relations. We hypothesize that maintaining the properties of such a small number of wires allows preserving the defining characteristics of the entire object. We introduce an analyzeandedit approach, where prior to editing, we perform a lightweight analysis of the input shape to extract a descriptive set of wires. Analyzing the individual and mutual properties of the wires, and augmenting them with geometric attributes makes them intelligent and ready to be manipulated. Editing the object by modifying the intelligent wires leads to a powerful editing framework that retains the original design intent and object characteristics. We show numerous results of manipulation of manmade shapes using our editing technique.
A Survey on Shape Correspondence
, 2010
"... We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in ..."
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Cited by 75 (8 self)
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We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in the field such as those requiring the correspondence of nonrigid or timevarying surfaces and a recent trend towards semantic shape analysis, of which shape correspondence is one of the central tasks. Establishing a meaningful shape correspondence is a difficult problem since it typically relies on an understanding of the structure of the shapes in question at both a local and global level, and sometimes also the shapes ’ functionality. However, despite its inherent complexity, shape correspondence is a recurrent problem and an essential component in numerous geometry processing applications. In this report, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria which can be used by the reader to objectively compare the methods. We finalize the report by discussing open problems and future perspectives.
Folding meshes: Hierarchical mesh segmentation based on planar symmetry
, 2006
"... Meshes representing real world objects, both artistcreated and scanned, contain a high level of redundancy due to (possibly approximate) planar reflection symmetries, either global or localized to different subregions. An algorithm is presented for detecting such symmetries and segmenting the mes ..."
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Cited by 48 (4 self)
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Meshes representing real world objects, both artistcreated and scanned, contain a high level of redundancy due to (possibly approximate) planar reflection symmetries, either global or localized to different subregions. An algorithm is presented for detecting such symmetries and segmenting the mesh into the symmetric and remaining regions. The method, inspired by techniques in Computer Vision, has foundations in robust statistics and is resilient to structured outliers which are present in the form of the non symmetric regions of the data. Also introduced is an application of the method: the folding tree data structure. The structure encodes the non redundant regions of the original mesh as well as the reflection planes and is created by the recursive application of the detection method. This structure
Curve Skeleton Extraction from Incomplete Point Cloud
, 2009
"... We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of an oriented point set. Specifically, given a subset S of orient ..."
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Cited by 42 (10 self)
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We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of an oriented point set. Specifically, given a subset S of oriented points, we introduce a variational definition for an oriented point that is most rotationally symmetric with respect to S. Our formulation effectively utilizes normal information to compensate for the missing data and leads to robust curve skeleton computation over regions of a shape that are generally cylindrical. We present an iterative algorithm via planar cuts to compute the ROSA of a point cloud. This is complemented by special handling of noncylindrical joint regions to obtain a centered, topologically clean, and complete 1D skeleton. We demonstrate that quality curve skeletons can be extracted from a variety of shapes captured by incomplete point clouds. Finally, we show how our algorithm assists in shape completion under these challenges by developing a skeletondriven point cloud completion scheme.
Full and Partial Symmetries of NonRigid Shapes
 INTERNATIONAL JOURNAL OF COMPUTER VISION
"... Symmetry and selfsimilarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection ..."
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Cited by 42 (11 self)
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Symmetry and selfsimilarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for nonrigid ones: extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we present a generalization of symmetries for nonrigid shapes and a numerical framework for their analysis, addressing the problems of full and partial exact and approximate symmetry detection and classification.
Upright orientation of manmade objects
 ACM Trans. Graphics
, 2008
"... Figure 1: Left: A manmade model with unnatural orientation. Middle: Six orientations obtained by aligning the model into a canonical coordinate frame using Principal Component Analysis. Right: Our method automatically detects the upright orientation of the model from its geometry alone. Humans usua ..."
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Cited by 41 (11 self)
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Figure 1: Left: A manmade model with unnatural orientation. Middle: Six orientations obtained by aligning the model into a canonical coordinate frame using Principal Component Analysis. Right: Our method automatically detects the upright orientation of the model from its geometry alone. Humans usually associate an upright orientation with objects, placing them in a way that they are most commonly seen in our surroundings. While it is an open challenge to recover the functionality of a shape from its geometry alone, this paper shows that it is often possible to infer its upright orientation by analyzing its geometry. Our key idea is to reduce the twodimensional (spherical) orientation space to a small set of orientation candidates using functionalityrelated geometric properties of the object, and then determine the best orientation using an assessment function of several functional geometric attributes defined with respect to each candidate. Specifically we focus on obtaining the upright orientation for manmade objects that typically stand on some flat surface (ground, floor, table, etc.), which include the vast majority of objects in our everyday surroundings. For these types of models orientation candidates can be defined according to static equilibrium. For each candidate, we introduce a set of discriminative attributes linking shape to function. We learn an assessment function of these attributes from a training set using a combination of Random Forest classifier and Support Vector Machine classifier. Experiments demonstrate that our method generalizes well and achieves about 90 % prediction accuracy for both a 10fold crossvalidation over the training set and a validation with an independent test set. 1
Symmetry factored embedding and distance
 ACM Trans. Graph. (Proc. SIGGRAPH
, 2010
"... We introduce the Symmetry Factored Embedding (SFE) and the Symmetry Factored Distance (SFD) as new tools to analyze and represent symmetries in a point set. The SFE provides new coordinates in which symmetry is “factored out, ” and the SFD is the Euclidean distance in that space. These constructions ..."
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Cited by 40 (6 self)
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We introduce the Symmetry Factored Embedding (SFE) and the Symmetry Factored Distance (SFD) as new tools to analyze and represent symmetries in a point set. The SFE provides new coordinates in which symmetry is “factored out, ” and the SFD is the Euclidean distance in that space. These constructions characterize the space of symmetric correspondences between points – i.e., orbits. A key observation is that a set of points in the same orbit appears as a clique in a correspondence graph induced by pairwise similarities. As a result, the problem of finding approximate and partial symmetries in a point set reduces to the problem of measuring connectedness in the correspondence graph, a wellstudied problem for which spectral methods provide a robust solution. We provide methods for computing the SFE and SFD for extrinsic global symmetries and then extend them to consider partial extrinsic and intrinsic cases. During experiments with difficult examples, we find that the proposed methods can characterize symmetries in inputs with noise, missing data, nonrigid deformations, and complex symmetries, without a priori knowledge of the symmetry group. As such, we believe that it provides a useful tool for automatic shape analysis in applications such as segmentation and stationary point detection. 1
Illustrating How Mechanical Assemblies Work
, 2010
"... How things work visualizations use a variety of visual techniques to depict the operation of complex mechanical assemblies. We present an automated approach for generating such visualizations. Starting with a 3D CAD model of an assembly, we first infer the motions of individual parts and the inter ..."
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Cited by 39 (7 self)
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How things work visualizations use a variety of visual techniques to depict the operation of complex mechanical assemblies. We present an automated approach for generating such visualizations. Starting with a 3D CAD model of an assembly, we first infer the motions of individual parts and the interactions between parts based on their geometry and a few user specified constraints. We then use this information to generate visualizations that incorporate motion arrows, frame sequences and animation to convey the causal chain of motions and mechanical interactions between parts. We present results for a wide variety of assemblies.