Results 1  10
of
67
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 78 (9 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.
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 33 (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 24 (6 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.
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 23 (7 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
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
Probabilistic reasoning for assemblybased 3d modeling
 In Proc. SIGGRAPH, ACM
, 2011
"... Assemblybased modeling is a promising approach to broadening the accessibility of 3D modeling. In assemblybased modeling, new models are assembled from shape components extracted from a database. A key challenge in assemblybased modeling is the identification of relevant components to be presente ..."
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Cited by 20 (3 self)
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Assemblybased modeling is a promising approach to broadening the accessibility of 3D modeling. In assemblybased modeling, new models are assembled from shape components extracted from a database. A key challenge in assemblybased modeling is the identification of relevant components to be presented to the user. In this paper, we introduce a probabilistic reasoning approach to this problem. Given a repository of shapes, our approach learns a probabilistic graphical model that encodes semantic and geometric relationships among shape components. The probabilistic model is used to present components that are semantically and stylistically compatible with the 3D model that is being assembled. Our experiments indicate that the probabilistic model increases the relevance of presented components.
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 20 (4 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
The Columbia grasp database
 IEEE Intl. Conf. on Robotics and Automation
, 2009
"... Abstract — Collecting grasp data for learning and benchmarking purposes is very expensive. It would be helpful to have a standard database of graspable objects, along with a set of stable grasps for each object, but no such database exists. In this work we show how to automate the construction of a ..."
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Cited by 18 (6 self)
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Abstract — Collecting grasp data for learning and benchmarking purposes is very expensive. It would be helpful to have a standard database of graspable objects, along with a set of stable grasps for each object, but no such database exists. In this work we show how to automate the construction of a database consisting of several hands, thousands of objects, and hundreds of thousands of grasps. Using this database, we demonstrate a novel grasp planning algorithm that exploits geometric similarity between a 3D model and the objects in the database to synthesize form closure grasps. Our contributions are this algorithm, and the database itself, which we are releasing to the community as a tool for both grasp planning and benchmarking. I.
A Photometric Approach for Estimating Normals and Tangents
"... This paper presents a technique for acquiring the shape of realworld objects with complex isotropic and anisotropic reflectance. Our method estimates the local normal and tangent vectors at each pixel in a reference view from a sequence of images taken under varying point lighting. We show that for ..."
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Cited by 16 (3 self)
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This paper presents a technique for acquiring the shape of realworld objects with complex isotropic and anisotropic reflectance. Our method estimates the local normal and tangent vectors at each pixel in a reference view from a sequence of images taken under varying point lighting. We show that for many realworld materials and a restricted set of light positions, the 2D slice of the BRDF obtained by fixing the local view direction is symmetric under reflections of the halfway vector across the normaltangent and normalbinormal planes. Based on this analysis, we develop an optimization that estimates the local surface frame by identifying these planes of symmetry in the measured BRDF. As with other photometric methods, a key benefit of our approach is that the input is easy to acquire and is less sensitive to calibration errors than stereo or multiview techniques. Unlike prior work, our approach allows estimating the surface tangent in the case of anisotropic reflectance. We confirm the accuracy and reliability of our approach with analytic and measured data, present several normal and tangent fields acquired with our technique, and demonstrate applications to appearance editing.
Paneling Architectural Freeform Surfaces
"... The emergence of largescale freeform shapes in architecture poses big challenges to the fabrication of such structures. A key problem is the approximation of the design surface by a union of patches, socalled panels, that can be manufactured with a selected technology at reasonable cost, while meet ..."
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Cited by 15 (8 self)
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The emergence of largescale freeform shapes in architecture poses big challenges to the fabrication of such structures. A key problem is the approximation of the design surface by a union of patches, socalled panels, that can be manufactured with a selected technology at reasonable cost, while meeting the design intent and achieving the desired aesthetic quality of panel layout and surface smoothness. The production of curved panels is mostly based on molds. Since the cost of mold fabrication often dominates the panel cost, there is strong incentive to use the same mold for multiple panels. We cast the major practical requirements for architectural surface paneling, including mold reuse, into a global optimization framework that interleaves discrete and continuous optimization steps to minimize production cost while meeting userspecified quality constraints. The search space for optimization is mainly generated through controlled deviation from the design surface and tolerances on positional and normal continuity between neighboring panels. A novel 6dimensional metric space allows us to quickly compute approximate interpanel distances, which dramatically improves the performance of the optimization and enables the handling of complex arrangements with thousands of panels. The practical relevance of our system is demonstrated by paneling solutions for real, cuttingedge architectural freeform design projects.