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82
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 148 (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.
Restricted Delaunay triangulations and normal cycle
 SOCG'03
, 2003
"... We address the problem of curvature estimation from sampled smooth surfaces. Building upon the theory of normal cycles, we derive a definition of the curvature tensor for polyhedral surfaces. This definition consists in a very simple and new formula. When applied to a polyhedral approximation of a s ..."
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Cited by 147 (3 self)
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We address the problem of curvature estimation from sampled smooth surfaces. Building upon the theory of normal cycles, we derive a definition of the curvature tensor for polyhedral surfaces. This definition consists in a very simple and new formula. When applied to a polyhedral approximation of a smooth surface, it yields an efficient and reliable curvature estimation algorithm. Moreover, we bound the difference between the estimated curvature and the one of the smooth surface in the case of restricted Delaunay triangulations.
Estimating differential quantities using polynomial fitting of osculating jets
"... This paper addresses the pointwise estimation of differential properties of a smooth manifold S —a curve in the plane or a surface in 3D — assuming a point cloud sampled over S is provided. The method consists of fitting the local representation of the manifold using a jet, and either interpolation ..."
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Cited by 117 (7 self)
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This paper addresses the pointwise estimation of differential properties of a smooth manifold S —a curve in the plane or a surface in 3D — assuming a point cloud sampled over S is provided. The method consists of fitting the local representation of the manifold using a jet, and either interpolation or approximation. A jet is a truncated Taylor expansion, and the incentive for using jets is that they encode all local geometric quantities —such as normal, curvatures, extrema of curvature. On the way to using jets, the question of estimating differential properties is recasted into the more general framework of multivariate interpolation / approximation, a wellstudied problem in numerical analysis. On a theoretical perspective, we prove several convergence results when the samples get denser. For curves and surfaces, these results involve asymptotic estimates with convergence rates depending upon the degree of the jet used. For the particular case of curves, an error bound is also derived. To the best of our knowledge, these results are among the first ones providing accurate estimates for differential quantities of order three and more. On the algorithmic side, we solve the interpolation/approximation problem using Vandermonde systems. Experimental results for surfaces of R 3 are reported. These experiments illustrate the asymptotic convergence results, but also the robustness of the methods on general Computer Graphics models.
Sparse points matching by combining 3D mesh saliency with statistical descriptors
, 2008
"... This paper proposes new methodology for the detection and matching of salient points over several views of an object. The process is composed by three main phases. In the first step, detection is carried out by adopting a new perceptuallyinspired 3D saliency measure. Such measure allows the detecti ..."
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Cited by 49 (4 self)
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This paper proposes new methodology for the detection and matching of salient points over several views of an object. The process is composed by three main phases. In the first step, detection is carried out by adopting a new perceptuallyinspired 3D saliency measure. Such measure allows the detection of few sparse salient points that characterize distinctive portions of the surface. In the second step, a statistical learning approach is considered to describe salient points across different views. Each salient point is modelled by a Hidden Markov Model (HMM), which is trained in an unsupervised way by using contextual 3D neighborhood information, thus providing a robust and invariant point signature. Finally, in the third step, matching among points of different views is performed by evaluating a pairwise similarity measure among HMMs. An extensive and comparative experimental session has been carried out, considering real objects acquired by a 3D scanner from different points of view, where objects come from standard 3D databases. Results are promising, as the detection of salient points is reliable, and the matching is robust and accurate.
On the Repeatability and Quality of Keypoints for Local Featurebased 3D Object Retrieval from Cluttered Scenes
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2009
"... 3D object recognition from local features is robust to occlusions and clutter. However, local features must be extracted from a small set of feature rich keypoints to avoid computational complexity and ambiguous features. We present an algorithm for the detection of such keypoints on 3D models and p ..."
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Cited by 49 (5 self)
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3D object recognition from local features is robust to occlusions and clutter. However, local features must be extracted from a small set of feature rich keypoints to avoid computational complexity and ambiguous features. We present an algorithm for the detection of such keypoints on 3D models and partial views of objects. The keypoints are highly repeatable between partial views of an object and its complete 3D model. We also propose a quality measure to rank the keypoints and select the best ones for extracting local features. Keypoints are identified at locations where a unique local 3D coordinate basis can be derived from the underlying surface in order to extract invariant features. We also propose an automatic scale selection technique for extracting multiscale and scale invariant features to match objects at different unknown scales. Features are projected to a PCA subspace and matched to find correspondences between a database and query object. Each pair of matching features gives a transformation that aligns the query and database object. These transformations are clustered and the biggest cluster is used to identify the query object. Experiments on a public database revealed that the proposed quality measure relates correctly to the repeatability of keypoints and the multiscale features have a recognition rate of over 95 % for up to 80 % occluded objects.
EFFICIENT HOUGH TRANSFORM FOR AUTOMATIC DETECTION OF CYLINDERS IN POINT CLOUDS
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A Bag of Words Approach for 3D Object Categorization
"... Abstract. In this paper we propose a novel framework for 3D object categorization. The object is modeled it in terms of its subparts as an histogram of 3D visual word occurrences. We introduce an effective method for hierarchical 3D object segmentation driven by the minima rule that combines spectr ..."
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Cited by 20 (0 self)
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Abstract. In this paper we propose a novel framework for 3D object categorization. The object is modeled it in terms of its subparts as an histogram of 3D visual word occurrences. We introduce an effective method for hierarchical 3D object segmentation driven by the minima rule that combines spectral clustering – for the selection of seedregions – with region growing based on fast marching. The front propagation is driven by local geometry features, namely the Shape Index. Finally, after the coding of each object according to the BagofWords paradigm, a Support Vector Machine is learnt to classify different objects categories. Several examples on two different datasets are shown which evidence the effectiveness of the proposed framework. 1
Geometric Modeling Based on Triangle Meshes
"... This course is designed to cover the entire geometry processing pipeline based on triangle meshes. We will present the latest concepts for mesh generation and mesh repair, for geometry and topology optimizations like mesh smoothing, decimation, and remeshing, for parametrization, segmentation, and s ..."
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Cited by 18 (0 self)
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This course is designed to cover the entire geometry processing pipeline based on triangle meshes. We will present the latest concepts for mesh generation and mesh repair, for geometry and topology optimizations like mesh smoothing, decimation, and remeshing, for parametrization, segmentation, and shape editing. In addition to describing and discussing the related algorithms, we will also give valuable implementation hints and provide source code for most of the covered topics. The course assumes only very basic knowledge on geometric concepts in general, but does not require specific knowledge on polygonal meshes and how to discretize the respective problems for those. It is intended for computer graphics researchers, software developers and engineers from CAGD, computer games, or the movie industry, who are interested in geometry processing
Surface mesh segmentation and smooth surface extraction through region growing
 COMPUTER AIDED GEOMETRIC DESIGN
, 2005
"... Laser rangescanners are used in fields as diverse as product design, reverse engineering, and rapid prototyping to quickly acquire geometric surface data of parts and models. This data is often in the form of a dense, noisy surface mesh that must be simplified into piecewisesmooth surfaces. The me ..."
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Cited by 18 (2 self)
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Laser rangescanners are used in fields as diverse as product design, reverse engineering, and rapid prototyping to quickly acquire geometric surface data of parts and models. This data is often in the form of a dense, noisy surface mesh that must be simplified into piecewisesmooth surfaces. The method presented here facilitates this timeconsuming task by automatically segmenting a dense mesh into regions closely approximated by single surfaces. The algorithm first estimates the noise and curvature of each vertex. Then it filters the curvatures and partitions the mesh into regions with fundamentally different shape characteristics. These regions are then contracted to create seed regions for region growing. For each seed region, the algorithm iterates between region growing and surface fitting to maximize the number of connected vertices approximated by a single underlying surface. The algorithm finishes by filling segment holes caused by outlier noise. We demonstrate the algorithm effectiveness on real data sets.
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
 In PG ’04: Proceedings of the Computer Graphics and Applications, 12th Pacific Conference on (PG’04
, 2004
"... We introduce a new technique for estimating the curvature tensor of a triangular mesh. The input of the algorithm is only a single triangle equipped with its (exact or estimated) vertex normals. This way we get a smooth function of the curvature tensor inside each triangle of the mesh. We show that ..."
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Cited by 17 (4 self)
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We introduce a new technique for estimating the curvature tensor of a triangular mesh. The input of the algorithm is only a single triangle equipped with its (exact or estimated) vertex normals. This way we get a smooth function of the curvature tensor inside each triangle of the mesh. We show that the error of the new method is comparable with the error of a cubic fitting approach if the incorporated normals are estimated. If the exact normals of the underlying surface are available at the vertices, the error drops significantly. We demonstrate the applicability of the new estimation at a rather complex data set. 1.