Decomposition Algorithms in Geometry

Chazelle, Bernard; Palios, Leonidas

doi:10.1007/978-1-4612-2628-4_27

Cited by 26 publications

(14 citation statements)

References 27 publications

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“…This theory states that humans perform decomposition at negative minima of principal curvature, which lead to a shape decomposition on convex regions. However, other researchers [3,4] see that instead of generating cuts in concave boundaries they generate parts which correspond to convex boundaries. Such segmentation is useful for applications such as collision detection.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Hierarchical 3D Mesh Segmentation Using Negative Curvature and Dihedral Angle

Arhid¹,

Zakani²,

Bouksim³

et al. 2017

IJIES

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Decomposing a 3D mesh into significant regions is considered as a fundamental process in computer graphics, since several algorithms use the segmentation results as an initial step, such as, skeleton extraction, shape retrieval, shape correspondence, and compression. In this work, we present a new segmentation algorithm using spectral clustering where the affinity matrix is constructed by combining the minimal curvature and dihedral angles to detect both concave and convex properties of each edge. Experimental results show that the proposed method outperforms some of the existing segmentation methods, which highlight the performance of our approach.

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Section: Introductionmentioning

confidence: 99%

An Efficient Hierarchical 3D Mesh Segmentation Using Negative Curvature and Dihedral Angle

Arhid¹,

Zakani²,

Bouksim³

et al. 2017

IJIES

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“…Many different decomposition methods have been proposed -see, e.g., Chazelle and Palios [6] for a brief review of some common strategies. Of these, decomposition into convex components has been of great interest because many algorithms, such as collision detection and mesh generation, perform more efficiently on convex objects.…”

Section: Introductionmentioning

confidence: 99%

Approximate convex decomposition of polyhedra

Lien

Amato

2004

ACM SIGGRAPH 2004 Posters on - SIGGRAPH '04

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Decomposition is a technique commonly used to partition complex models into simpler components. While decomposition into convex components results in pieces that are easy to process, such decompositions can be costly to construct and can result in representations with an unmanageable number of components. In this paper, we explore an alternative partitioning strategy that decomposes a given model into "approximately convex" pieces that may provide similar benefits as convex components, while the resulting decomposition is both significantly smaller (typically by orders of magnitude) and can be computed more efficiently. Indeed, for many applications, an approximate convex decomposition (ACD) can more accurately represent the important structural features of the model by providing a mechanism for ignoring less significant features, such as surface texture. We describe a technique for computing ACDs of three-dimensional polyhedral solids and surfaces of arbitrary genus. We provide results illustrating that our approach results in high quality decompositions with very few components and applications showing that comparable or better results can be obtained using ACD decompositions in place of exact convex decompositions (ECD) that are several orders of magnitude larger. 1 ECD ECD Figure 1: The approximate convex decompositions (ACD) of the Armadillo and the David models consist of a small number of nearly convex components that characterize the important features of the models better than the exact convex decompositions (ECD) that have orders of magnitude more components. The Armadillo (500K edges, 12.1MB) has a solid ACD with 98 components (14.2MB) that was computed in 232 seconds while the solid "ECD" has more than 726,240 components (20+ GB) and could not be completed because disk space was exhausted after nearly 4 hours of computation. The David (750K edges, 18MB) has a surface ACD with 66 components (18.1MB) while the surface ECD has 85,132 components (20.1MB).

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“…It is generally the case that a decomposition into convex solids is sought (e.g, [2,3,6,9,11,12,23]), since convex shapes are considered useful for representation, manipulation and rendering. Most algorithms proposed are hard to implement and debug and they all suffer a quadratic blow-up, which is often prohibitive in practice.…”

Section: Introductionmentioning

confidence: 99%

Polyhedral surface decomposition with applications

Zuckerberger

Tal

Shlafman

2002

Computers & Graphics

143

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This paper addresses the problem of decomposing a polyhedral surface into "meaningful" patches. We describe two decomposition algorithms -flooding convex decomposition and watershed decomposition, and show experimental results. Moreover, we discuss three applications which can highly benefit from surface decomposition. These applications include content-based retrieval of threedimensional models, metamorphosis of three-dimensional models and simplification.

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Decomposition Algorithms in Geometry

Cited by 26 publications

References 27 publications

An Efficient Hierarchical 3D Mesh Segmentation Using Negative Curvature and Dihedral Angle

An Efficient Hierarchical 3D Mesh Segmentation Using Negative Curvature and Dihedral Angle

Approximate convex decomposition of polyhedra

Polyhedral surface decomposition with applications

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