Surface reconstruction from point clouds by transforming the medial scaffold

Chang, Ming-Ching; Leymarie, Frederic Fol; Kimia, Benjamin B.

doi:10.1016/j.cviu.2009.04.001

Cited by 30 publications

(24 citation statements)

References 53 publications

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“…In order to overcome them, Lin et al in [26] introduced the Intrinsic Property Driven (IPD) algorithm, which improves the way of searching for the points to be triangulated. As stated by Chang et al in [2], all the methods based on mesh-growing approaches are fast, efficient and simple to implement but they, however, may fall short whenever two surfaces are either close together or near sharp features. More recently, Li et al in [1] proposed a method based on a Priority Driven approach that evaluates shape changes from an estimation of the original surface that is made at the front of the mesh-growing area.…”

Section: Mesh-growing Methodsmentioning

confidence: 97%

“…The candidate triangles are those triangles inside the Cocone region, which is the complement of a double cone which has its apex at the point under analysis (p) and an assigned opening angle and whose axis is the normal at p. The Cocone's worst time complexity is Θ(n 2 ), where n is the number of points. As pointed out by Chang et al in [2], the theoretical guarantee of obtaining a correct reconstruction with the Crust and Cocone methods is only possible as long as the point cloud is well sampled. Dey and Goswami proposed other Cocone versions, one suited to provide a watertight closed surface reconstruction, which they called Tight Cocone [16] and the other suited for noisy data called Robust Cocone [17].…”

Section: Voronoi/delaunay-based Methodsmentioning

confidence: 97%

“…Some recent exhaustive overviews are available in [1] and [2]. Surface reconstruction algorithms are generally divided into three categories: · implicit; · Voronoi/Delaunay-based; · mesh growing -based.…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

Angelo¹,

Stefano²,

Giaccari³

2013

Computer-Aided Design and Applications

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In a previous paper these authors presented a new mesh-growing approach based on the Gabriel 2 -Simplex (G2S) criterion. If compared with the Cocone family and the Ball Pivoting methods, G2S demonstrated to be competitive in terms of tessellation rate, quality of the generated triangles and defectiveness produced when the surface to be reconstructed was locally flat. Nonetheless, its major limitation was that, in the presence of a mesh which was locally non -flat or which was not sufficiently sampled, the method was less robust and holes and non -manifold vertices were generated. In order to overcome these limitations, in this paper, the performance of the G2S meshgrowing method is fully improved in terms of robustness. The performances of the new version of the G2S approach (in the following Robust G2S) has been compared with that of the old one, and that of the Cocone family and the Ball Pivoting methods in the tessellation of some benchmark point clouds and artificially noised test cases. The results obtained show that the use of the Robust G2S is advantageous, as opposed to the other methods here considered, even in the case of noised point clouds. Unlike the other methods, the one which is proposed preserves manifoldness and geometric details of the point cloud to be meshed.

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Section: Mesh-growing Methodsmentioning

confidence: 97%

Section: Voronoi/delaunay-based Methodsmentioning

confidence: 97%

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A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

Angelo¹,

Stefano²,

Giaccari³

2013

Computer-Aided Design and Applications

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“…For n = 2, S Ω is a set of curves which meet at the so-called skeleton junction points [20]. For n = 3, S Ω is a set of manifolds with boundaries which meet along a set of so called Y-intersection curves [14], [17], [36].…”

Section: Introductionmentioning

confidence: 99%

An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization

Jalba

Sobiecki

Telea

2016

IEEE Trans. Pattern Anal. Mach. Intell.

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Computing skeletons of 2D shapes, and medial surface and curve skeletons of 3D shapes, is a challenging task. In particular, there is no unified framework that detects all types of skeletons using a single model, and also produces a multiscale representation which allows to progressively simplify, or regularize, all skeleton types. In this paper, we present such a framework. We model skeleton detection and regularization by a conservative mass transport process from a shape's boundary to its surface skeleton, next to its curve skeleton, and finally to the shape center. The resulting density field can be thresholded to obtain a multiscale representation of progressively simplified surface, or curve, skeletons. We detail a numerical implementation of our framework which is demonstrably stable and has high computational efficiency. We demonstrate our framework on several complex 2D and 3D shapes.

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“…This classification has been used by Leymarie and Kimia [20] to propose the notion of a medial scaffold (MS), a hierarchical representation of the MA points. Algorithms for computing the MS from unorganized points have been developed [20,6], which also effectively meshes the surface as well, Figure 1a,b. The MA structure is complete, but is also complex and redundant with respect to a qualitative representation of the structure: as the shape is perturbed it undergoes transitions, or sudden changes in the MS topology, so that highly similar shapes can have drastically different MS topology.…”

Section: Introductionmentioning

confidence: 99%

Regularizing 3D medial axis using medial scaffold transforms

Chang

Kimia

2008

2008 IEEE Conference on Computer Vision and Pattern Recognition

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This paper addresses a key bottleneck in the use of the 3D medial axis (MA) representation, namely, how the complex MA structure can be regularized so that similar, withincategory 3D shapes yield similar 3D MA that are distinct from the non-category shapes. We rely on previous work which (i) constructs a hierarchical MA hypergraph, the medial scaffold (MS), and (ii) the theoretical classification of the instabilities of this structure, or transitions (sudden topological changes due to a small perturbation). The shapes at transition point are degenerate. Our approach is to recognize the transitions which are close-by to a given shape and transform the shape to this transition point, and repeat until no close-by transitions exists. This move towards degeneracy is the basis of simplification of shape. We derive 11 transforms from 7 transitions and follow a greedy scheme in applying the transform. The results show that the simplified MA preserves with-in-category similarity, thus indicating its potential use in various applications including shape analysis, manipulation, and matching.

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Surface reconstruction from point clouds by transforming the medial scaffold

Cited by 30 publications

References 53 publications

A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization

Regularizing 3D medial axis using medial scaffold transforms

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