Erosion thickness on medial axes of 3D shapes

Yan, Ying; Sykes, Kyle A.; Chambers, Erin Wolf; Letscher, David; Ju, Tao

doi:10.1145/2897824.2925938

Cited by 49 publications

(48 citation statements)

References 36 publications

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“…The comparison of the simplified medial meshes of Yan's method [YSC*16](Top Row) by different parameters (θ 1 , θ 2 ) and ours(Bottom Row) at different simplification levels. (#v is the number of vertices of the medial meshes).…”

Section: Resultsmentioning

confidence: 99%

Topology Preserving Simplification of Medial Axes in 3D Models

Chu

Hou

Wang

et al. 2019

Computer Graphics Forum

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We propose an efficient method for topology‐preserving simplification of medial axes of 3D models. Existing methods either cannot preserve the topology during medial axes simplification or have the problem of being geometrically inaccurate or computationally expensive. To tackle these issues, we restrict our topology‐checking to the areas around the topological holes to avoid unnecessary checks in other areas. Our algorithm can keep high precision even when the medial axis is simplified to be in very few vertices. Furthermore, we parallelize the medial axes simplification procedure to enhance the performance significantly. Experimental results show that our method can preserve the topology with highly efficient performance, much superior to the existing methods in terms of topology preservation, accuracy and performance.

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Section: Resultsmentioning

confidence: 99%

Topology Preserving Simplification of Medial Axes in 3D Models

Chu

Hou

Wang

et al. 2019

Computer Graphics Forum

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“…Added Split and moved Figure 22: Semi-automatic approximation of the fertility model by anisotropic convolution surface. Left: Fertility model and output (black polyline) of the skeletonization algorithm in [56]. Middle: Circular splines after manual editing -adding the base (black lines) and splitting the top (red and green splines).…”

Section: Approximation Experiments and Discussionmentioning

confidence: 99%

“…Other than the simple and intuitive modeling of shapes, we also investigate the use of anisotropic convolution surfaces for shape approximation. Starting from a mesh of the shape and its skeletonization [30,56], we propose a pipeline to best fit an anisotropic convolution surface. The new shape so obtained has a compact representation, and can be seen as a lossy compression of the original model.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic convolution surfaces

Suárez¹,

Hubert²,

Zanni

2019

Computers & Graphics

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Convolution surfaces with 1D skeletons have been limited to close-to-circular normal sections. The new formalism presented here allows for ellipsoidal normal sections. Anisotropy is prescribed on G 1 skeletal curves, chosen as circular splines, by a rotation angle and the three radii of an ellipsoid at each extremity. This lightweight model creates smooth shapes that previously required tweaking the skeleton or supplementing it with 2D pieces. The scale invariance of our formalism achieves excellent radii control and thus lends itself to approximate a variety of shapes. The construction of a scaffold is extended to skeletons with G 1 branches. It projects onto the convolution surface as a quad mesh with skeleton bound edge-flow.

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“…In [32], these functions are meant to aid in pruning the medial axis to obtain a simpler version that is more useful in applications, and to obtain a 1D skeletal shape representation. In contrast, our paper aims to provide a new function on the skeleton, similar to WEDF in 2D, able to measure part saliency.…”

Section: D Shape Decompositionmentioning

confidence: 99%

“…• The medial burn time (MBT) is defined as the geodesic distance of a medial axis point to the shape boundary associated to the closest extremity of the widest medial axis sheet containing this point [32].…”

Section: Local Analysis Of the Shape Around The Axismentioning

confidence: 99%

A salience measure for 3D shape decomposition and sub-parts classification

et al. 2018

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Open Archive Toulouse Archive OuverteOATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible a A B S T R A C T This paper introduces a measure of significance on a curve skeleton of a 3D piecewise linear shape mesh, allowing the computation of both the shape's parts and their saliency. We begin by reformulating three existing pruning measures into a non-linear PCA along the skeleton. From this PCA, we then derive a volume-based salience measure, the 3D WEDF, that determines the relative importance to the global shape of the shape part associated to a point of the skeleton. First, we provide robust algorithms for computing the 3D WEDF on a curve skeleton, independent on the number of skeleton branches. Then, we cluster the WEDF values to partition the curve skeleton, and coherently map the decomposition to the associated surface mesh. Thus, we develop an unsupervised hierarchical decomposition of the mesh faces into visually meaningful shape regions that are or-dered according to their degree of perceptual salience. The shape analysis tools introduced in this paper are important for many applications including shape comparison, editing, and compression.

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Erosion thickness on medial axes of 3D shapes

Cited by 49 publications

References 36 publications

Topology Preserving Simplification of Medial Axes in 3D Models

Topology Preserving Simplification of Medial Axes in 3D Models

Anisotropic convolution surfaces

A salience measure for 3D shape decomposition and sub-parts classification

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