Consistent mesh partitioning and skeletonisation using the shape diameter function

By Lior Shapira, Ariel Shamir, Daniel Cohen-Or. The Visual Computer, 2008

599 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/4337970e775aade9f7ac7d463d967cd61c02f972

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Contextual Part Analogies in 3D Objects (2010, methodology): “We use a partitioning of the shapes guided by the shape diameter function (SDF) (Shapira et al. 2008).”
PointGrid: A Deep Network for 3D Shape Understanding (2018, background): “), dihedral angles between triangles [58], curvatures (Gaussian curvature or mean curvature) [30], geodesic distances on a mesh [17, 64], slippage [61], symmetry, convexity, medial axis [33], shape diameter [44] and motion characteristics [43], shape contexts [4], spin images [21], etc.”
Schelling points on 3D surface meshes (2012, methodology): “• Shape Diameter Function (SDF): the median length of rays traced from V through the interior of M as described in [Shapira et al. 2008] using the implementation provided by [Kalogerakis et al.”
Data-driven suggestions for creativity support in 3D modeling (2010, methodology): “SDF captures the local thickness of the shape at a sample point, as measured by a ray along the inward normal.”
GWCNN: A Metric Alignment Layer for Deep Shape Analysis (2017, unknown): “For extrinsic per-point features of polygon soups we use PCA-based features in the local point neighborhoods [KHS10], height, shape diameter function [SSCO08], and absolute curvature using the publicly available implementation [KCGF14].”
Joint shape segmentation with linear programming (2011, methodology): “…seven single-shape segmentation approaches included in the benchmark, Table 1 only lists the performance of the leading two: shape diameter (SD, [Shapira et al. 2008]) and randomized cuts (RC, [Golovinskiy and Funkhouser 2008]); statistics for the other algorithms are provided in the original…”
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment (2016, methodology): “For example, we are witnessing the consolidation of methods based on (auto)diffusion processes [GBAL09, SOG09], quantum mechanics [ASC11] and gravitational laws [MDTS09], as well as the introduction of functions encoding shape properties [SSCO08, KBBK12, GL12] never considered before.”
Active co-analysis of a set of shapes (2012, methodology): “For the K-means clustering step, we use the same shape descriptors as Sidi et al. [2011], which are based on the position and orientation of faces, and also on the shape diameter function [Shapira et al. 2008].”
Min-cut based segmentation of point clouds (2009, methodology): “Some methods (such as [15]) create a scalar function over the surface of the mesh, and then decompose the mesh along discontinuities in that function using min-cut based methods.”
Point Cloud Skeletons via Laplacian Based Contraction (2010, unknown): “Previous methods to convert a point cloud to a curve skeleton, such as [49] and [9], require joint identification and delicate parameter tuning to handle a contracted shape with different local shape characteristics, as in Fig.”