Computing medial axes of generic 3D regions bounded by B-spline surfaces

Musuvathy, Suraj; Cohen, Elaine; Damon, James

doi:10.1016/j.cad.2011.08.023

Cited by 9 publications

(6 citation statements)

References 32 publications

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“…However, the specific sampling and interpolation decisions with respect to the surface S used by such representations affect the definition of DT S . Skeletonization can also treat shapes represented using rational curves in 2D [Tzo11] and 3D [MCD11]. Many methods allow computing skeletons of voxel shapes [AL01, HR08, ASS11,SBdB15].…”

Section: Challenges Of Practical Skeletonizationmentioning

confidence: 99%

“…Many methods allow computing skeletons of voxel shapes [AL01, HR08, ASS11, SBdB15]. Skeletonization can also treat shapes represented using rational curves in 2D [Tzo11] and 3D [MCD11]. Yet, changing the shape representation often requires one to adapt the MAT definition, including the ways to evaluate the distance transform DT 풮 . Boundary points : We need a way to practically determine when two points on 풮 are different (term x 1 ≠ x 2 in Eqn.…”

Section: Theoretical Foundationsmentioning

confidence: 99%

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3D Skeletons: A State‐of‐the‐Art Report

Tagliasacchi

Delame

Spagnuolo

et al. 2016

Computer Graphics Forum

206

152

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International audienceGiven a shape, a skeleton is a thin centered structure which jointly describes the topology and the geometry of the shape. Skeletons provide an alternative to classical boundary or volumetric representations, which is especially effective for applications where one needs to reason about, and manipulate, the structure of a shape. These skeleton properties make them powerful tools for many types of shape analysis and processing tasks. For a given shape, several skeleton types can be defined, each having its own properties, advantages, and drawbacks. Similarly, a large number of methods exist to compute a given skeleton type, each having its own requirements, advantages, and limitations. While using skeletons for two-dimensional (2D) shapes is a relatively well covered area, developments in the skeletonization of three-dimensional (3D) shapes make these tasks challenging for both researchers and practitioners. This survey presents an overview of 3D shape skeletonization. We start by presenting the definition and properties of various types of 3D skeletons. We propose a taxonomy of 3D skeletons which allows us to further analyze and compare them with respect to their properties. We next overview methods and techniques used to compute all described 3D skeleton types, and discuss their assumptions, advantages, and limitations. Finally, we describe several applications of 3D skeletons, which illustrate their added value for different shape analysis and processing tasks

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Section: Challenges Of Practical Skeletonizationmentioning

confidence: 99%

Section: Theoretical Foundationsmentioning

confidence: 99%

3D Skeletons: A State‐of‐the‐Art Report

Tagliasacchi

Delame

Spagnuolo

et al. 2016

Computer Graphics Forum

206

152

View full text Add to dashboard Cite

show abstract

“…Note that the extraction of the exact medial axis is not restricted to piecewise linear representations. Recently the authors of [Tzoumas 2011] demonstrated how to compute the medial axis of rational curves in the plane, while [Musuvathy et al 2011] addressed a similar problem in the three dimensional domain.…”

Section: Exact Medial Computationmentioning

confidence: 99%

Skeletal Representations and Applications

Tagliasacchi¹

2013

Preprint

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When representing a solid object there are alternatives to the use of traditional explicit (surface meshes) or implicit (zero crossing of implicit functions) methods. Skeletal representations encode shape information in a mixed fashion: they are composed of a set of explicit primitives, yet they are able to efficiently encode the shape's volume as well as its topology. I will discuss, in two dimensions, how symmetry can be used to reduce the dimensionality of the data (from a 2D solid to a 1D curve), and how this relates to the classical definition of skeletons by Medial Axis Transform. While the medial axis of a 2D shape is composed of a set of curves, in 3D it results in a set of sheets connected in a complex fashion. Because of this complexity, medial skeletons are difficult to use in practical applications. Curve skeletons address this problem by strictly requiring their geometry to be one dimensional, resulting in an intuitive yet powerful shape representation. In this report I will define both medial and curve skeletons and discuss their mutual relationship. I will also present several algorithms for their computation and a variety of scenarios where skeletons are employed, with a special focus on geometry processing and shape analysis.

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“…This method primarily extracted the symmetrical nodes from the mesh and then used a voting algorithm to extract the symmetry. Musuvathy et al (2011) used the Eikonal equation to estimate _______________________________ * Corresponding author parameters of a 3D volume based on the B-spline surface which embraced the entire volume. Berner et al (2009) proposed a method which could detect mild deviation from the symmetry of an object by registering different topographical planes.…”

Section: Introductionmentioning

confidence: 99%

Central Axis Estimation for Ancient Chinese Pagodas Based on Geometric Modelling and Uav-Based Photogrammetry

Chan

Xia

Tang

et al. 2020

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Abstract. Pagodas are common historical structures in China and some other Asian countries. Symmetries of the pagodas play an important role on cultural and structural aspects. In this paper, we proposed a method estimating the central axis of a typical ancient pagoda in China for examination of its symmetry. We developed a novel geometric model to fit to the point cloud of the pagoda obtained from photogrammetric reconstruction based on UAV imagery. More specifically, we developed a novel geometric model possessing 16 parameters to fit to the point cloud of different parts of the pagodas simultaneously to estimate a central axis for the symmetry. The results show that the proposed model is superior to the conventional cylindrical models for the central axis estimation. More importantly, the estimated parameters are in realistic ranges, as well as the reconstructed central axis and the sextant number are well visualized, so the symmetry of the pagodas can be readily analysed.

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Computing medial axes of generic 3D regions bounded by B-spline surfaces

Cited by 9 publications

References 32 publications

3D Skeletons: A State‐of‐the‐Art Report

3D Skeletons: A State‐of‐the‐Art Report

Skeletal Representations and Applications

Central Axis Estimation for Ancient Chinese Pagodas Based on Geometric Modelling and Uav-Based Photogrammetry

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