# Medial/skeletal linking structures for multi-region configurations

@article{Damon2014MedialskeletalLS, title={Medial/skeletal linking structures for multi-region configurations}, author={James N. Damon and Ellen Gasparovic}, journal={arXiv: Differential Geometry}, year={2014} }

We consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{\Omega_i\}$ in $\mathbb{R}^{n+1}$ which may be either smooth regions disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way. We introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the "positional geometry" of the…

## 7 Citations

### Modeling Multi-object Configurations via Medial/Skeletal Linking Structures

- Computer ScienceInternational Journal of Computer Vision
- 2017

We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical “skeletal linking structure” which will simultaneously capture the individual shape features of…

### Shape and Positional Geometry of Multi-Object Configurations

- Computer ScienceArXiv
- 2017

Numerical invariants for positional properties which measure the closeness of neighboring objects, including identifying the parts of the objects which are close, and the "relative significance" of objects compared with the other objects in the configuration are introduced.

### Rigidity Properties of the Blum Medial Axis

- MathematicsJ. Math. Imaging Vis.
- 2021

It is shown that in the generic case, along a Y -branching submanifold, that there are three cross ratios involving the three limiting tangent planes of the three smooth sheets and each of the hyperplanes defined by one of the radial lines and the tangent space to the Y - Branches sub manifold at the point, which must be preserved.

### Rigidity Properties of the Blum Medial Axis

- MathematicsJournal of Mathematical Imaging and Vision
- 2020

We consider the Blum medial axis of a region in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

### Skeletons, Object Shape, Statistics

- Computer ScienceFrontiers in Computer Science
- 2022

This paper lays out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s- reps to single- and multi-object boundaries, method for measuring the statistics of these object andMulti-object representations, and examples of such applications involving statistics.

### Medial Fragments for Segmentation of Articulating Objects in Images

- Physics
- 2018

This work proposes a method for combining fragments of the medial axis, generated from the Voronoi diagram of an edge map of a natural image, into a coherent whole using techniques from persistent homology and graph theory to aggregate parts of the same object into a larger whole.

### CGWeek Young Researchers Forum 2020

- Computer Science
- 2020

An algorithm for Boolean operations on two polygonal regions designed so that degeneracies typically requiring special handling are treated as general cases is detailed.

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