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Research in Shape Analysis

Part of the Association for Women in Mathematics Series Book Series (volume 12)

Editors: Genctav, Asli; Leonard, Kathryn; Tari, Sibel; Hubert, Evelyne; Morin, Geraldine; El-Zehiry, Noha; Chambers, Erin

DOI: 10.1007/978-3-319-77066-6

ISBN: 978-3-319-77065-9

Publisher: Springer International Publishing - Springer Journals

May 18, 2018

1 - 10 of 10 Chapters

LitStream

Chapter 1Medial Fragments for Segmentation of Articulating Objects in Images

Chambers, Erin; Gasparovic, Ellen; Leonard, Kathryn

Pages: 1 –15

[The Blum medial axis is known to provide a useful representation of pre-segmented shapes. Very little work to date, however, has examined its usefulness for extracting objects from natural images. We propose a method for combining fragments of the medial axis, generated from the Voronoi diagram...
LitStream

Chapter 2Scaffolding a Skeleton

Panotopoulou, Athina; Ross, Elissa; Welker, Kathrin; Hubert, Evelyne; Morin, Géraldine

Pages: 17 –35

[The goal of this paper is to construct a quadrilateral mesh around a one-dimensional skeleton that is as coarse as possible, the “scaffold.” A skeleton allows one to quickly describe a shape, in particular a complex shape of high genus. The constructed scaffold is then a potential support for...
LitStream

Chapter 3Convolution Surfaces with Varying Radius: Formulae for Skeletons Made of Arcs of Circles and Line Segments

Suárez, Alvaro Javier Fuentes; Hubert, Evelyne

Pages: 37 –60

[In skeleton-based geometric modeling, convolution is an established technique: smooth surfaces around a skeleton made of curves are given as the level set of a convolution field. Varying the radius or making the surface scale sensitive along the skeleton are desirable features. This article...
LitStream

Chapter 4Exploring 2D Shape Complexity

Chambers, Erin; Emerson, Tegan; Grimm, Cindy; Leonard, Kathryn

Pages: 61 –83

[In this paper, we explore different notions of shape complexity, drawing from established work in mathematics, computer science, and computer vision. Our measures divide naturally into three main categories: skeleton-based, symmetry-based, and those based on boundary sampling. We apply these to...
LitStream

Chapter 5Phase Field Topology Constraints

Acar, Rüyam; Sağırlı, Necati

Pages: 85 –94

[This paper presents a morphological approach to extract topologically critical regions in phase field models. There are a few studies regarding topological properties of phase fields. One line of work related to our problem addresses constrained phase field evolution. This approach is based on...
LitStream

Chapter 6Adaptive Deflation Stopped by Barrier Structure for Equating Shape Topologies Under Topological Noise

Genctav, Asli; Tari, Sibel

Pages: 95 –109

[Using level sets of a pair of transformations, we adaptively bring two shapes to be matched to a comparable topology prior to a correspondence search. One of the transformations readily provides a central structure for each shape. We utilize the central structure as a reference volume for scale...
LitStream

Chapter 7Joint Segmentation and Nonlinear Registration Using Fast Fourier Transform and Total Variation

Atta-Fosu, Thomas; Guo, Weihong

Pages: 111 –132

[Image segmentation and registration play active roles in machine vision and medical image analysis of historical data. We explore the joint problem of segmenting and registering a template (current) image given a reference (past) image. We formulate the joint problem as a minimization of a...
LitStream

Chapter 8Multi-parameter Mumford-Shah Segmentation

Genctav, Murat; Tari, Sibel

Pages: 133 –141

[Mumford-Shah functional has two parameters that define a two-dimensional scale space of solutions. Instead of using the solution obtained at a predetermined fine-tuned parameter setting, we consider solutions at multiple parameter settings simultaneously. Using multiple solutions, we construct...
LitStream

Chapter 9L1-Regularized Inverse Problems for Image Deblurring via Bound- and Equality-Constrained Optimization

Bardsley, Johnathan M.; Howard, Marylesa

Pages: 143 –159

[Image deblurring is typically modeled as an ill-posed, linear inverse problem. By adding an L1-penalty to the negative-log likelihood function, the resulting minimization problem becomes well-posed. Moreover, the penalty enforces sparsity. The difficulty with L1-penalties, however, is that they...
LitStream

Chapter 10Shape Patterns in Digital Fabrication: A Survey on Negative Poisson’s Ratio Metamaterials

Yılmaz, Bengisu; Adanova, Venera; Acar, Rüyam; Tari, Sibel

Pages: 161 –172

[Poisson’s ratio for solid materials is defined as the ratio of the lateral length shrinkage to the longitudinal part extension on a simple tension test. While Poisson’s ratio for almost every material in nature is a positive number, materials having negative Poisson’s ratio may be engineered. We...

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