Relaxations for Minimizing Metric Distortion and Elastic Energies for 3D Shape Matching

Daniel Cremers; Emanuele Rodolà; Thomas Windheuser

Displaying similar documents to “Relaxations for Minimizing Metric Distortion and Elastic Energies for 3D Shape Matching”

Numerical solution of the pressing devices shape optimization problem in the glass industry

Petr Salač (2018)

Applications of Mathematics

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In this contribution, we present the problem of shape optimization of the plunger cooling which comes from the forming process in the glass industry. We look for a shape of the inner surface of the insulation barrier located in the plunger cavity so as to achieve a constant predetermined temperature on the outward surface of the plunger. A rotationally symmetric system, composed of the mould, the glass piece, the plunger, the insulation barrier and the plunger cavity, is considered....

Closed surfaces with different shapes that are indistinguishable by the SRNF

Eric Klassen, Peter W. Michor (2020)

Archivum Mathematicum

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The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [5], provides a way of representing immersed surfaces in $ℝ^{3}$ , and equipping the set of these immersions with a “distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of $ℝ^{3}$ . Thus, it induces a distance function on the shape space of immersions, i.e.,...

Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

Tao Liao, Hao-Chih Lee, Ge Yang, Yongjie Jessica Zhang (2015)

Molecular Based Mathematical Biology

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The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the...

Movability and limits of polyhedra

V. Laguna, M. Moron, Nhu Nguyen, J. Sanjurjo (1993)

Fundamenta Mathematicae

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We define a metric $d_{S}$ , called the shape metric, on the hyperspace $2^{X}$ of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyhedra in the shape metric. This fact is applied to show that the hyperspace $(2^{ℝ} 2$ , dS) $i s s e p a r a b l e . O n t h e o t h e r h a n d, w e g i v e a n e x a m p l e s h o w i n g t h a t$ 2ℝ2 $i s n o t s e p a r a b l e i n t h e f u n d a m e n t a l m e t r i c i n t r o d u c e d b y B o r s u k .$

The Whitehead and the Smale theorems in shape theory

Jerzy Dydak

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CONTENTS§1. Introduction................................................................................................................................... 5§2. Some classes of objects and morphisms in pro-categories..................................................... 5§3. Shape category.................................................................................................................................... 14§4. Deformation dimension........................................................................................................................

Triangular mesh analysis with application on hip bone

Pajerová, Nikola, Linkeová, Ivana

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Shape analyses and similarity measuring is a very often solved problem in computer graphics. The shape distribution approach based on shape functions is frequently used for this determination. The experience from a comparison of ball-bar standard triangular meshes was used to match hip bones triangular meshes. The aim is to find relation between similarity measures obtained by shape distributions approach.

Function spaces and shape theories

Jerzy Dydak, Sławomir Nowak (2002)

Fundamenta Mathematicae

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The purpose of this paper is to provide a geometric explanation of strong shape theory and to give a fairly simple way of introducing the strong shape category formally. Generally speaking, it is useful to introduce a shape theory as a localization at some class of “equivalences”. We follow this principle and we extend the standard shape category Sh(HoTop) to Sh(pro-HoTop) by localizing pro-HoTop at shape equivalences. Similarly, we extend the strong shape category of Edwards-Hastings...

Mesh Generation and Flexible Shape Comparisons for Bio-Molecules

Zhanheng Gao, Reihaneh Rostami, Xiaoli Pang, Zhicheng Fu, Zeyun Yu (2016)

Molecular Based Mathematical Biology

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Novel approaches for generating and comparing flexible (non-rigid) molecular surface meshes are developed. The mesh-generating method is fast and memory-efficient. The resulting meshes are smooth and accurate, and possess high mesh quality. An isometric-invariant shape descriptor based on the Laplace- Beltrami operator is then explored for mesh comparing. The new shape descriptor is more powerful in discriminating different surface shapes but rely only on a small set of signature values....

Strong shape of the Stone-Čech compactification

Sibe Mardešić (1992)

Commentationes Mathematicae Universitatis Carolinae

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J. Keesling has shown that for connected spaces $X$ the natural inclusion $e : X \to β X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.