Reference : Similarity Metric For Curved Shapes In Euclidean Space

	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Engineering, computing & technology : Computer science
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/26730

Title :	Similarity Metric For Curved Shapes In Euclidean Space
Language :	English
Author, co-author :	Demisse, Girum [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
	Aouada, Djamila [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
	Ottersten, Björn [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
Publication date :	26-Jun-2016
Main document title :	IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2016
Peer reviewed :	Yes
Audience :	International
Event name :	IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2016
Event date :	from 26-06-2016 to 01-07-2016
Event organizer :	IEEE
Event place (city) :	Las vegas
Event country :	USA
Keywords :	[en] Curve modelling ; Metric for curved shapes
Abstract :	[en] In this paper, we introduce a similarity metric for curved shapes that can be described, distinctively, by ordered points. The proposed method represents a given curve as a point in the deformation space, the direct product of rigid transformation matrices, such that the successive action of the matrices on a fixed starting point reconstructs the full curve. In general, both open and closed curves are represented in the deformation space modulo shape orientation and orientation preserving diffeomorphisms. The use of direct product Lie groups to represent curved shapes led to an explicit formula for geodesic curves and the formulation of a similarity metric between shapes by the $L^{2}$-norm on the Lie algebra. Additionally, invariance to reparametrization or estimation of point correspondence between shapes is performed as an intermediate step for computing geodesics. Furthermore, since there is no computation of differential quantities on the curves, our representation is more robust to local perturbations and needs no pre-smoothing. We compare our method with the elastic shape metric defined through the square root velocity (SRV) mapping, and other shape matching approaches
Research centres :	University of Luxembourg-SnT
Target :	Researchers ; Professionals ; Students ; General public ; Others
Permalink :	http://hdl.handle.net/10993/26730

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