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Deformation Based Curved Shape Representation
Univesity of Luxembourg.ORCID iD: 0000-0003-2298-6774
2018 (English)In: IEEE Transaction on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, E-ISSN 1939-3539, Vol. 40, no 6, p. 1338-1351Article in journal (Refereed) Published
Abstract [en]

n this paper, we introduce a deformation based representation space for curved shapes in R-n. Given an ordered set of points sampled from a curved shape, the proposed method represents the set as an element of a finite dimensional matrix Lie group. Variation due to scale and location are filtered in a preprocessing stage, while shapes that vary only in rotation are identified by an equivalence relationship. The use of a finite dimensional matrix Lie group leads to a similarity metric with an explicit geodesic solution. Subsequently, we discuss some of the properties of the metric and its relationship with a deformation by least action. Furthermore, invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function. Thereafter, two possible approaches are presented to solve the point correspondence estimation problem. Finally, we propose an adaptation of k-means clustering for shape analysis in the proposed representation space. Experimental results show that the proposed representation is robust to uninformative cues, e.g., local shape perturbation and displacement. In comparison to state of the art methods, it achieves a high precision on the Swedish and the Flavia leaf datasets and a comparable result on MPEG-7, Kimia99 and Kimia216 datasets.

Place, publisher, year, edition, pages
IEEE Computer Society, 2018. Vol. 40, no 6, p. 1338-1351
Keywords [en]
Estimation;Extraterrestrial measurements;Manifolds;Mathematical model;Robustness;Shape;Shape representation;curved-shape-deformation;curved-shape-modelling;curved-shape-representation;deformation;shape matching;shape-matching;similarity metric;similarity-metric
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-258987DOI: 10.1109/TPAMI.2017.2711607ISI: 000431524700005Scopus ID: 2-s2.0-85021827916OAI: oai:DiVA.org:kth-258987DiVA, id: diva2:1350475
Note

QC 20191021

Available from: 2019-09-11 Created: 2019-09-11 Last updated: 2019-10-21Bibliographically approved

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Ottersten, Björn
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CiteExportLink to record
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  • apa
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