A New Geometric Metric in the Shape and Size Space of Curves in R n
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A New Geometric Metric in the Shape and Size Space of Curves in R nData de publicació
2020-10-01Editor
MDPICita bibliogràfica
Epifanio, I.; Gimeno, V.; Gual-Arnau, X.; Ibáñez-Gual, M.V. A New Geometric Metric in the Shape and Size Space of Curves in R n . Mathematics 2020, 8, 1691.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://www.mdpi.com/2227-7390/8/10/1691Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale ... [+]
Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale and orientation. The combination of these features, shape, orientation and scale (size), gives different geometrical spaces. In this work, we define a new metric in the shape and size space, S2, which allows us to decompose S2 into a product space consisting of two components: S4×R, where S4 is the shape space. This new metric will be associated with a distance function, which will clearly distinguish the contribution that the difference in shape and the difference in size of the elements considered makes to the distance in S2, unlike the previous proposals. The performance of this metric is checked on a simulated data set, where our proposal performs better than other alternatives and shows its advantages, such as its invariance to changes of scale. Finally, we propose a procedure to detect outlier contours in S2 considering the square-root velocity function (SRVF) representation. For the first time, this problem has been addressed with nearest-neighbor techniques. Our proposal is applied to a novel data set of foot contours. Foot outliers can help shoe designers improve their designs. [-]
Proyecto de investigación
Grants ts: DPI2017-87333-R from the Spanish Ministry of Science,Innovation and Universities (AEI/FEDER, EU) and UJI-B2017-13 from Universitat Jaume IDrets d'accés
©2020 by the authors. Licensee MDPI, Basel, Switzerl
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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