A New Geometric Metric in the Shape and Size Space of Curves in R n
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Other documents of the author: Epifanio, Irene; Gimeno, Vicent; Gual-Arnau, Ximo; Ibáñez Gual, Maria Victoria
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
A New Geometric Metric in the Shape and Size Space of Curves in R nDate
2020-10-01Publisher
MDPIBibliographic citation
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.Type
info:eu-repo/semantics/articlePublisher version
https://www.mdpi.com/2227-7390/8/10/1691Version
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Abstract
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. [-]
Investigation project
Grants ts: DPI2017-87333-R from the Spanish Ministry of Science,Innovation and Universities (AEI/FEDER, EU) and UJI-B2017-13 from Universitat Jaume IRights
©2020 by the authors. Licensee MDPI, Basel, Switzerl
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