Abstract
The Global-Local transformation, a shape representation technique for manifolds of multiple dimensions is presented in this chapter. Useful properties of the transform space are examined and through experiments, unique advantages of the GL-transform are revealed. Applications in shape matching and radar shadow analysis demonstrate its effectiveness in real life scenarios.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Manay, D. Cremers, B.-W. Hong, A. Yezzi, S. Soatto, Integral invariants for shape matching. IEEE Trans. Pattern Anal. Mach. Intell. 28(10), 1602–1618 (2006)
K.A. Raftopoulos, S.D. Kollias, The Global-Local transformation for noise resistant shape representation. Comput. Vis. Image Underst. 115(8), 1170–1186 (2011)
T.B. Sebastian, P.N. Klein, B.B. Kimia, On aligning curves. IEEE Trans. PAMI 25, 116–125 (2003)
H. Ling, D. Jacobs, Shape classification using the inner-distance. IEEE Trans. Pattern Anal. Mach. Intell. 29(2), 286–299 (2007)
P. Donatini, P. Frosini, Natural pseudo-distances between closed curves. Forum Math. 21(6), 981–999 (2009)
D. Groisser, Certain optimal correspondences between plane curves II. Existence, local uniqueness, regularity, and other properties. Trans. Am. Math. Soc. 361(6), 3001–3030 (2009)
D. Groisser, Certain optimal correspondences between plane curves I. Manifolds of shapes and bimorphisms. Trans. Am. Math. Soc. 361(6), 2959–3000 (2009)
P.W. Michor, D. Mumford, Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc. 8(1), 1–48 (2006)
[Online]. Available: http://vision.lems.brown.edu/content/available-software-and-databases#Datasets-Shape
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Raftopoulos, K.A. (2020). The Global-Local Transformation. In: Daras, N., Rassias, T. (eds) Computational Mathematics and Variational Analysis. Springer Optimization and Its Applications, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-030-44625-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-44625-3_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44624-6
Online ISBN: 978-3-030-44625-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)