Abstract
In this paper we focus on distances between textures, and develop metrics on image spaces in contexts of image transformations. Given a metric on the range space, we can generate the initial topology for the domain space. For this topology we can obtain a corresponding metric using well-known metrization constructions, also providing granularity of the metrics. Examples are drawn from the Spatial Gray Level Dependency (SGLD) transformation and the application domain is texture recognition in medical imaging.
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J. Serra. Image Analysis and Mathematical Morphology, volume 1. Academic Press, 1982.
D.L. Wilson, A.J. Baddeley, and R.A. Owens. A new metric for gray-scale image comparison. International Journal of Computer Vision, 24:5–17, 1997.
R. Lowen, and W. Peeters. On various classes of semi-pseudometrics used in pattern recognition. In Proc. Seventh IFSA World Congress, pages 232–237, 1997.
R.M. Haralick, K. Shanmugam, and I. Dinstein. Textural Features for Image Classification. IEEE Trans. Systems, man and Cybernetics, 3:610–621, 1973.
B. Sahiner, H.P. Chan, N. Petrick, M.A. Helvie, D.D. Adler, and M.M. Godsitt. Classification of Masses on Mammograms using Rubber-Band Straightening Transform and Feature Analysis. SPIE, proceedings series, 2710:44–50. 1996.
F. Georgsson, and S. Carlson, A Framework for Computer Aided Mammographic Screening for Breast Cancer, in N. Karssemeijer, M. Thijssen, J. Hendriks, and L.v. Erning(editors)Digital Mammography, Kluwer Academic Publishers, pages:415–418, 1998.
J.F. Veenland, T.M. Link, W. Konermann, N. Meier, J.L. Grashuis, and E.S. Gelsema. Unraveling the role of structure and density in determining vertebral bone strength. Calcified Tissue Int, (61):474–479, 1997.
J.L. Kelley. General Topology. Van Nostrand, New York, 1955.
P. Urysohn. Über die Machtigheit der Zusammenhägen Mengen. Math. Ann., 94:262–295, 1925.
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© 1999 Springer-Verlag Berlin Heidelberg
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Eklund, P., Georgsson, F. (1999). Unraveling the Thrill of Metric Image Spaces. In: Bertrand, G., Couprie, M., Perroton, L. (eds) Discrete Geometry for Computer Imagery. DGCI 1999. Lecture Notes in Computer Science, vol 1568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49126-0_21
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DOI: https://doi.org/10.1007/3-540-49126-0_21
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