The "enhanced spectrum" of an image g[.] is a function h[.] of wave-number u obtained by a sequence of operations on the power spectral density of g[.]. The main properties and the available theorems on the correspondence between spectrum enhancement and spatial differentiation, of either integer or fractional order, are stated. In order to apply the enhanced spectrum to image classification, one has to go, by interpolation, from h[.] to a polynomial q[.]. The graph of q[.] provides the set of morphological descriptors of the original image, suitable for submission to a multivariate statistical classifier. Since q[.] depends on an n-tuple, ψ, of parameters which control image pre-processing, spectrum enhancement and interpolation, then one can train the classifier by tuning ψ. In fact, classifier training is more articulated and relies on a "design", whereby different training sets are processed. The best performing n-tuple, ψ*, is selected by maximizing a "design-wide" figure of merit. Next one can apply the trained classifier to recognize new images. A recent application to materials science is summarized. © 2009 Copyright SPIE - The International Society for Optical Engineering.

Crosta, G. (2010). Image analysis and classification by spectrum enhancement: new developments. In J.T. Astola, K.O. Egiazarian (a cura di), Image Processing: Algorithms and Systems VIII (pp. 75320L-01-75320L-12). Bellingham, WA : SPIE [10.1117/12.838694].

Image analysis and classification by spectrum enhancement: new developments

CROSTA, GIOVANNI FRANCO FILIPPO
2010

Abstract

The "enhanced spectrum" of an image g[.] is a function h[.] of wave-number u obtained by a sequence of operations on the power spectral density of g[.]. The main properties and the available theorems on the correspondence between spectrum enhancement and spatial differentiation, of either integer or fractional order, are stated. In order to apply the enhanced spectrum to image classification, one has to go, by interpolation, from h[.] to a polynomial q[.]. The graph of q[.] provides the set of morphological descriptors of the original image, suitable for submission to a multivariate statistical classifier. Since q[.] depends on an n-tuple, ψ, of parameters which control image pre-processing, spectrum enhancement and interpolation, then one can train the classifier by tuning ψ. In fact, classifier training is more articulated and relies on a "design", whereby different training sets are processed. The best performing n-tuple, ψ*, is selected by maximizing a "design-wide" figure of merit. Next one can apply the trained classifier to recognize new images. A recent application to materials science is summarized. © 2009 Copyright SPIE - The International Society for Optical Engineering.
Capitolo o saggio
fractional differentiation; Fourier analysis; multivariate statistics; image understanding
English
Image Processing: Algorithms and Systems VIII
Astola, JT; Egiazarian, KO
2010
978-081947925-9
7532
SPIE
75320L-01
75320L-12
75320L
Crosta, G. (2010). Image analysis and classification by spectrum enhancement: new developments. In J.T. Astola, K.O. Egiazarian (a cura di), Image Processing: Algorithms and Systems VIII (pp. 75320L-01-75320L-12). Bellingham, WA : SPIE [10.1117/12.838694].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/9350
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