Optimal interpolation and lp norm minimisation in colour indexing

Author: Finlayson Graham D.   Montagna Roberto  

Publisher: Society for Imaging Science and Technology

ISSN: 2166-9635

Source: Color and Imaging Conference, Vol.2008, Iss.1, 2008-01, pp. : 274-278

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Abstract

Colour has proven to be a very powerful feature for image indexing. There are many examples of image retrieval systems based on colour or chromaticity histograms in the literature, following on from the histogram intersection method of Swain and Ballard. In this paper, after proposing a compact representation of the chromaticity histogram, based on the Padua point interpolation, we try to verify which of its properties facilitates its good performance. The Padua point methodology has the property that a histogram is represented as a linear sum of a small number of polynomial basis functions. Further, the linear combination chosen bounds a certain maximum deviation as opposed to a leasts-quares criterion as used in previous work. Given this, we compare it directly to a method that uses a Chebyshev polynomial basis approximation of the histogram, found by minimising different lp norms of the error.The main result of this paper is to confirm the good performance of the Padua points and their superiority to other approximation methods based on the Chebyshev polynomials.