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https://open.uns.ac.rs/handle/123456789/5752
Title: | The discrete moments of the circles | Authors: | Žunić J. | Issue Date: | 1-Jan-1999 | Journal: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Abstract: | © Springer-Verlag Berlin Heidelberg 1999. The moment of (p,q)-order, mp,q(C), of a circle C given by (x-a)2 + (y-b)2 ≤ r2, is defined to be (Formula Presented). It is naturally to c assume that the discrete moments dmp,q(C), defined as (Formula Presented) can be a good approximation for mp,q(C). This paper gives an answer what is the order of magnitude for the difference between a real moment mp,q(C) and its approximation dmp,q(C), calculated from the corresponding digital picture. Namely, we estimate (Formula Presented) in function of the size of the considered circle C and its center position if p and q are assumed to be integers. These differences are upper bounded with (Formula Presented), where e is an arbitrary small positive number. The established upper bound can be understood as very sharp. The result has a practical importance, especially in the area of image processing and pattern recognition, because it shows what the picture resolution should be used in order to obtain a required precision in the parameter estimation from the digital data taken from the corresponded binary picture. | URI: | https://open.uns.ac.rs/handle/123456789/5752 | ISBN: | 3540656855 | ISSN: | 3029743 | DOI: | 10.1007/3-540-49126-0_4 |
Appears in Collections: | PMF Publikacije/Publications |
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