Authors: Žunić, Joviša 
Title: The discrete moments of the circles
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 1568
First page: 41
Last page: 49
Conference: 8th International Conference on Discrete Geometry for Computer Imagery, DGCI 1999; Marne-la-Vallee; France; 17 March 1999 through 19 March 1999
Issue Date: 1-Jan-1999
Rank: M21
ISBN: 978-3-540-65685-5
ISSN: 0302-9743
DOI: 10.1007/3-540-49126-0_4
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.
Keywords: Digital geometry | Discrete shapes | Parameter estimation
Publisher: Springer Link

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