|Title:||Least squares fitting of digital polynomial segments||Journal:||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)||Volume:||1176||First page:||17||Last page:||23||Conference:||6th International Workshop on Discrete Geometry for Computer Imagery, DGCI 1996; Lyon; France; 13 November 1996 through 15 November 1996||Issue Date:||1-Jan-1996||ISBN:||978-3-540-62005-1||ISSN:||0302-9743||DOI:||10.1007/3-540-62005-2_2||Abstract:||
It is proved that digital polynomial segments and their least squares polynomial fits are in one-to-one correspondence. This enables an efficient representation of digital polynomial segments by n+3 parameters, under the condition that an upper bound, say n, for the degrees of the digitized polynomials is assumed. One of such representations is (x 1, m, an, an−1,…, a 0), where x 1 and m are the x-coordinate of the left endpoint and the number of digital points, respectively, while a n, a n−1,..., a 0 are the coefficients of the least squares polynomial fit Y=a nXn+an− 1Xn−1+ ...+a0, for a given digital polynomial segment.
|Keywords:||Coding | Computer vision | Digital polynomial segment | Image processing | Least squares fitting||Publisher:||Springer Link|
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