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A fast algorithm for orthogonalizing polynomials on an arbitrarily shaped region (revised version)

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Abstract
Segmented image coding segments an image into non-rectangular regions and approximates the texture in each region by a weighted sum of orthonormal base functions. These orthonormal base functions, which are region-specific, used to be generated by the Gram-Schmidt (GS) algorithm, which is unfortunately very time-consuming. This paper presents the polynomial recursive orthogonalization (PRO) algorithm which generates the same orthonormal base functions as GS, but which is faster than GS because it is based on a recurrence which has fewer terms than the corresponding GS equation. The paper presents theoretical and experimental results which show that PRO is two to three times faster in practice (depending on the number of computed base functions).
Keywords
segmented image-coding, orthogonalizing polynomials, PRO, fast algorithm, WEAKLY SEPARABLE BASES, IMAGE

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MLA
Philips, Wilfried. “A Fast Algorithm for Orthogonalizing Polynomials on an Arbitrarily Shaped Region (Revised Version).” MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, vol. 8, no. 4, 1997, pp. 409–21, doi:10.1023/A:1008208408359.
APA
Philips, W. (1997). A fast algorithm for orthogonalizing polynomials on an arbitrarily shaped region (revised version). MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, 8(4), 409–421. https://doi.org/10.1023/A:1008208408359
Chicago author-date
Philips, Wilfried. 1997. “A Fast Algorithm for Orthogonalizing Polynomials on an Arbitrarily Shaped Region (Revised Version).” MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 8 (4): 409–21. https://doi.org/10.1023/A:1008208408359.
Chicago author-date (all authors)
Philips, Wilfried. 1997. “A Fast Algorithm for Orthogonalizing Polynomials on an Arbitrarily Shaped Region (Revised Version).” MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 8 (4): 409–421. doi:10.1023/A:1008208408359.
Vancouver
1.
Philips W. A fast algorithm for orthogonalizing polynomials on an arbitrarily shaped region (revised version). MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING. 1997;8(4):409–21.
IEEE
[1]
W. Philips, “A fast algorithm for orthogonalizing polynomials on an arbitrarily shaped region (revised version),” MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, vol. 8, no. 4, pp. 409–421, 1997.
@article{184878,
  abstract     = {{Segmented image coding segments an image into non-rectangular regions and approximates the texture in each region by a weighted sum of orthonormal base functions. These orthonormal base functions, which are region-specific, used to be generated by the Gram-Schmidt (GS) algorithm, which is unfortunately very time-consuming. This paper presents the polynomial recursive orthogonalization (PRO) algorithm which generates the same orthonormal base functions as GS, but which is faster than GS because it is based on a recurrence which has fewer terms than the corresponding GS equation. The paper presents theoretical and experimental results which show that PRO is two to three times faster in practice (depending on the number of computed base functions).}},
  author       = {{Philips, Wilfried}},
  issn         = {{0923-6082}},
  journal      = {{MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING}},
  keywords     = {{segmented image-coding,orthogonalizing polynomials,PRO,fast algorithm,WEAKLY SEPARABLE BASES,IMAGE}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{409--421}},
  title        = {{A fast algorithm for orthogonalizing polynomials on an arbitrarily shaped region (revised version)}},
  url          = {{http://dx.doi.org/10.1023/A:1008208408359}},
  volume       = {{8}},
  year         = {{1997}},
}

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