Finite precision error analysis of Zernike moments computation schemes and a new, efficient, robust recursive algorithm

Here, a new approach is introduced that tackles the problem of the quantization error generation and accumulation in any algorithm. This approach offers understanding of the actual cause of generation of finite precision error and the exact tracking of the number of erroneous digits accumulated in a...

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Bibliographic Details
Published in:Digital signal processing Vol. 79; pp. 75 - 90
Main Authors: Chalatsis, Constantinos, Papaodysseus, Constantin, Arabadjis, Dimitris, Giannopoulos, Fotios
Format: Journal Article
Language:English
Published: Elsevier Inc 01.08.2018
Subjects:
Finite precision error
Polar pixels
Quantization error
Recursive computation of Zernike polynomials
Zernike moments
Zernike radial polynomials
Zernike radial polynomials
Zernike moments
Finite precision error
Quantization error
Polar pixels
Recursive computation of Zernike polynomials
ISSN:1051-2004, 1095-4333
Online Access:Get full text
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Summary:Here, a new approach is introduced that tackles the problem of the quantization error generation and accumulation in any algorithm. This approach offers understanding of the actual cause of generation of finite precision error and the exact tracking of the number of erroneous digits accumulated in all quantities of any algorithm. This approach is applied in the study of popular algorithms evaluating Zernike radial polynomials and moments. The actual sources of the finite precision error in these algorithms are identified and the exact amount of the corresponding numerical error is evaluated. It is shown that, as far as Zernike moments are concerned, this error is independent of the content of the image; it instead depends on the nature of the employed algorithm, the shape of the pixels and the image dimensions. Subsequently, a new, fast, recursive algorithm for the computation of the Polar Zernike polynomials and moments is introduced. The proposed algorithm generates particularly small geometric and integration errors, due to the employed shape of the pixels and the associated recursive relations; it also manifests a considerable resistance to finite precision error. Thus, the algorithm may be applied to high dimensions images (e.g. 2048×2048) and correspondingly large Pmax.
ISSN:1051-2004
1095-4333
DOI:10.1016/j.dsp.2018.04.004