# An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids

• Volume: 1, page 75-89
• ISSN: 2299-3266

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## Abstract

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Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.

## How to cite

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Atilla Sit, et al. "An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids." Molecular Based Mathematical Biology 1 (2013): 75-89. <http://eudml.org/doc/267024>.

@article{AtillaSit2013,
abstract = {Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.},
author = {Atilla Sit, Julie C Mitchell, George N Phillips, Stephen J Wright},
journal = {Molecular Based Mathematical Biology},
keywords = {Zernike polynomials; 3D shape retrieval; reconstruction; Gram-Schmidt orthogonalization; Electron Microscopy Data Bank; electron microscopy data bank},
language = {eng},
pages = {75-89},
title = {An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids},
url = {http://eudml.org/doc/267024},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Atilla Sit
AU - Julie C Mitchell
AU - George N Phillips
AU - Stephen J Wright
TI - An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids
JO - Molecular Based Mathematical Biology
PY - 2013
VL - 1
SP - 75
EP - 89
AB - Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.
LA - eng
KW - Zernike polynomials; 3D shape retrieval; reconstruction; Gram-Schmidt orthogonalization; Electron Microscopy Data Bank; electron microscopy data bank
UR - http://eudml.org/doc/267024
ER -

## References

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