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

100%

Sit A. , Mitchell J. C. , Phillips G. N. , Wright S. J.

Molecular Based Mathematical Biology

2013

tom 1

75-89

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.

Visual acuity with computer simulated and lens-induced astigmatism

86%

Remón L. , Benlloch J. , Pons A. , Monsoriu J. A. , Furlan W. D.

Optica Applicata

2014

tom Vol. 44, nr 4

521--531

The relationship between spherical and astigmatic refractive errors and their associated visual acuity is investigated in this work by means of two different approaches. In the first one, different refractive errors were induced in normal subjects by trial lenses. In the second one, defocused images were simulated numerically by the optical transfer function of a model eye and then judged by the same subjects. The amount of defocus (measured in terms of the modulus of the dioptric power vector) necessary to reduce the visual acuity to 0.1 logMAR and to 0.4 logMAR was computed with each method and then compared. We found that the visual system is clearly more tolerant to lens-induced defocus than for the computer simulated one. However, no significant differences in visual acuity were found for astigmatism of the same power but different axes in each method.