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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.

Statistical analysis of diabetes mellitus

86%

Drygas H.

Discussiones Mathematicae Probability and Statistics

2009

tom 29

nr 1

69-90

This paper deals with an application of regression analysis to the regulation of the blood-sugar under diabetes mellitus. Section 2 gives a description of Gram-Schmidt orthogonalization, while Section 3 discusses the difference between Gauss-Markov estimation and Least Squares Estimation. Section 4 is devoted to the statistical analysis of the blood-sugar during the night. The response change of blood-sugar is explained by three variables: time, food and physical activity ("Bewegung"). At the beginning of the section it is shown that the proposed method was very successful in 2007.