Comparison of B-spline and Zernike fitting techniques in complex wavefront surfaces

Abstract

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3D Face Recognition by Functional Data Analysis

“…The following equation provides a relationship between these parameters and the number of control points n + 1, defined in Eq. 2 [1]:…”

“…One of the main features of these bases is their orthogonality [1], which implies total linear independence among each mode and the others. In the case of a discrete domain, orthogonality is fulfilled only approximately.…”

“…The Bivariate Splines -The B-spline surfaces are a generalization of the univariate B-spline curves, with the simplest generalization obtained by a tensor product of univariate B-splines [15]. The main advantage of B-splines in representing surfaces of high local variability is their intrinsic zonal character [1]. The B-splines are polynomial curves of degree k − 1 along each interval [t j , t j+1 ]; products of such functions are polynomial surfaces of degree (…”

“…Then, the cloud of points of a scan is regarded as providing samples of a surface modeled by a function over a spatial domain. Based on the characteristics of the data and the results of state of the art studies [1], Bivariate Splines [9] on a rectangular domain, and Zernike polynomials [12] on a circular domain, together with their local counterparts on multi-rectangles and annular supports [10], have been considered as basis functions to model this type of data. In all the cases, the functions are fitted to the 3D data by using the least squares method.…”