Titlebook: Variational Regularization of 3D Data; Experiments with MAT Hebert Montegranario,Jairo Espinosa Book 2014 The Author(s) 2014 MATLAB.Tikhono

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BANAL

Optometrist

Function Spaces and Reconstruction,ill be a particular method to obtain or define this function, many of them are included in the theory of function spaces. In this chapter we will see the alphabet that permit us to understand the language for the rest of the book. The basic idea is to consider functions as simple points that behaves

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Interpolation. From One to Several Variables,itations of the classical Lagrange interpolation and the way splines may help to a better formulation of the problem and the concrete algorithm to solve it. Here the reader will see how to apply the abstract theory of function spaces, both in the problem of curve reconstruction and its generalizatio

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finale

Regularization and Inverse Theory, splines. Inverse theory is one of the great achievements of applied mathematics and its applications are at the core of modern technology. Thus we formulate the theory in general terms and then, to the interpolation problem.

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3D Interpolation and Approximation, particular we deal with 3D data. As a consequence of interpolation and smoothness conditions we obtain by a constructive proof, the Thin Plate Spline (TPS), whose explicit expression is given in terms of a convolution with the fundamental solutions of the biharmonic differential operator. In this c

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Radial Basis Functions,ta. The general interpolation and smoothing problems are described in terms of radial basis functions; we then illustrate some characterizations of these functions. The theory is applied to noisy data by tuning the regularization parameter with generalized cross validation and we finally give some e