Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Function Approximation by Fusing Its Different Order Derivatives
Hajimu KAWAKAKIYasuaki KUROETakehiro MORI
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1996 Volume 9 Issue 5 Pages 210-218

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Abstract

Progress in recent sensor technology has inspired us to start research on recovering an object surface from depth data together with additional sensory information, i.e. data on its differential geometry or a priori knowledge about its smoothness. Any method for the recovery with both classes of the additional information, however, has not been proposed yet. Such a problem can be generalized to that of function approximation using its different order derivatives, which covers many important applications. To solve the problems generally, we propose a method of fusing all the information as follows : (1) To evaluate the smoothness and penalties for the derivative data of each order, we define a functional. (2) All the information are related to one another by restricting the fused results in the set of stationary functions of the functional. By the fusion, a new approximation is realized as the stationary function that minimizes all penalties simultaneously.

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