区分的3次関数を用いた2次元データの平滑化の自動的方法

概要

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A method is described for smoothing two-dimensional data by a least squares fitting with a piecewise bicubic polynomial of class C^1. The number of knots and their positions are determined automatically. A condition for the good positions of knots is introduced. The condition is based on the fact that if the partial second derivatives of the underlying function of data are sufficiently close to those of the approximating function, we can obtain a good approximation. The values of the partial second derivatives are estimated from data. The estimated values of the partial second derivatives are approximated by a discontinuous piecewise linear function. The positions of knots are determined using the breakpoints of this function. The number of knots is decided by use of an information theoretical criterion (AIC).
一般社団法人情報処理学会の論文
1977-02-15