Piecewise-linear surface approximation from noisy scattered samples

Abstract

We consider the problem of approximating a smooth surface f(x, y), based on n scattered samples {(x/sub i/, y/sub i/, z/sub i/)/sub i=1//sup n/} where the sample values {z/sub i/} are contaminated with noise: z/sub i/=f(x/sub i/, y/sub i/)=/spl epsiv//sub i/. We present an algorithm that generates a PLS (piecewise linear surface) f', defined on a triangulation of the sample locations V={(x/sub i/, y/sub i/)/sub i=1//sup n/}, approximating f well. Constructing the PLS involves specifying both the triangulation of V and the values of f' at the points of V. We demonstrate that even when the sampling process is not noisy, a better approximation for f is obtained using our algorithm, compared to existing methods. This algorithm is useful for DTM (digital terrain map) manipulation by polygon-based graphics engines for visualization applications.<>