Piecewise-linear surface approximation from noisy scattered samples

摘要

We consider the problem of approximating a smooth surface f(x,y), based on n scattered samples {(xi, yi, zi)ⁿi=1} where the sample values {zi} are contaminated with noise: zi = f(xi, yi) + εi. We present an algorithm that generates a PLS (Piecewise Linear Surface) f¹, defined on a triangulation of the sample locations V = {(xi, yi)ⁿi=1}, approximating f well. Constructing the PLS involves specifying both the triangulation of V and the values of f¹ 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.