Computing point-set surfaces with controlled spatial variation of residuals

This paper presents an accurate method for computing point-set surfaces from input data that can suppress the noise effect in the resulting point-set surface. This is accomplished by controlling spatial variation of residual errors between the input data and the resulting point-set surface and offsetting any systematic bias. More specifically, this method first reduces random noise of input data based on spatial autocorrelation statistics: the statistics Z via Moran’s I. The bandwidth of the surface is adjusted until the surface reaches desired value of the statistics Z corresponding to a given significance level. The method then compensates for potential systematic bias of the resultant surface by offsetting along computed normal vectors. Computational experiments on various point sets demonstrate that the method leads to an accurate surface with controlled spatial variation of residuals and reduced systematic bias.