Eliminating extrapolation using point distribution criteria in scattered data interpolation

Abstract

Extrapolation off the boundaries of scattered data is an intrinsic feature of interpolation. However, extrapolation causes serious problems in stereo-vision and mapping, which has not been investigated carefully. In this paper, we present novel schemes to eliminate the extrapolation effects. We choose a sample application of the generation of a digital elevation model (DEM) to demonstrate the development of the schemes and to assess their performance. As a first step, we devise point distribution criteria, namely COG (center-of-gravity) and ECI (empty-center-index), and apply rigorous and robust elimination based on the criteria. The COG and ECI criteria exploit the characteristics of extrapolation, that scattered points are distributed unevenly or on the edge of a search disc of interpolation. Next, the hole-fill segmentation counterbalances excessive elimination by the COG and ECI elimination. Finally, the noise-remove segmentation compensates for incomplete performance of the COG and ECI elimination. The qualitative and quantitative assessments of the final DEMs reveal that extrapolation effects have been eliminated successfully. Compared with other methods, the proposed schemes are computationally fast and applicable to a wide range of interpolation techniques.