A robust variable order facet model for image data

The underlying piecewise continuous surface of a digital image can be estimated through robust statistical procedures. This paper contains a systematic Monte Carlo study of M estimation and LMS estimation for image surface approximation, an examination of the merits of postprocessing and tuning various parameters in the robust estimation procedures, and a new robust variable order facet model paradigm. Several new goodness-of-fit measures are introduced and systematically compared. We show that the M estimation tuning parameters are not crucial, postprocessing is cheap and well worth the cost, and the robust algorithm for variable order facet models (using M estimation, new statistical goodness-of-fit measures, and postprocessing) manages to retain most of the statistical efficiency of M estimation, yet displays good robustness properties, and preserves the main geometric features of an image surface: step edges, roof edges, and corners.