PERFORMANCE EVALUATION OF A CLASS OF M-ESTIMATORS FOR SURFACE PARAMETER-ESTIMATION IN NOISY RANGE DATA

Depth maps are frequently analyzed as if the errors are normally, iden tically, and independently distributed. This noise model does not cons ider at least two types of anomalies encountered in sampling: a few la rge deviations in the data, often thought of as outliers, and a unifor mly distributed error component arising from rounding and quantization . Estimates based on the least squares (LS) philosophy, appropriate un der a Gaussian noise assumption, can be excessively influenced by such rogue observations. The theory of robust statistics formally addresse s these problems and is efficiently used in a robust sequential estima tor (RSE) of our own design. The RSE assigns different weights to each observation based on the maximum likelihood analysis when it is suppo sed that the errors follow a t distribution which, being heavy tailed, represents the outliers more realistically. This work extends this co ncept to several well known maximum-likelihood estimators (M-estimator s). Since most M-estimators do not have a target distribution, the wei ghts are obtained by a simple linearization and then embedded in the s ame RSE algorithm. We include experimental results over a variety of r eal and synthetic range imagery acquired from independent sources. We evaluate the performance of these estimators under different noise con ditions. We highlight the effects of tuning constants and the necessit y of simultaneous scale and parameter estimation. We emphasize the cho ice of the t distribution model because of its relative performance an d simple mechanism for simultaneous scale estimation. We emphasize the potential application of this approach in simultaneous parametrizatio n and surface-based range image segmentation.