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, identically, and independently distributed. This noise model does not consider at least two types of anomalies encountered in sampling: a few large deviations in the data, often thought of as outliers, and a uniformly distributed error component arising from rounding and quantization. Estimates based on the least squares (LS) philosophy, appropriate under a Gaussian noise assumption, can be excessively influenced by such rogue observations. The theory of robust statistics formally addresses these problems and is efficiently used in a robust sequential estimator (RSE) of our own design. The RSE assigns different weights to each observation based on the maximum likelihood analysis when it is supposed that the errors follow a t distribution which, being heavy tailed, represents the outliers more realistically. This work extends this concept to several well known maximum-likelihood estimators (M-estimators). Since most M-estimators do not have a target distribution, the weights are obtained by a simple linearization and then embedded in the same RSE algorithm. We include experimental results over a variety of real and synthetic range imagery acquired from independent sources. We evaluate the performance of these estimators under different noise conditions. We highlight the effects of tuning constants and the necessity of simultaneous scale and parameter estimation. We emphasize the choice of the t distribution model because of its relative performance and simple mechanism for simultaneous scale estimation. We emphasize the potential application of this approach in simultaneous parametrization and surface-based range image segmentation.