A FAST SEQUENTIAL APPROACH TO ROBUST SURFACE PARAMETER-ESTIMATION

In this paper we pose the problem of surface curvature computation as parameter estimation. A robust sequential functional approximation (RS FA) approach is developed to compute the parameters of surfaces in noi sy range data, modeled by a linear set of parameters. At the heart of our scheme is the Robust Sequential Estimator (RSE) whose basic philos ophy is to compute the parameters using the entire data set belonging to a surface patch without sacrificing speed and to model the errors b y a heavy tailed distribution to handle the Gaussian noise and the out liers br extreme deviations, simultaneously. Given a seed point on the object surface, the algorithm obtains a least squares estimates of th e parameter vector in a small neighborhood. Robustification of the est imated parameters is carried out using iteratively reweighted least sq uares (IRLS), The weights are obtained by maximum likelihood (ML) anal yses when it is supposed that, rather than following a normal distribu tion, the errors follow a t-distribution having degree of freedom f. W ith the robust initial estimates, the RSE grows the surface until it e ncounters another surface whose data points are regarded as outliers w ith respect to the current surface data and hence are rejected. We dem onstrate the accuracy, speed of convergence, and immunity to large dev iations of a t distribution model by comparing its performance with th e least squares (LS) and Least Median of Squares (LMS). We demonstrate the potential application of our scheme in simultaneous parameterizat ion and organization of surfaces in noisy, outlier ridden real data.