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 (RSFA) approach is developed to compute the parameters of surfaces in noisy range data, modeled by a linear set of parameters. At the heart of our scheme is the Robust Sequential Estimator (RSE) whose basic philosophy is to compute the parameters using the entire data set belonging to a surface patch without sacrificing speed and to model the errors by a heavy tailed distribution to handle the Gaussian noise and the outliers br extreme deviations, simultaneously. Given a seed point on the object surface, the algorithm obtains a least squares estimates of the parameter vector in a small neighborhood. Robustification of the estimated parameters is carried out using iteratively reweighted least squares (IRLS), The weights are obtained by maximum likelihood (ML) analyses when it is supposed that, rather than following a normal distribution, the errors follow a t-distribution having degree of freedom f. With the robust initial estimates, the RSE grows the surface until it encounters another surface whose data points are regarded as outliers with respect to the current surface data and hence are rejected. We demonstrate the accuracy, speed of convergence, and immunity to large deviations of a t distribution model by comparing its performance with the least squares (LS) and Least Median of Squares (LMS). We demonstrate the potential application of our scheme in simultaneous parameterization and organization of surfaces in noisy, outlier ridden real data.