Feature point based methods for the estimation of three dimensional motion parameters

There are various problems associated with estimating the motion of an object. We address the following in this thesis: (a) presence of sensor noise in both frames, (b) difficulty in obtaining an optimal solution while processing a long sequence of data, (c) possible mismatches in feature point corresondences, (d) need for pre-establishing such correspondences and (e) occlusion of features during successive time instants. The applicability of the total least squares (TLS) model is investigated in improving the accuracy of the estimate. The error covariances for the TLS estimate are found to be very close to the corresponding Cramer-Rao lower bound when the perturbations in both frames are independent and normally distributed. We also develop an optimal recursive motion estimation scheme for the processing of a long sequence of noisy data. We pose the sequential TLS method as an iterative subspace updating problem, and obtain a computationally efficient algorithm. The TLS model assumes point correspondences between frames, which may, however, be established with limited accuracy only. To alleviate the problem caused by such outliers, we propose the use of the least median of squares (LMEDS) estimator in conjuction with the TLS model. The robust estimates of the motion parameters are obtained by minimizing the median of the squared orthogonal residuals. The computational requirement for the LMEDS estimator is drastically reduced by using a Monte-Carlo sampling technique. We obtain a closed form solution for the motion parameters from range data when only subset correspondences of feature points are available, and a nonlinear solution when no such corresondences have been established. These methods require matching spatial moments of various orders of the available sets of points at two different time instants. In order to circumvent the above problem, we present a method for 3-D motion recovery in which there need not exist any point correspondence between frames and which may allow occlusion of features. The proposed method is based on the interpolation of sparse range data. A fast method of obtaining a dense depth map of the smooth surface is developed. (Abstract shortened with permission of author.)