Estimation of surface parameters using orthogonal distance criterion

Fitting surfaces to 3-D data is one of the basic methods for surface description for 3-D vision. Most techniques of surface fitting proposed in the literature are “least-squares”-based that rarely produce satisfactory results if a certain level of noise is present in the data or if the data points are locally sampled from a small area. We propose a new approach that minimizes the mean squared approximate orthogonal distances with linearization using the Newton iteration method. This approach usually yields a good fit and the algorithm is reliable and efficient for real applications. Results are reported for one of the real range images that we have experimented. The results demonstrate that the approximate orthogonal distance performs better than the least squares based methods