Comparison and Evaluation of First Derivatives Estimation

摘要

Computing derivatives from observed integral data is known as an ill-posed inverse problem. The ill-posed qualifier refers to the noise amplification that can occur in the numerical solution if appropriate measures are not taken (small errors for measurement values on specified points may induce large errors in the derivatives). For example, the accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution, affecting the accuracy of segmentation methods. In our case, we want to obtain an upper airways segmentation, so it is necessary to compute the first derivatives as accurately as possible, in order to use gradient-based segmentation techniques. For this reason, the aim of this paper is to present a comparative analysis of several methods (finite differences, interpolation, operators and regularization), that have been developed for numerical differentiation. Numerical results are presented for artificial and real data sets.