Performance Analysis of Maximum Likelihood Estimator for Recovery of Depth from Defocused Images and Optimal Selection ofCamera Parameters

Abstract

The recovery of depth from defocused images involves calculating the depth of various points in a scene by modeling the effect that the focal parameters of the camera have on images acquired with a small depth of field. In the existing methods on depth from defocus (DFD), two defocused images of a scene are obtained by capturing the scene with different sets of camera parameters. Although the DFD technique is computationally simple, the accuracy is somewhat limited compared to the stereo algorithms. Further, an arbitrary selection of the camera settings can result in observed images whose relative blurring is insufficient to yield a good estimate of the depth. In this paper, we address the DFD problem as a maximum likelihood (ML) based blur identification problem. We carry out performance analysis of the ML estimator and study the effect of the degree of relative blurring on the accuracy of the estimate of the depth. We propose a criterion for optimal selection of camera parameters to obtain an improved estimate of the depth. The optimality criterion is based on the Cramer-Rao bound of the variance of the error in the estimate of blur. A number of simulations as well as experimental results on real images are presented to substantiate our claims.