<title>Analysis of defocused image data for 3D shape recovery using a regularization technique</title>

Abstract

The reconstruction of three-dimensional (3D) information from defocused image data is formulated as an inverse-problem that is solved through a regularization technique. The technique is based on modeling the sensing of defocused images in a camera system using a three-dimensional (3D) point spread function (PSF). Many images are acquired at different levels of defocus. The difference (mean-square error) between this acquired image data and the estimated image data corresponding to an initial solution for 3D shape is minimized. The initial solution for 3D shape is obtained from a focus and defocus analysis approach. A regularization approach that uses a smoothness constraint is proposed to improve this initial solution iteratively. The performance of this approach is compared with two other approaches: (1) gradient descent based on planar surface patch approximation, and (2) a local error minimization based on a limited search. We exploit some constraints such as the positivity of image brightness unique to this problem in the optimization procedure. Our experiments show that the regularization approach performs better than the other two and that high accuracy is attainable with relatively moderate computation. Experimental results are demonstrated for geometric optics model of 3D PSF on simulated image data.