| Defocused images are a rich source of depth information. Several methods to extract depth from defocused images, generally known as "depth-from-defocus" (DFD) techniques, have been proposed recently. A new approach to DFD, that results in high-resolution depth-maps, is presented in this dissertation. In this method, a defocused image is viewed as the outcome of a combinatorial process, where a set of three-dimensional voxels, some in-focus and the others out-of-focus, are mapped via a two-dimensional projection to an image (pixel) plane. The restoration of depth information is realized by formulating the DFD process as a combinatorial optimization problem. A priori knowledge of the geometrical and optical properties of the object, such as finite size, smoothness, opacity, and coarse depth, is used to form constraints that reduce the ambiguity of the solution. Several constrained optimization techniques could be adapted to solve the depth restoration problem. The methods considered in this thesis are simulated annealing, Kaczmarz's row-action projections, and linear programming. These methods have been applied to several test objects. The results obtained using a combination of the Kaczmarz and the simulated annealing algorithm are shown to yield the best performance. A segmentation scheme that enables an efficient parallel implementation of the algorithms is also presented. The significant results of this research include (1) a new framework, referred to as depth restoration, for the recovery of high-resolution depth information from defocused images; (2) the analysis of discretized defocused image formation; (3) a new algorithm for multilevel depth recovery via stochastic surface evolutions. |
