Novel diffusion based techniques for depth estimation and image restoration from defocused images

An intrinsic property of real aperture based imaging is the blurring of an observation due to defocus. There are two major aspects related to the defocus blur present in the image. The first aspect is based on use of the defocus blur for estimating the depth in the scene. The other aspect relates to restoration of the image. This problem manifests itself as a challenging blind, space varying deconvolution problem. In this thesis we explore diffusion based methods for depth estimation and image restoration from defocused observations. We are given two observations of a scene that are taken with different camera parameters and are defocused to different extents. We use the idea of defocus morphing in the spectral domain to define a defocus space of observations from the two observations given. The defocus morphing technique is obtained from the use of linear diffusion equation. Based on the defocus space we estimate depth in the scene and the pin-hole observation. The framework proposed demonstrates the equivalence between depth from defocus and depth from focus based techniques. Since the depth in the scene is varying, one has to use a local spectral morphing procedure using a windowed (short-term) Fourier transform. The windowing procedure introduces artifacts in the defocus morphing procedure. We therefore consider the defocus blur by evolving the heat equation in the spatial domain. The defocus blur can be estimated by evolving the diffusion equation in the spatial domain. This implies that the defocus blur kernel is Gaussian. However, on account of self occlusion and aperture artifacts there are deformations of the Gaussian point spread function. We therefore propose a stochastically perturbed diffusion model that implicitly handles the departure from the Gaussian assumption. We use stochastic level sets for propagating the stochastically perturbed diffusion and thereby estimating depth in the scene. An additional advantage of using this technique is that a global minimization procedure is adopted instead of a convex gradient descent technique. Thus problems of local minima are avoided in this technique. The models of linear diffusion and stochastically perturbed diffusion, however, do not