Ph.D Thesis

Ph.D StudentZachevsky Ido
SubjectModels of Stochastic Textures and their Applications
in Image Processing
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROFESSOR EMERITUS Yehoshua Zeevi
Full Thesis textFull thesis text - English Version


Images are subject to various degradations such as blur, noise or resolution reduction. A prior model is required for reconstruction of such images. Image models traditionally rely on the piecewise-smoothness assumption. While this assumption is valid for many natural images, it ignores their important textural content.

Textures are what differentiates real-life images from cartoon-like image representations. The latter emphasize edges with smooth content in between the edges or contours, whereas the former contains important structural detailed information within the contours. Textures are found in scenery, aerial, medical and other types of images, and affect the image perception.

This study is devoted to a subset of random textures known as Natural Stochastic Textures (NST). Textures can, in general, be ordered along a spectrum, varying from completely regular to pure stochastic. Regular textures exhibit geometrical repetition of local structure. They can be modelled using periodic models. On the other hand, pure stochastic textures resemble noise in their frequency decomposition, and are, therefore, challenging to process in the presence of degradations.

Stochastic textures are best modelled as random processes, as their repetitive structures are characterized in the statistical sense. The main properties of NST are Gaussianity and self-similarity. The latter is a known property characteristic of images, but in random textures it is satisfied only statistically. An edge, for example, is self-similar in that it is expected to retain its appearance across scales. To compare with, a Brownian motion process is statistically self-similar in that it is expected to retain its variance across scales, but its sampled pixels do not exhibit the same structure.

The main property differentiating NST from regular textures and natural images is Gaussianity. While early classical models had considered images to be Gaussian, this turned out not to be the case, as natural images in general are strictly non-Gaussian due to their smooth areas and edge structure. However, we find that inspecting the subset of NST, Gaussianity emerges again. In this study we assess Gaussianity of NST using known image datasets and analyze them in the wavelet domain, as is common for natural images.

Using the fractional Brownian motion (fBm), a Gaussian and self-similar model, we propose denoising, deblurring, blind deblurring, super resolution and other algorithms for NST.

Some NST cannot be fully represented by a Gaussian model. The do contain, however, some structure that is still not suitable for natural images models. The complementary information for NST is encoded in the Fourier phase. We propose a local phase model for images and textures, that can be used in Bayesian frameworks for phase reconstruction.

We conclude this study by proposing a framework for embedding textures in low-dimensional spaces. This framework provides means of NST analysis and synthesis, showing that properties discussed in the former part of this study rise naturally by data-driven analysis. The framework makes it possible to synthesize new textures by using a combination of existing NST embedded in a low-dimensional space. We also show the intrinsic geometrical properties of the proposed manifold.