On Texture and Geometry in Image Analysis – Københavns Universitet

On Texture and Geometry in Image Analysis

Ph.d forsvar ved David Gustavsson, The Image Group, Department of Computer Science, Copenhagen University


Images are composed of geometric structure and texture. Large scale structures are considered to be the geometric structure, while small scale details are considered to be the texture.

In this dissertation, we will argue that the most important difference between geometric structure and texture is not the scale - instead, it is the requirement on representation or reconstruction. Geometric structure must be reconstructed exactly and can be represented sparsely.

Texture does not need to be reconstructed exactly, a random sample from the distribution being sufficient. Furthermore, texture can not be represented sparsely. In image inpainting, the image content is missing in a region and should be reconstructed using information from the rest of the image.

The main challenges in inpainting are: prolonging and connecting geometric structure and reproducing the variation found in texture. We argue that many 'textures' contain details that must be inpainted exactly.

Simultaneous reconstruction of geometric structure and texture is a difficult problem, therefore, a two-phase reconstruction procedure is proposed.

A method for measuring and quantifying the image content in terms of geometric structure and texture is proposed. It is assumed that geometric structures can be represented sparsely, while texture can not. Reversing the argumentation, we argue that if the image can be represented sparsely then it contains mainly geometric structure, and if it cannot be represented sparsely then it contains texture. The degree of geometric structure is determined by the sparseness of the representation.

The image content does not depend solely on the objects in the scene, but also on the viewing distance. Increasing the viewing distance influences the image content in two different ways. As the viewing distance increases, details are suppressed because the inner scale also increases. By increasing the viewing distance, the spatial lay-out of the captured scene will also change. How much of the visual appearance in terms of geometry and texture of an image can be explained by the classical results from natural image statistics?

Instructors: Kim Steenstrup Pedersen, DIKU and Mads Nielsen, DIKU

Luc Florac, Professor, Department of Mathematics and Computer Science and  Department of Biomedical Engineering, Eindhoven University of Technology.
YingnianWu, Professor, Department of Statistics, University of California
Jon Sporring, Associate Professor, University of Copenhagen, Chairman