The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
Aalto

Extensions of Independent Component Analysis for Natural Image Data

Mika Inki

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Computer Science and Engineering for public examination and debate in Auditorium T2 at Helsinki University of Technology (Espoo, Finland) on the 10th of December, 2004, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-7363-2)   [1316 KB]
Dissertation is also available in print (ISBN 951-22-7362-4)

Abstract

An understanding of the statistical properties of natural images is useful for any kind of processing to be performed on them. Natural image statistics are, however, in many ways as complex as the world which they depict. Fortunately, the dominant low-level statistics of images are sufficient for many different image processing goals. A lot of research has been devoted to second order statistics of natural images over the years.

Independent component analysis is a statistical tool for analyzing higher than second order statistics of data sets. It attempts to describe the observed data as a linear combination of independent, latent sources. Despite its simplicity, it has provided valuable insights of many types of natural data. With natural image data, it gives a sparse basis useful for efficient description of the data. Connections between this description and early mammalian visual processing have been noticed.

The main focus of this work is to extend the known results of applying independent component analysis on natural images. We explore different imaging techniques, develop algorithms for overcomplete cases, and study the dependencies between the components by using a model that finds a topographic ordering for the components as well as by conditioning the statistics of a component on the activity of another. An overview is provided of the associated problem field, and it is discussed how these relatively small results may eventually be a part of a more complete solution to the problem of vision.

This thesis consists of an overview and of the following 7 publications:

  1. Mika Inki, 2003. ICA features of image data in one, two and three dimensions. Proceedings of the Fourth International Symposium on Independent Component Analysis and Blind Signal Separation (ICA 2003). Nara, Japan, 1-4 April 2003, pages 861-866. © 2003 by author.
  2. Mika Inki and Aapo Hyvärinen, 2002. Two approaches to estimation of overcomplete independent component bases. Proceedings of the International Joint Conference on Neural Networks (IJCNN 2002). Honolulu, Hawaii, USA, 12-17 May 2002, pages 454-459. © 2002 IEEE. By permission.
  3. Aapo Hyvärinen and Mika Inki, 2002. Estimating overcomplete independent component bases for image windows. Journal of Mathematical Imaging and Vision 17, number 2, pages 139-152. © 2002 Kluwer Academic Publishers. By permission.
  4. Aapo Hyvärinen, Patrik O. Hoyer and Mika Inki, 2001. Topographic independent component analysis. Neural Computation 13, number 7, pages 1527-1558.
  5. Mika Inki, 2003. Examining the dependencies between ICA features of image data. Proceedings of the 13th International Conference on Artificial Neural Networks / 10th International Conference on Neural Information Processing (ICANN/ICONIP 2003). Istanbul, Turkey, 26-29 June 2003, pages 298-301. © 2003 by author.
  6. Mika Inki, 2004. A model for analyzing dependencies between two ICA features in natural images. Proceedings of the Fifth International Conference on Independent Component Analysis and Blind Signal Separation (ICA 2004). Granada, Spain, 22-24 September 2004, pages 914-921. © 2004 Springer-Verlag. By permission.
  7. Mika Inki, 2004. Natural image patch statistics conditioned on activity of an independent component. Helsinki University of Technology, Publications in Computer and Information Science, Report A79. Espoo, Finland, 28 pages. © 2004 by author.

Keywords: independent component analysis, latent variable models, natural image data, overcomplete models, topographic mapping, higher order structures

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© 2004 Helsinki University of Technology

Last update 2011-05-26