Group Theoretical Methods in Image Processing

  title={Group Theoretical Methods in Image Processing},
  author={Reiner Lenz},
  booktitle={Lecture Notes in Computer Science},
  • R. Lenz
  • Published in
    Lecture Notes in Computer…
    7 March 1990
  • Mathematics
Preliminaries.- Representations of groups.- Representations of somes matrix groups.- Fourier series on compact groups.- Applications. 

Group-Theoretical Structure in Multispectral Color and Image Databases

Understanding the structure of the spaces of nonnegative signals is of interest in many different areas because many applications lead to signals with nonnegative function values.

Symmetries, Automorphisms and Groups

In this chapter we see how group theory enters in an explicit manner in the study of symmetry, and in what way the connections between group theory and symmetry are relevant to the study of signals

General Theory of Image Normalization

We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the

Image representation based on the affine symmetry group

  • A. Calway
  • Mathematics
    Proceedings of 3rd IEEE International Conference on Image Processing
  • 1996
The representation of 2-D signals which are symmetric under the affine group of transformations is considered. An extension of the multiresolution Fourier transform (MFT) is presented and shown to

G-Lets: Signal Processing Using Transformation Groups

An algorithm using transformation groups and their irre-ducible representations to generate an orthogonal basis for a signal in the vector space of the signal, showing that multiresolution analysis can be done with amplitudes using a transformation group and that a multiresolved and multiscale analysis for each resolution is possible in terms of frequencies.

Nonstationary texture modeling by G-invariant random fields

The Cholesky factorization is applied for the synthesis of random fields showing this generalized invariance property of second-order stationarity to the second- order invariance under a group of transforms.

Symmetry and Locality in Image Representation

The way in which symmetry and locality affect the choice of an image representation is described and a number of applications of the ideas to problems such as image segmentation and motion estimation are described briefly.

Some Applications of Representaions of Lie Algebras and Lie Groups

This paper describes iterative algorithms to normalize coefficient vectors computed by expanding functions on the unit sphere into a series of spherical harmonics which can be used to linearize highly-non-linear problems.