 
Summary: Algorithms for the construction of invariant features ?
Hanns SchulzMirbach
Technische Universit¨at HamburgHarburg
Institut f¨ur Technische Informatik I
21071 Hamburg, Germany
Abstract. The paper presents algorithms for the construction of featu
res which are invariant with respect to a given transformation group. The
methods are based on integral calculus and are applicable to parametric
groups (Lie groups) and finite groups as well. To illustrate the concepts
we discuss in detail how to construct invariant features for the general
linear group which is of importance in computer vision applications. We
describe how to combine the algorithms with Hilbert space methods for
the description of continuous signals.
1 Introduction
The usual pattern recognition paradigm consists of the steps data acquisition,
preprocessing, feature extraction and classification. Features should describe pro
perties of the patterns which are important for classification. No general appli
cable theory for feature extraction is known. However, it has proven to be useful
(cf. [5, 4, 7]) to use invariance properties as a guideline. The basic idea is that it
is often possible to find transformations of the patterns which do not affect the
