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Algorithms for the construction of invariant features ? Hanns SchulzMirbach

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


Source: Albert-Ludwigs-Universität Freiburg, Institut für Informatik,, Lehrstuhls für Mustererkennung und Bildverarbeitung


Collections: Computer Technologies and Information Sciences