A complete system of measurement invariants for Abelian lie transformation groups

Yaron Gvili, Nir Sochen

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We present a complete system of functionally independent invariants for Abelian Lie transformation groups acting on an image. The invariants are based on measurements, given by inner product of predesigned functions and the image. We build on steerable filters and adopt a Lie theoretical approach that is applicable to any dimensionality. A complete characterization of Lie measurement invariants of a general irreducible component of the group, termed block invariants, is provided. We show that invariants for the entire group can be taken as the union of the invariants of its components. The system is completed by deriving invariants between components of the group, termed cross invariants.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsLewis D. Griffin, Martin Lillholm
PublisherSpringer Verlag
Pages72-85
Number of pages14
ISBN (Print)354040368X
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2695
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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