Parametric estimation of multi-dimensional affine transformations: An exact linear solution

Rami Hagege, Joseph M. Francos

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

We consider the general framework of planar object recognition based on a set of known templates. While the set of templates is known, the tremendous set of possible affine transformations that may relate the template and the observed signature, makes any detection and recognition problem ill-defined unless this variability is taken into account. Given an observation on one of the known objects, subject to an unknown affine transformation of it, our goal is to estimate the deformation that transforms some pre-chosen representation of this object (template) into the current observation. The direct approach for estimating the transformation is to apply each of the deformations in the affine group to the template in search for the deformed template that matches the observation. We propose a method that employs a set of non-linear operators to replace this high dimensional problem by an equivalent linear problem, expressed in terms of the unknown affine transformation parameters. This solution is further extended to include the case where the deformation relating the observed signature of the object and the template is composed both of the geometric deformation due to the affine transformation of the co-ordinate system and a constant illumination change. The proposed solution is unique and exact and is applicable to any affine transformation regardless of the magnitude of the deformation.

Original languageEnglish
Title of host publication2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05 - Proceedings - Image and Multidimensional Signal Processing Multimedia Signal Processing
PagesII861-II864
DOIs
StatePublished - 1 Dec 2005
Event2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05 - Philadelphia, PA, United States
Duration: 18 Mar 200523 Mar 2005

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
VolumeII
ISSN (Print)1520-6149

Conference

Conference2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05
Country/TerritoryUnited States
CityPhiladelphia, PA
Period18/03/0523/03/05

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