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Invariant representation of image functions under gamma correction and similarity transformations Siebert, Andreas

Abstract

This work focuses on image retrieval and recognition in environments where the images are subject to a non-linear brightness change known in image processing as gamma correction. Our empirical data shows that gamma correction changes images significantly, resulting in poor retrieval results if not addressed. The proposed solution is based on a novel differential invariant under this kind of radiometric transformation. Since imaged objects are often subject not only to radiometric changes but also to variations of the scene geometry, we propose a representation of two-dimensional image functions that is simultaneously invariant under gamma correction and some geometric transformations, namely translation, rotation, and scaling. An implementation of the proposed invariants based on derivatives of the Gaussian is given. For gamma correction without geometric scaling, improved image retrieval performance based on the invariant representation is demonstrated in both a template matching scenario and a histogram based retrieval system. The proposed invariants perform unsatisfactorily under scaling. The key reasons for this behavior are discussed, and empirical data on the accuracy of the proposed invariants are provided.

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