Mathematical foundations of quaternion image matching

Stephen P. DelMarco

doi:10.1117/12.2558712

21 April 2020 Mathematical foundations of quaternion image matching

Stephen P. DelMarco

Proceedings Volume 11399, Mobile Multimedia/Image Processing, Security, and Applications 2020; 1139907 (2020) https://doi.org/10.1117/12.2558712
Event: SPIE Defense + Commercial Sensing, 2020, Online Only

Abstract

In recent years, the utility of multi-channel image processing techniques has increased. Applications to image processing include color image registration, edge detection, filtering, and color space correction, and multi-channel image matching. These techniques represent multiple image channels, such as three color channels, as image functions taking values in a finite-dimensional algebra, for example, the algebra of quaternions. Use of these algebras enables processing a multichannel image as a single entity, holistically. This holistic processing provides the opportunity to exploit cross-channel dependencies for improved performance, for example, improved matching performance in image matching or registration applications. In this paper, we make a critical analysis of the foundations of quaternion-valued image matching. We investigate standard alternatives to using quaternions for four-channel image matching including image tiling, image averaging, independent component processing, and coordinated component translation approaches. We examine the advantages that quaternion-based processing provides over these alternatives. We interpret the quaternion match metric as an inner product, which provides motivation for image matching using quaternion correlation. We generalize the quaternion match metric to use arbitrary combinations of component correlations to define new match metrics. We show that these new match metrics correspond to new product structures on four-dimensional algebras. We present numerical results demonstrating and validating aspects of the theory.

Conference Presentation

Citation Download Citation

Stephen P. DelMarco "Mathematical foundations of quaternion image matching", Proc. SPIE 11399, Mobile Multimedia/Image Processing, Security, and Applications 2020, 1139907 (21 April 2020); https://doi.org/10.1117/12.2558712

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