Abstract
In this work we introduce a new kernel for image processing called the atomic function. This kernel is compact in the spatial domain, and it can be adapted to the behavior of the input signal by broadening or narrowing its band ensuring a maximum signal-to-noise ratio. It can be used for smooth differentiation of images in the quaternion algebra framework. We discuss the role of the quaternion atomic function with respect to monogenic signals. We then propose a steerable quaternion wavelet scheme for image structure and contour detection. Making use of the generalized Radon transform and images processed with the quaternion wavelet atomic function transform, we detect shape contours in color images. We believe that the atomic function is a promising kernel for image processing and scene analysis.
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We want to thank the financial support of the SEP/CONACYT - 2007-1 82084 grant.
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Bayro-Corrochano, E., Moya-Sánchez, E.U. (2011). Quaternion Atomic Function for Image Processing. In: Dorst, L., Lasenby, J. (eds) Guide to Geometric Algebra in Practice. Springer, London. https://doi.org/10.1007/978-0-85729-811-9_8
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DOI: https://doi.org/10.1007/978-0-85729-811-9_8
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