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A Quaternion Framework for Color Image Smoothing and Segmentation

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Abstract

In this paper, we present feature/detail preserving models for color image smoothing and segmentation using the Hamiltonian quaternion framework. First, we introduce a novel quaternionic Gabor filter (QGF) which can combine the color channels and the orientations in the image plane. We show that these filters are optimally localized both in the spatial and frequency domains and provide a good approximation to quaternionic quadrature filters. Using the QGFs, we extract the local orientation information in the color images. Second, in order to model this derived orientation information, we propose continuous mixtures of appropriate exponential basis functions and derive analytic expressions for these models. These analytic expressions take the form of spatially varying kernels which, when convolved with a color image or the signed distance function of an evolving contour (placed in the color image), yield a detail preserving smoothing and segmentation, respectively. Several examples on widely used image databases are shown to depict the performance of our algorithms.

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Authors and Affiliations

  1. Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 32611, USA

    Özlem N. Subakan & Baba C. Vemuri

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  1. Özlem N. Subakan
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  2. Baba C. Vemuri
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Correspondence to Baba C. Vemuri.

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This research was in part funded by the NSF grant IOS-0920145.

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Subakan, Ö.N., Vemuri, B.C. A Quaternion Framework for Color Image Smoothing and Segmentation. Int J Comput Vis 91, 233–250 (2011). https://doi.org/10.1007/s11263-010-0388-9

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