Abstract
The aim of this chapter is to propose two different approaches for color object recognition, both using the recently defined color Clifford Fourier transform. The first one deals with so-called Generalized Fourier Descriptors, the definition of which relies on plane motion group actions. The proposed color extension leads to more compact descriptors, with lower complexity and better recognition rates, than the already existing descriptors based on the processing of the r, g and b channels separately. The second approach concerns color phase correlation for color images. The idea here is to generalize in the Clifford framework the usual means of measuring correlation from the well-known shift theorem. Both methods necessitate to choose a 2-blade B of ℝ4 which corresponds to an analysis plane in the color space. The relevance of proposed methods for classification purposes is discussed on several color image databases. In particular, the influence of parameter B is studied regarding the type of images.
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Notes
- 1.
A typical setting for μ is \((\mathbf {e}_{\mathbf{1}}+\mathbf{e}_{\mathbf{2}}+\mathbf{e}_{\mathbf{3}})/\sqrt{3}\), which corresponds to select the achromatic axis.
- 2.
More precisely, the two functions in the square brackets in (9.10).
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Acknowledgements
This work is partially supported by the ONR Grant N00014-09-1-0493 and “La Région Poitou-Charentes”.
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Mennesson, J., Saint-Jean, C., Mascarilla, L. (2011). Color Object Recognition Based on a Clifford Fourier Transform. In: Dorst, L., Lasenby, J. (eds) Guide to Geometric Algebra in Practice. Springer, London. https://doi.org/10.1007/978-0-85729-811-9_9
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