Abstract
We propose in this chapter to introduce a spinor representation for images based on the work of T. Friedrich. This spinor representation generalizes the usual Weierstrass representation of minimal surfaces (i.e., surfaces with constant mean curvature equal to zero) to arbitrary surfaces (immersed in \(\mathbb{R}^3\) ). We investigate applications to image processing focusing on segmentation and Clifford–Fourier analysis. All these applications involve sections of the spinor bundle of image graphs, that is spinor fields, satisfying the so-called Dirac equation.
Mathematics Subject Classification (2010). Primary 68U10, 53C27; secondary 53A05, 43A32.
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Batard, T., Berthier, M. (2013). Clifford–Fourier Transform and Spinor Representation of Images. In: Hitzer, E., Sangwine, S. (eds) Quaternion and Clifford Fourier Transforms and Wavelets. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0603-9_9
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DOI: https://doi.org/10.1007/978-3-0348-0603-9_9
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