Spin Geometry and Image Processing

Michel Berthier (1)

1 MIA - Mathématiques, Image et Applications - EA 3165

We give a survey of applications of spin geometry to image processing. We mainly focus on the problem of defining geometric Fourier transforms for both grey-level and color images. The definitions we propose rely on a spin generalization of the usual notion of character. We consider three possibilities for the actions of these spin characters: by using the spinor representation of grey-level image surfaces; by considering grey-level and color images as sections of associated bundles built first with standard representations and then with spin representations. Examples of applications to low-pass filtering are presented.

Mots clés: Clifford Fourier Trasnform.; Spin Geometry; Image Processing; Clifford Fourier Trasnform

Domaines: Géométrie différentielle [math.DG]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]

Michel Berthier. Spin Geometry and Image Processing. 2013. ⟨hal-00801224⟩