Geometric Wavelets for Image Processing: Metric Curvature of Wavelets

Emil Saucan (1) , Chen Sagiv (2) , Eli Appleboim (3)

1 TECHNION - Department of Mathematics
2 SagivTech Ltd.
3 EE-Technion - Department of Electrical Engineering - Technion [Haïfa]

We introduce a semi-discrete version of the Finsler-Haantjes metric curvature to define curvature for wavelets and show that scale and curvature play similar roles with respect to image presentation and analysis. More precisely, we show that there is an inverse relationship between local scale and local curvature in images. This allows us to use curvature as a geometrically motivated automatic scale selection in signal and image processing, this being an incipient bridging of the gap between the methods employed in Computer Graphics and Image Processing. A natural extension to ridgelets and curvelets is also given. Further directions of study, in particular the development of a curvature transform and the study of its link with wavelet and the scale transforms are also suggested.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Emil Saucan, Chen Sagiv, Eli Appleboim. Geometric Wavelets for Image Processing: Metric Curvature of Wavelets. SAMPTA'09, May 2009, Marseille, France. Special session on geometric multiscale analysis. ⟨hal-00451837⟩