Title :
Heat kernels of generalized laplacians-application to color image smoothing
Author :
Batard, Thomas ; Berthier, Michel
Author_Institution :
Lab. Math. Image et Applic., Univ. de La Rochelle, La Rochelle, France
Abstract :
In this paper, we explore the theory of vector bundles over Riemannian manifolds in order to smooth multivalued images. In this framework, we consider standard PDE´s used in image processing as generalized heat equations, related to the geometries of the base manifold, given by its metric and the subsequent Levi-Cevita connection and of the vector bundle, given by a connection. As a consequence, the smoothing is made through a convolution with a 2D kernel, generalizing Gaussian, Beltrami and oriented kernel. In particular, we construct an extension of the oriented kernel, and illustrate it with an application to color image smoothing.
Keywords :
Laplace transforms; convolution; image colour analysis; smoothing methods; 2D kernel convolution; Levi Cevita connection; PDE; Riemannian manifolds; base manifold geometries; color image smoothing; generalized heat equations; generalized laplacians; heat kernels; image processing; vector bundles theory; Color; Convolution; Diffusion processes; Geometry; Image processing; Kernel; Laplace equations; Smoothing methods; Color image smoothing; Heat kernel; Vector bundle; generalized Laplacian;
Conference_Titel :
Image Processing (ICIP), 2009 16th IEEE International Conference on
Conference_Location :
Cairo
Print_ISBN :
978-1-4244-5653-6
Electronic_ISBN :
1522-4880
DOI :
10.1109/ICIP.2009.5414385