Large deviation spectrum estimation in two dimensions
Résumé
This paper deals with image processing. This study takes place in a segmentation process based on texture analysis. We use the multifractal ap-proach to characterize the textures. More precisely we study a particular multi-fractal spectrum called the large deviation spectrum. We consider two statistical methods to numerically compute this spectrum. The resulting spectrum, com-puted by both methods over an image, is a one dimension spectrum. In the scope of this article, we extend these methods in order to obtain a two dimen-sions spectrum which could be assimilated to an image. This 2D spectrum al-lows a local characterization of the image singularities while a 1D spectrum is a global characterization. Moreover, the computation of the spectrum requires the use of a measure. We introduce here a pre processing based on the gradient to improve the measure. We show results on both synthetic and real world images. Finally, we remark that the resulting 2D spectrum is close to the resulting im-age of an edge detection process while edge detection using one dimension spectrum requires post processing methods. This statement will be used for fu-ture works.