Laplacian transfer across a rough interface: numerical resolution in the conformal plane

Abstract

We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can be efficiently treated in the conformal plane. We show in particular that an expansion of the potential on a basis of evanescent waves in the conformal plane allows to write a well-conditioned 1D linear system. These general principle are illustrated by numerical results on rough interfaces.

A novel parallel mammogram sharpening framework using modified Laplacian filter for lumps identification on GPU

“…In this case, the noise quickly gains in the sharpen image while the image is over sharpening. As an alternative, in the proposed method, the sharpen pixel intensity is varying with the difference of pixel values by 3 × 3 mask within predefined filter constraints [27][28][29]. In sharpening, a large deviation of gray values indicates that the image details are improved and the noise is attenuated, whereas a lower deviation is means that the pixel intensity should be lower.…”

“…These operations almost always slide the mask to all the spatial positions of pixels within the processed image by placing the top left corner of the mask isotropically over the whole image. Consequently, the mask 'overlaps' the image on the right side and bottom region of edges within the convoluted image [27][28][29]. Fig.…”