Anisotropic Diffusion with Deep Learning

Abstract

We propose a deep learning framework for anisotropic diffusion which is based on a complex algorithm for a single image. Our network can be applied not only to a single image but also to multiple images. Also by blurring the image, the noise in the image is reduced. But the important features of objects remain. To apply anisotropic diffusion to deep learning, we use total variation for our loss function. Also, total variation is used in image denoising pre-process.[1] With this loss, our network makes successful anisotropic diffusion images. In these images, the whole parts are blurred, but edge and important features remain. The effectiveness of the anisotropic diffusion image is shown with the classification task.

Graph Representation Learning

“…Subsequent research has focused on enhancing training methods [34], [35], [65], [66]. Many studies have explored Graph Neural Networks based on diffusion equations on graphs [8], [9], [83]. [5] extended Neural ODEs to graph neural networks (GNNs) with the GRAND model, which utilizes graph diffusion equations to model feature-updating dynamics.…”

“…BLEND [58] incorporates the positional feature into the node features and utilizes the Beltrami flow to jointly evolve them. However, pure diffusion processes often lead to the oversmoothing problem [7]- [9]. To mitigate this issue, one common approach is adding an additional term to prevent Dirichlet energy from decaying to zero [8], [37], [67].…”

“…To mitigate this issue, one common approach is adding an additional term to prevent Dirichlet energy from decaying to zero [8], [37], [67]. GREAD, proposed by [9], incorporates nearly all commonly used additional terms based on the reaction-diffusion equation.…”

“…There is a close connection between message passing and graph diffusion equations, leading to the development of numerous continuous graph neural networks based on diffusion [5], [7]- [9], [29], [58]. However, the diffusion process exhibits Kaiyuan Cui is with the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, China.…”

“…Recently, [9] propose a reaction diffusion equation-based GNN (GREAD) that considers the most popular types of reaction equations expressed as:…”