Over the past few decades, the mathematical community has accumulated a significant
amount of pure mathematical data, which has been analyzed through supervised, semi …

Automating the current bridge visual inspection practices using drones and image
processing techniques is a prominent way to make these inspections more effective, robust …

We build on the recently introduced PDE-G-CNN framework, which proposed the concept of
non-linear morphological convolutions that are motivated by solving HJB-PDEs on lifted …

Content and image generation consist in creating or generating data from noisy information
by extracting specific features such as texture, edges, and other thin image structures. We …

We develop and analyze a new algorithm to find the connected components of a compact
set I from a Lie group G endowed with a left-invariant Riemannian distance. For a given …

Euclidean deep learning is often inadequate for addressing real-world signals where the
representation space is irregular and curved with complex topologies. Interpreting the …

PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) utilize solvers of
geometrically meaningful evolution PDEs as substitutes for the conventional components in …

The roto-translation group SE2 has been of active interest in image analysis due to methods
that lift the image data to multi-orientation representations defined on this Lie group. This …

The field of machine learning is currently undergoing rapid development, with applications
in various areas, including image processing. In particular, Convolutional Neural Networks …

A new neural network model called Tensorial Restoration Neural Network Model (TRNNM)
is proposed, which can repair the noise, blur, and information missing of digital textual …