Deep Learning (DL) has achieved remarkable success in tackling complex Artificial
Intelligence tasks. The standard training of neural networks employs backpropagation to …

As data is a predominant resource in applications, Riemannian geometry is a natural
framework to model and unify complex nonlinear sources of data. However, the …

In this article, we introduce a family of elastic metrics on the space of parametrized surfaces
in 3D space using a corresponding family of metrics on the space of vector-valued one …

Given data, deep generative models, such as variational autoencoders (VAE) and
generative adversarial networks (GAN), train a lower dimensional latent representation of …

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types
descends to stochastic evolution of shapes, images and landmarks. The stochasticity is …

This chapter introduces the basic concepts of differential geometry: Manifolds, charts,
curves, their derivatives, and tangent spaces. The addition of a Riemannian metric enables …

The existence of media in augmented reality learning will make students more helpful in
understanding Geometry material. The existence of augmented reality learning media in a …

We introduce two constructions in geometric deep learning for 1) transporting orientation-
dependent convolutional filters over a manifold in a continuous way and thereby defining a …

Stochastically evolving geometric systems are studied in shape analysis and computational
anatomy for modeling random evolutions of human organ shapes. The notion of geodesic …

The quantitative analysis of the uncertainty influence on thermodynamic parameters and
performance parameters is usually difficult to achieve due to the strong nonlinear working …