Related papers: A Simple Riemannian Manifold Network for Image Set…

Semantic segmentation is an important branch of image processing and computer vision. With the popularity of deep learning, various convolutional neural networks have been proposed for pixel-level classification and segmentation tasks. In…

Visual Place Recognition (VPR) demands representations robust to drastic environmental and viewpoint shifts. Existing aggregation paradigms either depend on extensive supervised training or rely on first-order pooling, often struggling to…

Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…

The main objective of image segmentation is to divide an image into homogeneous regions for further analysis. This is a significant and crucial task in many applications such as medical imaging. Deep learning (DL) methods have been proposed…

We consider two Riemannian geometries for the manifold $\mathcal{M}(p,m\times n)$ of all $m\times n$ matrices of rank $p$. The geometries are induced on $\mathcal{M}(p,m\times n)$ by viewing it as the base manifold of the submersion…

This paper introduces an extension of the backpropagation algorithm that enables us to have layers with constrained weights in a deep network. In particular, we make use of the Riemannian geometry and optimization techniques on matrix…

Magnetic Resonance Imaging (MRI) is widely used in clinical practice, but suffered from prolonged acquisition time. Although deep learning methods have been proposed to accelerate acquisition and demonstrate promising performance, they rely…

Rotation estimation of high precision from an RGB-D object observation is a huge challenge in 6D object pose estimation, due to the difficulty of learning in the non-linear space of SO(3). In this paper, we propose a novel rotation…

Visual data such as videos are often sampled from complex manifold. We propose leveraging the manifold structure to constrain the deep action feature learning, thereby minimizing the intra-class variations in the feature space and…

Pose estimation, i.e. predicting a 3D rigid transformation with respect to a fixed co-ordinate frame in, SE(3), is an omnipresent problem in medical image analysis with applications such as: image rigid registration, anatomical standard…

Capsule Networks (CapsNets) show exceptional graph representation capacity via dynamic routing and vectorized hierarchical representations, but they model the complex geometries of real\-world graphs poorly by fixed\-curvature space due to…

Medical image segmentation is a fundamental task for medical image analysis and surgical planning. In recent years, UNet-based networks have prevailed in the field of medical image segmentation. However, convolution-neural networks (CNNs)…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

Over the last few years, deep learning based approaches have achieved outstanding improvements in natural image matting. However, there are still two drawbacks that impede the widespread application of image matting: the reliance on…

Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…

In this paper, we investigate the fundamental problem of wireless link scheduling in device-to-device (D2D) networks, through the lens of Riemannian geometry. Our goal is to find a novel metric to characterize interference among D2D pairs,…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

High-dimensional data with intrinsic low-dimensional structure is ubiquitous in machine learning and data science. While various approaches allow one to learn a data manifold with a Riemannian structure from finite samples, performing…