相关论文: RiemanLine: Riemannian Manifold Representation of …

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…

A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise in the form of Krylov subspaces in matrix…

Monocular 3D lane detection remains challenging due to depth ambiguity and weak geometric constraints. Mainstream methods rely on depth guidance, BEV projection, and anchor- or curve-based heads with simplified physical assumptions,…

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model…

Manifold data analysis is challenging due to the lack of parametric distributions on manifolds. To address this, we introduce a series of Riemannian radial distributions on Riemannian symmetric spaces. By utilizing the symmetry, we show…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

Riemannian optimization is a principled framework for solving optimization problems where the desired optimum is constrained to a smooth manifold $\mathcal{M}$. Algorithms designed in this framework usually require some geometrical…

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…

Using geometric landmarks like lines and planes can increase navigation accuracy and decrease map storage requirements compared to commonly-used LiDAR point cloud maps. However, landmark-based registration for applications like loop closure…

Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in…

Local and global illumination were recently defined in Riemannian manifolds to visualize classical Non-Euclidean spaces. This work focuses on Riemannian metric construction in $\mathbb{R}^3$ to explore special effects like warping, mirages,…