Related papers: Beyond First-Order: Learning Riemannian Geometries…

Recent advances in rotation-invariant (RI) learning for 3D point clouds typically replace raw coordinates with handcrafted RI features to ensure robustness under arbitrary rotations. However, these approaches often suffer from the loss of…

Multi-view inverse rendering aims to recover geometry, materials, and illumination consistently across multiple viewpoints. When applied to multi-view images, existing single-view approaches often ignore cross-view relationships, leading to…

Cross-view geo-localization plays a critical role in Unmanned Aerial Vehicle (UAV) localization and navigation. However, significant challenges arise from the drastic viewpoint differences and appearance variations between images. Existing…

Visual place recognition (VPR) is the problem of recognising a previously visited location using visual information. Many attempts to improve the performance of VPR methods have been made in the literature. One approach that has received…

Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms…

Recent learning-based visual localization methods use global descriptors to disambiguate visually similar places, but existing approaches often derive these descriptors from geometric cues alone (e.g., covisibility graphs), limiting their…

Visual recognition models are not invariant to viewpoint changes in the 3D world, as different viewing directions can dramatically affect the predictions given the same object. Although many efforts have been devoted to making neural…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Localization is an essential capability for mobile robots. A rapidly growing field of research in this area is Visual Place Recognition (VPR), which is the ability to recognize previously seen places in the world based solely on images.…

Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to…

Recent text-to-image models, such as Stable Diffusion, have achieved impressive visual quality, yet they often suffer from geometric inconsistencies that undermine the structural realism of generated scenes. One prominent issue is vanishing…

One recent promising approach to the Visual Place Recognition (VPR) problem has been to fuse the place recognition estimates of multiple complementary VPR techniques using methods such as SRAL and multi-process fusion. These approaches come…

Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from…

Human visual scene understanding is so remarkable that we are able to recognize a revisited place when entering it from the opposite direction it was first visited, even in the presence of extreme variations in appearance. This capability…

Equilibrium computation on Riemannian manifolds provides a unifying framework for numerous problems in machine learning and data analytics. One of the simplest yet most fundamental methods is Riemannian gradient descent (RGD). While its…

Relative pose regressors (RPRs) localize a camera by estimating its relative translation and rotation to a pose-labelled reference. Unlike scene coordinate regression and absolute pose regression methods, which learn absolute scene…

Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…

This paper presents the first optimal-rate $p$-th order methods with $p\geq 1$ for finding first and second-order stationary points of non-convex smooth objective functions over Riemannian manifolds. In contrast to the geodesically convex…

This paper adapts a general dataset representation technique to produce robust Visual Place Recognition (VPR) descriptors, crucial to enable real-world mobile robot localisation. Two parallel lines of work on VPR have shown, on one side,…

The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework…