Related papers: KernelGPA: A Globally Optimal Solution to Deformab…

Generalized Procrustes Analysis (GPA) is the problem of bringing multiple shapes into a common reference by estimating transformations. GPA has been extensively studied for the Euclidean and affine transformations. We introduce GPA with…

We present a novel Simultaneous Localization and Mapping (SLAM) method that employs Gaussian Process (GP) based landmark (object) representations. Instead of conventional grid maps or point cloud registration, we model the environment on a…

In this paper, we study the back-end of simultaneous localization and mapping (SLAM) problem in deforming environment, where robot localizes itself and tracks multiple non-rigid soft surface using its onboard sensor measurements. An…

Simultaneous Localization and Mapping (SLAM) techniques play a key role towards long-term autonomy of mobile robots due to the ability to correct localization errors and produce consistent maps of an environment over time. Contrarily to…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

Deformable medical image registration is an essential task in computer-assisted interventions. This problem is particularly relevant to oncological treatments, where precise image alignment is necessary for tracking tumor growth, assessing…

Recent advancements in RGB-only dense Simultaneous Localization and Mapping (SLAM) have predominantly utilized grid-based neural implicit encodings and/or struggle to efficiently realize global map and pose consistency. To this end, we…

Geometric morphometrics (GMM) is widely used to quantify shape variation, more recently serving as input for machine learning (ML) analyses. Standard practice aligns all specimens via Generalized Procrustes Analysis (GPA) prior to splitting…

Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we…

Suppose that $\gamma$ and $\sigma$ are two continuous bounded variation paths which take values in a finite-dimensional inner product space $V$. Recent papers have introduced the truncated and the untruncated signature kernel of $\gamma$…

Robotic grinding is widely used for shaping workpieces in manufacturing, but it remains difficult to automate this process efficiently. In particular, efficiently grinding workpieces of different shapes and material hardness is challenging…

Neural implicit scene representations have recently shown encouraging results in dense visual SLAM. However, existing methods produce low-quality scene reconstruction and low-accuracy localization performance when scaling up to large indoor…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…

Neural RGBD SLAM techniques have shown promise in dense Simultaneous Localization And Mapping (SLAM), yet face challenges such as error accumulation during camera tracking resulting in distorted maps. In response, we introduce Loopy-SLAM…

Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce and the dimensionality is high. Although GPs are known for…

Global point cloud registration is essential in many robotics tasks like loop closing and relocalization. Unfortunately, the registration often suffers from the low overlap between point clouds, a frequent occurrence in practical…

Neural implicit representations have recently demonstrated compelling results on dense Simultaneous Localization And Mapping (SLAM) but suffer from the accumulation of errors in camera tracking and distortion in the reconstruction.…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…