Related papers: Nonparametric Continuous Sensor Registration
Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical…
We present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D…
Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…
Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear…
Scene-level point cloud registration is very challenging when considering dynamic foregrounds. Existing indoor datasets mostly assume rigid motions, so the trained models cannot robustly handle scenes with non-rigid motions. On the other…
This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental…
Analysis of longitudinal changes in imaging studies often involves both segmentation of structures of interest and registration of multiple timeframes. The accuracy of such analysis could benefit from a tailored framework that jointly…
In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental…
For any maximal surface group representation into $\mathrm{SO}_0(2,n+1)$, we introduce a non-degenerate scalar product on the the first cohomology group of the surface with values in the associated flat bundle. In particular, it gives rise…
Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the…
The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these…
In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin…
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the…
We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run.…
This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to…
An unsupervised human action modeling framework can provide useful pose-sequence representation, which can be utilized in a variety of pose analysis applications. In this work we propose a novel temporal pose-sequence modeling framework,…
Let $G$ be a connected, simply connected, nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for reproducing formulas associated with the left…
A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a…