Related papers: Diffusion-based method for producing density equal…
Localization in a pre-built map is a basic technique for robot autonomous navigation. Existing mapping and localization methods commonly work well in small-scale environments. As a map grows larger, however, more memory is required and…
In this paper, we present an approach to enhance and improve the current normal map rendering technique. Our algorithm is based on semi-discrete Optimal Mass Transportation (OMT) theory and has a solid theoretical base. The key difference…
Geomagnetic map interpolation aims to infer unobserved geomagnetic data at spatial points, yielding critical applications in navigation and resource exploration. However, existing methods for scattered data interpolation are not…
For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting…
The purpose of this paper is to explore a new way of autonomous mapping. Current systems using perception techniques like LAZER or SONAR use probabilistic methods and have a drawback of allowing considerable uncertainty in the mapping…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
The outcome of elections is strongly dependent on the districting choices, making thus possible (and frequent) the gerrymandering phenomenon, i.e.\ politicians suitably changing the shape of electoral districts in order to win the…
Score Distillation Sampling (SDS) has emerged as a prevalent technique for text-to-3D generation, enabling 3D content creation by distilling view-dependent information from text-to-2D guidance. However, they frequently exhibit shortcomings…
We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…
The number of sampling methods could be daunting for a practitioner looking to cast powerful machine learning methods to their specific problem. This paper takes a theoretical stance to review and organize many sampling approaches in the…
A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the…
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron…
Denoising diffusion probabilistic models (DDPMs) have achieved impressive performance on various image generation tasks, including image super-resolution. By learning to reverse the process of gradually diffusing the data distribution into…
A robust, resource-efficient, distributed, and minimally parameterized 3D map matching and merging algorithm is proposed. The suggested algorithm utilizes tomographic features from 2D projections of horizontal cross-sections of…
Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…