Related papers: Optimally sparse approximations of 3D functions by…

In this paper we survey the various implementations of a new data assimilation (downscaling) algorithm based on spatial coarse mesh measurements. As a paradigm, we demonstrate the application of this algorithm to the 3D Leray-$\alpha$…

Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…

We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…

Region-based methods have become increasingly popular for model-based, monocular 3D tracking of texture-less objects in cluttered scenes. However, while they achieve state-of-the-art results, most methods are computationally expensive,…

Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…

In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…

We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a…

With the emergence of Neural Radiance Fields (NeRF), neural implicit representations have gained widespread applications across various domains, including simultaneous localization and mapping. However, current neural implicit SLAM faces a…

Many biological learning systems such as the mushroom body, hippocampus, and cerebellum are built from sparsely connected networks of neurons. For a new understanding of such networks, we study the function spaces induced by sparse random…

3D scene graphs hierarchically represent the environment appropriately organizing different environmental entities in various layers. Our previous work on situational graphs extends the concept of 3D scene graph to SLAM by tightly coupling…

The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…

Efficient representations of multivariate functions are critical for the design of state-of-the-art methods of data restoration and image reconstruction. In this work, we consider the representation of spatio-temporal data such as temporal…

We propose $S^3$LAM, a novel RGB-D SLAM system that leverages 2D surfel splatting to achieve highly accurate geometric representations for simultaneous tracking and mapping. Unlike existing 3DGS-based SLAM approaches that rely on 3D…

Recent advancements in Radiance Fields have significantly improved novel-view synthesis. However, in many real-world applications, the more advanced challenge lies in inverse rendering, which seeks to derive the physical properties of a…

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…

Let $\mathcal{D}$ be the dictionary of Gaussian mixtures: the functions created by affine change of variables of a single Gaussian in $n$ dimensions. $\mathcal{D}$ is used pervasively in scientific applications to a degree that…

We present a method to infer a dense depth map from a color image and associated sparse depth measurements. Our main contribution lies in the design of an annealing process for determining co-visibility (occlusions, disocclusions) and the…

We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape…