Related papers: GOGMA: Globally-Optimal Gaussian Mixture Alignment
3D Gaussian splatting (3D-GS) has recently revolutionized novel view synthesis in the simultaneous localization and mapping (SLAM) problem. However, most existing algorithms fail to fully capture the underlying structure, resulting in…
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.…
We analyze the connection between minimizers with good generalizing properties and high local entropy regions of a threshold-linear classifier in Gaussian mixtures with the mean squared error loss function. We show that there exist…
We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
Simultaneous Localization and Planning (SLAP) under process and measurement uncertainties is a challenge. It involves solving a stochastic control problem modeled as a Partially Observed Markov Decision Process (POMDP) in a general…
Many modern machine learning algorithms such as generative adversarial networks (GANs) and adversarial training can be formulated as minimax optimization. Gradient descent ascent (GDA) is the most commonly used algorithm due to its…
This paper introduces a novel approach to improve robotic grasping in dynamic environments by integrating Gaussian Process Distance Fields (GPDF), SE(3) equivariant networks, and Riemannian Mixture Models. The aim is to enable robots to…
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…
The problem of packing equal circles in a circle is a classic and famous packing problem, which is well-studied in academia and has a variety of applications in industry. This problem is computationally challenging, and researchers mainly…
Global geolocation, which seeks to predict the geographical location of images captured anywhere in the world, is one of the most challenging tasks in the field of computer vision. In this paper, we introduce an innovative interactive…
The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling…
Incorporating prior structure information into the visual state estimation could generally improve the localization performance. In this letter, we aim to address the paradox between accuracy and efficiency in coupling visual factors with…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
The rigid registration of two 3D point sets is a fundamental problem in computer vision. The current trend is to solve this problem globally using the BnB optimization framework. However, the existing global methods are slow for two main…
Point management is critical for optimizing 3D Gaussian Splatting models, as point initiation (e.g., via structure from motion) is often distributionally inappropriate. Typically, Adaptive Density Control (ADC) algorithm is adopted,…
We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…
Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…