Related papers: Direct Fitting of Gaussian Mixture Models

3D reconstruction and simulation, although interrelated, have distinct objectives: reconstruction requires a flexible 3D representation that can adapt to diverse scenes, while simulation needs a structured representation to model motion…

We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation…

Since its introduction, 3D Gaussian Splatting (3DGS) has become an important reference method for learning 3D representations of a captured scene, allowing real-time novel-view synthesis with high visual quality and fast training times.…

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…

In this paper, we propose a novel 3D registration paradigm, Generative Point Cloud Registration, which bridges advanced 2D generative models with 3D matching tasks to enhance registration performance. Our key idea is to generate cross-view…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Neural 3D representations such as Neural Radiance Fields (NeRF), excel at producing photo-realistic rendering results but lack the flexibility for manipulation and editing which is crucial for content creation. Previous works have attempted…

We propose an end-to-end deep learning architecture that produces a 3D shape in triangular mesh from a single color image. Limited by the nature of deep neural network, previous methods usually represent a 3D shape in volume or point cloud,…

Finding corresponding pixels within a pair of images is a fundamental computer vision task with various applications. Due to the specific requirements of different tasks like optical flow estimation and local feature matching, previous…

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often…

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach…

Background modeling is widely used for intelligent surveillance systems to detect moving targets by subtracting the static background components. Most roadside LiDAR object detection methods filter out foreground points by comparing new…

Image-to-point cloud registration methods typically follow a coarse-to-fine pipeline, extracting patch-level correspondences and refining them into dense pixel-to-point matches. However, in scenes with repetitive patterns, images often lack…

We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point…

We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves…

The information lost in images of undersampled CCD cameras can be recovered with the technique of `dithering'. A number of subexposures is taken with sub-pixel shifts in order to record structures on scales smaller than a pixel. The…

This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…

Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…

We present Gaussian Splatting Alignment (GSA), a novel method for aligning two independent 3D Gaussian Splatting (3DGS) models via a similarity transformation (rotation, translation, and scale), even when they are of different objects in…