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This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of…

Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…

The reconstruction of real-world surfaces is on high demand in various applications. Most existing reconstruction approaches apply 3D scanners for creating point clouds which are generally sparse and of low density. These points clouds will…

Geometric perception problems are fundamental tasks in robotics and computer vision. In real-world applications, they often encounter the inevitable issue of outliers, preventing traditional algorithms from making correct estimates. In this…

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…

Learning to generate 3D point clouds without 3D supervision is an important but challenging problem. Current solutions leverage various differentiable renderers to project the generated 3D point clouds onto a 2D image plane, and train deep…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…

Recently, 3D Gaussian Splatting has emerged as a prominent research direction owing to its ultrarapid training speed and high-fidelity rendering capabilities. However, the unstructured and irregular nature of Gaussian point clouds poses…

Reconstructing a high-resolution 3D model of an object is a challenging task in computer vision. Designing scalable and light-weight architectures is crucial while addressing this problem. Existing point-cloud based reconstruction…

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…

Point clouds produced by 3D sensors are often sparse and noisy, posing challenges for tasks requiring dense and high-fidelity 3D representations. Prior work has explored both implicit feature-based upsampling and distance-function learning…

The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…

Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas…

Due to the diverse sparsity, high dimensionality, and large temporal variation of dynamic point clouds, it remains a challenge to design an efficient point cloud compression method. We propose to code the geometry of a given point cloud by…

We consider the problem of 3D shape recovery from ultra-fast motion-blurred images. While 3D reconstruction from static images has been extensively studied, recovering geometry from extreme motion-blurred images remains challenging. Such…

3D surface reconstruction from point clouds is a key step in areas such as content creation, archaeology, digital cultural heritage, and engineering. Current approaches either try to optimize a non-data-driven surface representation to fit…

Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…

Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…

In robotic inspection, joint registration of multiple point clouds is an essential technique for estimating the transformation relationships between measured parts, such as multiple blades in a propeller. However, the presence of noise and…