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3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…

Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D…

In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…

Learning accurate depth is essential to multi-view 3D object detection. Recent approaches mainly learn depth from monocular images, which confront inherent difficulties due to the ill-posed nature of monocular depth learning. Instead of…

Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…

We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones…

This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…

Urban reconstruction from a video captured by a surveying vehicle constitutes a core module of automated mapping. When computational power represents a limited resource and, a detailed map is not the primary goal, the reconstruction can be…

Face recognition has been of great importance in many applications as a biometric for its throughput, convenience, and non-invasiveness. Recent advancements in deep Convolutional Neural Network (CNN) architectures have boosted significantly…

Validation metrics are a key prerequisite for the reliable tracking of scientific progress and for deciding on the potential clinical translation of methods. While recent initiatives aim to develop comprehensive theoretical frameworks for…

This document presents PLVS: a real-time system that leverages sparse SLAM, volumetric mapping, and 3D unsupervised incremental segmentation. PLVS stands for Points, Lines, Volumetric mapping, and Segmentation. It supports RGB-D and Stereo…

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In a nutshell, we discuss how to construct disk…

We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask…

Depth prediction plays a key role in understanding a 3D scene. Several techniques have been developed throughout the years, among which Convolutional Neural Network has recently achieved state-of-the-art performance on estimating depth from…

Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…

There are still two problems in SDD causing some inaccurate results: (1) In the process of feature extraction, with the layer-by-layer acquisition of semantic information, local information is gradually lost, resulting into less…

Deep convolutional neural networks (CNNs) have dominated many computer vision domains because of their great power to extract good features automatically. However, many deep CNNs-based computer vison tasks suffer from lack of training data…

Stochastic gradient descent algorithm has been successfully applied on support vector machines (called PEGASOS) for many classification problems. In this paper, stochastic gradient descent algorithm is investigated to twin support vector…

Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF),…