Related papers: Convex Hull-based Algebraic Constraint for Visual …

We introduce a new method to reconstruct 3D objects using a set of volumetric primitives, i.e., superquadrics. The method hierarchically decomposes a target 3D object into pairs of superquadrics recovering finer and finer details. While…

Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…

Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to…

The integration of neural rendering and the SLAM system recently showed promising results in joint localization and photorealistic view reconstruction. However, existing methods, fully relying on implicit representations, are so…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

We introduce RACH-Space, an algorithm for labelling unlabelled data in weakly supervised learning, given incomplete, noisy information about the labels. RACH-Space offers simplicity in implementation without requiring hard assumptions on…

In safety-critical applications, guaranteeing the satisfaction of constraints over continuous environments is crucial, e.g., an autonomous agent should never crash into obstacles or go off-road. Neural models struggle in the presence of…

Understanding geometric, semantic, and instance information in 3D scenes from sequential video data is essential for applications in robotics and augmented reality. However, existing Simultaneous Localization and Mapping (SLAM) methods…

Most Simultaneous localisation and mapping (SLAM) systems have traditionally assumed a static world, which does not align with real-world scenarios. To enable robots to safely navigate and plan in dynamic environments, it is essential to…

Convex hull data structures are fundamental in computational geometry. We study insertion-only data structures, supporting various containment and intersection queries. When $P$ is sorted by $x$- or $y$-coordinate, convex hulls can be…

Sparse and feature SLAM methods provide robust camera pose estimation. However, they often fail to capture the level of detail required for inspection and scene awareness tasks. Conversely, dense SLAM approaches generate richer scene…

Despite advancements in SLAM technologies, robust operation under challenging conditions such as low-texture, motion-blur, or challenging lighting remains an open challenge. Such conditions are common in applications such as assistive…

The representation of geometry in real-time 3D perception systems continues to be a critical research issue. Dense maps capture complete surface shape and can be augmented with semantic labels, but their high dimensionality makes them…

This paper presents a visual SLAM system that uses both points and lines for robust camera localization, and simultaneously performs a piece-wise planar reconstruction (PPR) of the environment to provide a structural map in real-time. One…

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide…

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…

We study the convex hull of a set $S\subset \mathbb{R}^n$ defined by three quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take nonnegative linear combinations of the defining inequalities of $S$. We call…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

We propose a simple yet effective method to learn to segment new indoor scenes from video frames: State-of-the-art methods trained on one dataset, even as large as the SUNRGB-D dataset, can perform poorly when applied to images that are not…

We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…