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

Simultaneous Localization And Mapping (SLAM) is a fundamental problem in mobile robotics. While sparse point-based SLAM methods provide accurate camera localization, the generated maps lack semantic information. On the other hand, state of…

We present a novel Simultaneous Localization and Mapping (SLAM) method that employs Gaussian Process (GP) based landmark (object) representations. Instead of conventional grid maps or point cloud registration, we model the environment on a…

Let V be a semialgebraic set parameterized by quadratic polynomials over a quadratic set T. This paper studies semidefinite representation of its convex hull by projections of spectrahedra (defined by linear matrix inequalities). When T is…

In this paper, we present a monocular Simultaneous Localization and Mapping (SLAM) algorithm using high-level object and plane landmarks. The built map is denser, more compact and semantic meaningful compared to feature point based SLAM. We…

We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…

Object SLAM introduces the concept of objects into Simultaneous Localization and Mapping (SLAM) and helps understand indoor scenes for mobile robots and object-level interactive applications. The state-of-art object SLAM systems face…

Object-level SLAM introduces semantic meaningful and compact object landmarks that help both indoor robot applications and outdoor autonomous driving tasks. However, the back end of object-level SLAM suffers from singularity problems…

To study coisotropic reduction in the context of deformation quantization we introduce constraint manifolds and constraint algebras as the basic objects encoding the additional information needed to define a reduction. General properties of…

We investigate the problem of estimating the 3D shape of an object, given a set of 2D landmarks in a single image. To alleviate the reconstruction ambiguity, a widely-used approach is to confine the unknown 3D shape within a shape space…

We propose an approach for dense semantic 3D reconstruction which uses a data term that is defined as potentials over viewing rays, combined with continuous surface area penalization. Our formulation is a convex relaxation which we augment…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…

3D object reconstruction is a fundamental task of many robotics and AI problems. With the aid of deep convolutional neural networks (CNNs), 3D object reconstruction has witnessed a significant progress in recent years. However, possibly due…

Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric…

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…

Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geometry. Its objects of study include convex semialgebraic sets that arise in semidefinite programming and from sums of squares. This article…

Neural implicit representations have shown remarkable abilities in jointly modeling geometry, color, and camera poses in simultaneous localization and mapping (SLAM). Current methods use coordinates, positional encodings, or other geometry…

Data association in SLAM is fundamentally challenging, and handling ambiguity well is crucial to achieve robust operation in real-world environments. When ambiguous measurements arise, conservatism often mandates that the measurement is…

This paper presents Contrastive Reconstruction, ConRec - a self-supervised learning algorithm that obtains image representations by jointly optimizing a contrastive and a self-reconstruction loss. We showcase that state-of-the-art…

Recent advances in 3D Gaussian Splatting (3DGS) have enabled RGB-only SLAM systems to achieve high-fidelity scene representation. However, the heavy reliance of existing systems on photometric rendering loss for camera tracking undermines…