Related papers: A review on geometric constraint solving
Recent advances in 3D Gaussian Splatting (3DGS) have focused on accelerating optimization while preserving reconstruction quality. However, many proposed methods entangle implementation-level improvements with fundamental algorithmic…
The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location. As the dimension of the computation space grows, a higher percentage of the total…
Constraint programming is known for being an efficient approach for solving combinatorial problems. Important design choices in a solver are the branching heuristics, which are designed to lead the search to the best solutions in a minimum…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
Computer Aided Detection (CAD) is a valuable technique for precisely interpreting medical images and it has a global business opportunity of about USD 1.8 billion. The current aspects with reference to the four sub stages such as image…
Convex programming plays a fundamental role in machine learning, data science, and engineering. Testing convexity structure in nonlinear programs relies on verifying the convexity of objectives and constraints. Grant et al. (2006)…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
3D Gaussians have recently emerged as an effective scene representation for real-time splatting and accurate novel-view synthesis, motivating several works to adapt multi-view structure prediction networks to regress per-pixel 3D Gaussians…
3D scene reconstruction from 2D images has been a long-standing task. Instead of estimating per-frame depth maps and fusing them in 3D, recent research leverages the neural implicit surface as a unified representation for 3D reconstruction.…
Microstructures, characterized by intricate structures at the microscopic scale, hold the promise of important disruptions in the field of mechanical engineering due to the superior mechanical properties they offer. One fundamental…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
We report numerical results on solving constrained linear-quadratic model predictive control (MPC) problems by exploiting graphics processing units (GPUs). The presented method reduces the MPC problem by eliminating the state variables and…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Problem decomposition--the ability to break down a large task into smaller, well-defined components--is a critical skill for effectively designing and creating large programs, but it is often not included in introductory computer science…
Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
We describe a purely image-based method for finding geometric constructions with a ruler and compass in the Euclidea geometric game. The method is based on adapting the Mask R-CNN state-of-the-art image processing neural architecture and…
We propose a method to enhance 3D Gaussian Splatting (3DGS)~\cite{Kerbl2023}, addressing challenges in initialization, optimization, and density control. Gaussian Splatting is an alternative for rendering realistic images while supporting…
Full 3D estimation of human pose from a single image remains a challenging task despite many recent advances. In this paper, we explore the hypothesis that strong prior information about scene geometry can be used to improve pose estimation…