Related papers: On the Spline-Based Parameterisation of Plane Grap…
The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their difference is primarily in the choice of heuristics they include and in the actual tool implementation. It is…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
Polynomial splines are ubiquitous in the fields of computer aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly versatile since local mesh adaptivity enables efficient…
This paper presents a two-stage prediction-based control scheme for embedding the environment's geometric properties into a collision-free Pythagorean Hodograph spline, and subsequently finding the optimal path within the parameterized free…
Continuous spline functions are defined as piecewise polynomials on the faces of a polyhedral complex that agree on the intersections of two faces. Splines are used in approximation theory and numerical analysis, with applications in data…
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined…
This paper uses the smoothing and mapping framework to solve the SLAM problem in indoor environments; focusing on how some key issues such as feature extraction and data association can be handled by applying probabilistic techniques. For…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
Planar homography, with eight degrees of freedom (DOFs), is fundamental in numerous computer vision tasks. While the positional offsets of four corners are widely adopted (especially in neural network predictions), this parameterization…
In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…
Visual SLAM (Simultaneous Localization and Mapping) based on planar features has found widespread applications in fields such as environmental structure perception and augmented reality. However, current research faces challenges in…
We introduce a comprehensive benchmark for local features and robust estimation algorithms, focusing on the downstream task -- the accuracy of the reconstructed camera pose -- as our primary metric. Our pipeline's modular structure allows…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
Basis splines enable a time-continuous feasibility check with a finite number of constraints. Constraints apply to the whole trajectory for motion planning applications that require a collision-free and dynamically feasible trajectory.…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
The computational consuming and non-robust reconstruction from point clouds to either meshes or spline surfaces motivates the direct tool path planning for point clouds. In this paper, a novel approach for planning iso-parametric tool path…
The Coherence Length Diagram and the related maps have been shown to represent a useful tool for image analysis. Setting threshold parameters is one of the most important issues when dealing with such applications, as they affect both the…
Most genuine multi-sided surface representations depend on a 2D domain that enables a mapping between local parameters and global coordinates. The shape of this domain ranges from regular polygons to curved configurations, but the simple…
Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of…
This work proposes a RGB-D SLAM system specifically designed for structured environments and aimed at improved tracking and mapping accuracy by relying on geometric features that are extracted from the surrounding. Structured environments…