Related papers: L-systems in Geometric Modeling
Autonomous vehicles (AVs) rely on sophisticated perception systems to interpret their surroundings, a cornerstone for safe navigation and decision-making. The integration of Large Language Models (LLMs) into AV perception frameworks offers…
Graphs are an essential data structure utilized to represent relationships in real-world scenarios. Prior research has established that Graph Neural Networks (GNNs) deliver impressive outcomes in graph-centric tasks, such as link prediction…
Diffusion models (DMs) excel in photo-realistic image synthesis, but their adaptation to LiDAR scene generation poses a substantial hurdle. This is primarily because DMs operating in the point space struggle to preserve the curve-like…
In this paper we present a novel approach for lane detection and segmentation using generative models. Traditionally discriminative models have been employed to classify pixels semantically on a road. We model the probability distribution…
Driving in safety-critical scenarios requires quick, context-aware decision-making grounded in both situational understanding and experiential reasoning. Large Language Models (LLMs), with their powerful general-purpose reasoning…
Autonomous driving systems often degrade under adverse visibility conditions-such as rain, nighttime, or snow-where online scene geometry (e.g., lane dividers, road boundaries, and pedestrian crossings) becomes sparse or fragmented. While…
We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. Under…
The linear system $|D|$ of a divisor $D$ on a metric graph has the structure of a cell complex. We introduce the anchor divisors and anchor cells in it - they serve as the landmarks for us to compute the f-vector of the complex and find all…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
This article continues the investigation started in [9] on subdivision schemes refining 2D point-normal pairs, obtained by modifying linear subdivision schemes using the circle average. While in [9] the convergence of the Modified…
In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie…
We present a framework for constructing examples of smooth projective curves over number fields with explicitly given elements in their second K-group using elementary algebraic geometry. This leads to new examples for hyperelliptic curves…
We studied linear mappings in Beidleman near-vector spaces and explored their matrix representations using $R$-bases of $R$-subgroups. Additionally, we developed algorithms for determining the seed number and seed sets of $R$-subgroups…
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…
Motion planning framed as optimisation in structured latent spaces has recently emerged as competitive with traditional methods in terms of planning success while significantly outperforming them in terms of computational speed. However,…
We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…
Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…
An R package for specifying and estimating linear latent variable models is presented. The philosophy of the implementation is to separate the model specification from the actual data, which leads to a dynamic and easy way of modeling…
We present economical iterative algorithms built on the Biconjugate $A$-Orthonormalization Procedure for real unsymmetric and complex non-Hermitian systems. The principal characteristics of the developed solvers is that they are fast…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…