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Márton Vaitkus

Publications and source records attributed to Márton Vaitkus.

4 recordsLinked to original sources

F3DGS: Federated 3D Gaussian Splatting for Decentralized Multi-Agent World Modeling

We present F3DGS, a federated 3D Gaussian Splatting framework for decentralized multi-agent 3D reconstruction. Existing 3DGS pipelines assume centralized access to all observations, which limits their applicability in distributed robotic settings where agents operate independently, and centralized data aggregation may be restricted. Directly extending centralized training to multi-agent systems introduces communication overhead and geometric inconsistency. F3DGS first constructs a shared geometric scaffold by registering locally merged LiDAR point clouds from multiple clients to initialize a global 3DGS model. During federated optimization, Gaussian positions are fixed to preserve geometric alignment, while each client updates only appearance-related attributes, including covariance, opacity, and spherical harmonic coefficients. The server aggregates these updates using visibility-aware aggregation, weighting each client's contribution by how frequently it observed each Gaussian, resolving the partial-observability challenge inherent to multi-agent exploration. To evaluate decentralized reconstruction, we collect a multi-sequence indoor dataset with synchronized LiDAR, RGB, and IMU measurements. Experiments show that F3DGS achieves reconstruction quality comparable to centralized training while enabling distributed optimization across agents. The dataset, development kit, and source code will be publicly released.

cs.CV↗

A Note on Ribbon-based Biharmonic Surface Patches

In this short note we describe a simple adaptation of biharmonic surfaces to interpolate boundary cross-derivatives given in ribbon form, and compare with the recently proposed Generalized B-spline patches.

math.NA↗

Positive Geometries for Barycentric Interpolation

We propose a novel theoretical framework for barycentric interpolation, using concepts recently developed in mathematical physics. Generalized barycentric coordinates are defined similarly to Shepard's method, using positive geometries - subsets which possess a rational function naturally associated to their boundaries. Positive geometries generalize certain properties of simplices and convex polytopes to a large variety of geometric objects. Our framework unifies several previous constructions, including the definition of Wachspress coordinates over polytopes in terms of adjoints and dual polytopes. We also discuss potential applications to interpolation in 3D line space, mean-value coordinates and splines.

cs.CG↗

A Physical Perspective on Control Points and Polar Forms: Bézier Curves, Angular Momentum and Harmonic Oscillators

Bernstein polynomials and Bézier curves play an important role in computer-aided geometric design and numerical analysis, and their study relates to mathematical fields such as abstract algebra, algebraic geometry and probability theory. We describe a theoretical framework that incorporates the different aspects of the Bernstein-Bézier theory, based on concepts from theoretical physics. We relate Bézier curves to the theory of angular momentum in both classical and quantum mechanics, and describe physical analogues of various properties of Bézier curves -- such as their connection with polar forms -- in the context of quantum spin systems. This previously unexplored relationship between geometric design and theoretical physics is established using the mathematical theory of Hamiltonian mechanics and geometric quantization. An alternative description of spin systems in terms of harmonic oscillators serves as a physical analogue of Pólya's urn models for Bézier curves. We relate harmonic oscillators to Poisson curves and the analytical blossom as well. We present an overview of the relevant mathematical and physical concepts, and discuss opportunities for further research.

cs.CG↗