arXiv subjects

Michal Szabados

Publications and source records attributed to Michal Szabados.

4 recordsLinked to original sources

arXiv2020

Collaborative Augmented Reality on Smartphones via Life-long City-scale Maps

In this paper we present the first published end-to-end production computer-vision system for powering city-scale shared augmented reality experiences on mobile devices. In doing so we propose a new formulation for an experience-based mapping framework as an effective solution to the key issues of city-scale SLAM scalability, robustness, map updates and all-time all-weather performance required by a production system. Furthermore, we propose an effective way of synchronising SLAM systems to deliver seamless real-time localisation of multiple edge devices at the same time. All this in the presence of network latency and bandwidth limitations. The resulting system is deployed and tested at scale in San Francisco where it delivers AR experiences in a mapped area of several hundred kilometers. To foster further development of this area we offer the data set to the public, constituting the largest of this kind to date.

cs.CV↗

arXiv2017

Nivat's conjecture holds for sums of two periodic configurations

Nivat's conjecture is a long-standing open combinatorial problem. It concerns two-dimensional configurations, that is, maps $\mathbb Z^2 \rightarrow \mathcal A$ where $\mathcal A$ is a finite set of symbols. Such configurations are often understood as colorings of a two-dimensional square grid. Let $P_c(m,n)$ denote the number of distinct $m \times n$ block patterns occurring in a configuration $c$. Configurations satisfying $P_c(m,n) \leq mn$ for some $m,n \in \mathbb N$ are said to have low rectangular complexity. Nivat conjectured that such configurations are necessarily periodic. Recently, Kari and the author showed that low complexity configurations can be decomposed into a sum of periodic configurations. In this paper we show that if there are at most two components, Nivat's conjecture holds. As a corollary we obtain an alternative proof of a result of Cyr and Kra: If there exist $m,n \in \mathbb N$ such that $P_c(m,n) \leq mn/2$, then $c$ is periodic. The technique used in this paper combines the algebraic approach of Kari and the author with balanced sets of Cyr and Kra.

cs.DM↗

arXiv2016

An Algebraic Geometric Approach to Nivat's Conjecture

We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup when there is a non-trivial annihilating polynomial: a non-zero polynomial whose formal product with the power series is zero. Such annihilator exists, for example, if the number of distinct patterns of some finite shape $D$ in the configuration is at most the size $|D|$ of the shape. This is our low pattern complexity assumption. We prove that the configuration must be a sum of periodic configurations over integers, possibly with unbounded values. As a specific application of the method we obtain an asymptotic version of the well-known Nivat's conjecture: we prove that any two-dimensional, non-periodic configuration can satisfy the low pattern complexity assumption with respect to only finitely many distinct rectangular shapes $D$.

cs.DM↗

arXiv2015

An Algebraic Geometric Approach to Nivat's Conjecture

We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup when there is a non-trivial annihilating polynomial: a non-zero polynomial whose formal product with the power series is zero. Such annihilator exists, for example, if the number of distinct patterns of some finite shape D in the configuration is at most the size |D| of the shape. This is our low pattern complexity assumption. We prove that the configuration must be a sum of periodic configurations over integers, possibly with unbounded values. As a specific application of the method we obtain an asymptotic version of the well-known Nivat's conjecture: we prove that any two-dimensional, non-periodic configuration can satisfy the low pattern complexity assumption with respect to only finitely many distinct rectangular shapes D.

cs.DM↗