arXiv subjects

Marko Thiel

Publications and source records attributed to Marko Thiel.

15 recordsLinked to original sources

arXiv2024

UADA3D: Unsupervised Adversarial Domain Adaptation for 3D Object Detection with Sparse LiDAR and Large Domain Gaps

In this study, we address a gap in existing unsupervised domain adaptation approaches on LiDAR-based 3D object detection, which have predominantly concentrated on adapting between established, high-density autonomous driving datasets. We focus on sparser point clouds, capturing scenarios from different perspectives: not just from vehicles on the road but also from mobile robots on sidewalks, which encounter significantly different environmental conditions and sensor configurations. We introduce Unsupervised Adversarial Domain Adaptation for 3D Object Detection (UADA3D). UADA3D does not depend on pre-trained source models or teacher-student architectures. Instead, it uses an adversarial approach to directly learn domain-invariant features. We demonstrate its efficacy in various adaptation scenarios, showing significant improvements in both self-driving car and mobile robot domains. Our code is open-source and will be available soon.

cs.CV↗

arXiv2024

MCD: Diverse Large-Scale Multi-Campus Dataset for Robot Perception

Perception plays a crucial role in various robot applications. However, existing well-annotated datasets are biased towards autonomous driving scenarios, while unlabelled SLAM datasets are quickly over-fitted, and often lack environment and domain variations. To expand the frontier of these fields, we introduce a comprehensive dataset named MCD (Multi-Campus Dataset), featuring a wide range of sensing modalities, high-accuracy ground truth, and diverse challenging environments across three Eurasian university campuses. MCD comprises both CCS (Classical Cylindrical Spinning) and NRE (Non-Repetitive Epicyclic) lidars, high-quality IMUs (Inertial Measurement Units), cameras, and UWB (Ultra-WideBand) sensors. Furthermore, in a pioneering effort, we introduce semantic annotations of 29 classes over 59k sparse NRE lidar scans across three domains, thus providing a novel challenge to existing semantic segmentation research upon this largely unexplored lidar modality. Finally, we propose, for the first time to the best of our knowledge, continuous-time ground truth based on optimization-based registration of lidar-inertial data on large survey-grade prior maps, which are also publicly released, each several times the size of existing ones. We conduct a rigorous evaluation of numerous state-of-the-art algorithms on MCD, report their performance, and highlight the challenges awaiting solutions from the research community.

cs.RO↗

arXiv2023

Strange Expectations in Affine Weyl Groups

Our main result is a generalization, to all affine Weyl groups, of P. Johnson's proof of D. Armstrong's conjecture for the expected number of boxes in a simultaneous core. This extends earlier results by the second and third authors in simply-laced type. We do this by modifying and refining the appropriate notion of the "size" of a simultaneous core. In addition, we provide combinatorial core-like models for the coroot lattices in classical type and type $G_2$.

math.CO↗

arXiv2023

Towards a Robust Sensor Fusion Step for 3D Object Detection on Corrupted Data

Multimodal sensor fusion methods for 3D object detection have been revolutionizing the autonomous driving research field. Nevertheless, most of these methods heavily rely on dense LiDAR data and accurately calibrated sensors which is often not the case in real-world scenarios. Data from LiDAR and cameras often come misaligned due to the miscalibration, decalibration, or different frequencies of the sensors. Additionally, some parts of the LiDAR data may be occluded and parts of the data may be missing due to hardware malfunction or weather conditions. This work presents a novel fusion step that addresses data corruptions and makes sensor fusion for 3D object detection more robust. Through extensive experiments, we demonstrate that our method performs on par with state-of-the-art approaches on normal data and outperforms them on misaligned data.

cs.RO↗

arXiv2022

Comparison of Varied 2D Mapping Approaches by Using Practice-Oriented Evaluation Criteria

A key aspect of the precision of a mobile robots localization is the quality and aptness of the map it is using. A variety of mapping approaches are available that can be employed to create such maps with varying degrees of effort, hardware requirements and quality of the resulting maps. To create a better understanding of the applicability of these different approaches to specific applications, this paper evaluates and compares three different mapping approaches based on simultaneous localization and mapping, terrestrial laser scanning as well as publicly accessible building contours.

cs.RO↗

arXiv2018

Strange Expectations and the Winnie-the-Pooh Problem

Motivated by the study of simultaneous cores, we give three proofs (in varying levels of generality) for the expected norm of a weight in a highest weight representation of a complex simple Lie algebra. First, we argue directly using the polynomial method and the Weyl character formula. Second, we use the combinatorics of semistandard tableaux to obtain the result in type A. Third, and most interestingly, we relate this problem to the "Winnie-the-Pooh problem" regarding orthogonal decompositions of Lie algebras; although this approach offers the most explanatory power, it applies only to Cartan types other than A and C. We conclude with computations of many combinatorial cumulants.

math.CO↗

arXiv2017

The number of roots of full support

Chapoton has observed a simple product formula for the number of reflections in a finite Coxeter group that have full support. We give a uniform proof of his formula for Weyl groups. We furthermore refine his formula by the length of the roots.

math.CO↗

arXiv2016

On parking functions and the zeta map in types B,C and D

Let $Φ$ be an irreducible crystallographic root system with Weyl group $W$, coroot lattice $\check{Q}$ and Coxeter number $h$. Recently the second named author defined a uniform $W$-isomorphism $ζ$ between the finite torus $\check{Q}/(mh+1)\check{Q}$ and the set of non-nesting parking fuctions $\operatorname{Park}^{(m)}(Φ)$. If $Φ$ is of type $A_{n-1}$ and $m=1$ this map is equivalent to a map defined on labelled Dyck paths that arises in the study of the Hilbert series of the space of diagonal harmonics. In this paper we investigate the case $m=1$ for the other infinite families of root systems ($B_n$, $C_n$ and $D_n$). In each type we define models for the finite torus and for the set of non-nesting parking functions in terms of labelled lattice paths. The map $ζ$ can then be viewed as a map between these combinatorial objects. Our work entails new bijections between (square) lattice paths and ballot paths.

math.CO↗

arXiv2016

From Anderson to Zeta

For an irreducible crystallographic root system $Φ$ and a positive integer $p$ relatively prime to the Coxeter number $h$ of $Φ$, we give a natural bijection $\mathcal{A}$ from the set $\widetilde{W}^p$ of affine Weyl group elements with no inversions of height $p$ to the finite torus $\check{Q}/p\check{Q}$. Here $\check{Q}$ is the coroot lattice of $Φ$. This bijection is defined uniformly for all irreducible crystallographic root systems $Φ$ and is equivalent to the Anderson map $\mathcal{A}_{GMV}$ defined by Gorsky, Mazin and Vazirani when $Φ$ is of type $A_{n-1}$. Specialising to $p=mh+1$, we use $\mathcal{A}$ to define a uniform $W$-set isomorphism $ζ$ from the finite torus $\check{Q}/(mh+1)\check{Q}$ to the set of $m$-nonnesting parking functions $\mathsf{Park}_Φ^{(m)}$ of $Φ$. The map $ζ$ is equivalent to the zeta map $ζ_{HL}$ of Haglund and Loehr when $m=1$ and $Φ$ is of type $A_{n-1}$.

math.CO↗

arXiv2016

A new cyclic sieving phenomenon for Catalan objects

Based on computational experiments, Jim Propp and Vic Reiner suspected that there might exist a sequence of combinatorial objects $X_n$, each carrying a natural action of the cyclic group $C_{n-1}$ of order $n-1$ such that the triple $\left(X_n,C_{n-1},\frac{1}{[n+1]_q}{2n \brack n}_q\right)$ exhibits the cyclic sieving phenomenon. We prove their suspicion right.

math.CO↗

arXiv2015

Strange Expectations

Let gcd(a,b)=1. J. Olsson and D. Stanton proved that the maximum number of boxes in a simultaneous (a,b)-core is (a^2-1)(b^2-1)/24, and that this maximum was achieved by a unique core. P. Johnson combined Ehrhart theory with the polynomial method to prove D. Armstrong's conjecture that the expected number of boxes in a simultaneous (a,b)-core is (a-1)(b-1)(a+b+1)/24. We extend P. Johnson's method to compute the variance to be ab(a-1)(b-1)(a+b)(a+b+1)/1440. By extending the definitions of "simultaneous cores" and "number of boxes" to affine Weyl groups, we give uniform generalizations of all three formulae above to simply-laced affine types. We further explain the appearance of the number 24 using the "strange formula" of H. Freudenthal and H. de Vries.

math.CO↗

arXiv2014

Type C parking functions and a zeta map

We introduce type C parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type C parking functions to regions of the Shi arrangement of type C, encoded as diagonally labelled ballot paths and endowed with a natural statistic area'. This bijection is a natural analogue of the zeta map of Haglund and Loehr and maps dinv' to area'. We give three different descriptions of it.

math.CO↗

arXiv2014

On floors and ceilings of the k-Catalan arrangement

The set of dominant regions of the $k$-Catalan arrangement of a crystallographic root system $Φ$ is a well-studied object enumerated by the Fuß-Catalan number $Cat^{(k)}(Φ)$. It is natural to refine this enumeration by considering floors and ceilings of dominant regions. A conjecture of Armstrong states that counting dominant regions by their number of floors of a certain height gives the same distribution as counting dominant regions by their number of ceilings of the same height. We prove this conjecture using a bijection that provides even more refined enumerative information.

math.CO↗

arXiv2013

On the H-triangle of generalised nonnesting partitions

To a crystallographic root system Φ, and a positive integer k, there are associated two Fuss-Catalan objects, the set of nonnesting partitions NN^(k)(Φ), and the cluster complex Δ^(k)(Φ). These posess a number of enumerative coincidences, many of which are captured in a surprising identity, first conjectured by Chapoton for k=1 and later generalized to k>1 by Armstrong. We prove this conjecture, obtaining some structural and enumerative results on NN^(k)(Φ) along the way, including an earlier conjecture by Fomin and Reading giving a refined enumeration by Fuß-Narayana numbers.

math.CO↗

arXiv2013

The inversion number and the major index are asymptotically jointly normally distributed on words

In a recent paper, Baxter and Zeilberger show that the two most important Mahonian statistics, the inversion number and the major index, are asymptotically independently normally distributed on permutations. In another recent paper, Canfield, Janson and Zeilberger prove the result, already known to statisticians, that the Mahonian distribution is asymptotically normal on words. This leaves one question unanswered: What, asymptotically, is the joint distribution of the inversion number and the major index on words? We answer this question by establishing convergence to a bivariate normal distribution.

math.CO↗