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Maurizio Monge

Publications and source records attributed to Maurizio Monge.

At least 19 recordsLinked to original sources
arXiv2025

Benchmarking Egocentric Visual-Inertial SLAM at City Scale

Precise 6-DoF simultaneous localization and mapping (SLAM) from onboard sensors is critical for wearable devices capturing egocentric data, which exhibits specific challenges, such as a wider diversity of motions and viewpoints, prevalent dynamic visual content, or long sessions affected by time-varying sensor calibration. While recent progress on SLAM has been swift, academic research is still driven by benchmarks that do not reflect these challenges or do not offer sufficiently accurate ground truth poses. In this paper, we introduce a new dataset and benchmark for visual-inertial SLAM with egocentric, multi-modal data. We record hours and kilometers of trajectories through a city center with glasses-like devices equipped with various sensors. We leverage surveying tools to obtain control points as indirect pose annotations that are metric, centimeter-accurate, and available at city scale. This makes it possible to evaluate extreme trajectories that involve walking at night or traveling in a vehicle. We show that state-of-the-art systems developed by academia are not robust to these challenges and we identify components that are responsible for this. In addition, we design tracks with different levels of difficulty to ease in-depth analysis and evaluation of less mature approaches. The dataset and benchmark are available at https://www.lamaria.ethz.ch.

cs.CV↗
arXiv2025

Photoreal Scene Reconstruction from an Egocentric Device

In this paper, we investigate the challenges associated with using egocentric devices to photorealistic reconstruct the scene in high dynamic range. Existing methodologies typically assume using frame-rate 6DoF pose estimated from the device's visual-inertial odometry system, which may neglect crucial details necessary for pixel-accurate reconstruction. This study presents two significant findings. Firstly, in contrast to mainstream work treating RGB camera as global shutter frame-rate camera, we emphasize the importance of employing visual-inertial bundle adjustment (VIBA) to calibrate the precise timestamps and movement of the rolling shutter RGB sensing camera in a high frequency trajectory format, which ensures an accurate calibration of the physical properties of the rolling-shutter camera. Secondly, we incorporate a physical image formation model based into Gaussian Splatting, which effectively addresses the sensor characteristics, including the rolling-shutter effect of RGB cameras and the dynamic ranges measured by sensors. Our proposed formulation is applicable to the widely-used variants of Gaussian Splats representation. We conduct a comprehensive evaluation of our pipeline using the open-source Project Aria device under diverse indoor and outdoor lighting conditions, and further validate it on a Meta Quest3 device. Across all experiments, we observe a consistent visual enhancement of +1 dB in PSNR by incorporating VIBA, with an additional +1 dB achieved through our proposed image formation model. Our complete implementation, evaluation datasets, and recording profile are available at http://www.projectaria.com/photoreal-reconstruction/

cs.CV↗
arXiv2023

Project Aria: A New Tool for Egocentric Multi-Modal AI Research

Egocentric, multi-modal data as available on future augmented reality (AR) devices provides unique challenges and opportunities for machine perception. These future devices will need to be all-day wearable in a socially acceptable form-factor to support always available, context-aware and personalized AI applications. Our team at Meta Reality Labs Research built the Aria device, an egocentric, multi-modal data recording and streaming device with the goal to foster and accelerate research in this area. In this paper, we describe the Aria device hardware including its sensor configuration and the corresponding software tools that enable recording and processing of such data.

cs.HC↗
arXiv2023

Decentralization and Acceleration Enables Large-Scale Bundle Adjustment

Scaling to arbitrarily large bundle adjustment problems requires data and compute to be distributed across multiple devices. Centralized methods in prior works are only able to solve small or medium size problems due to overhead in computation and communication. In this paper, we present a fully decentralized method that alleviates computation and communication bottlenecks to solve arbitrarily large bundle adjustment problems. We achieve this by reformulating the reprojection error and deriving a novel surrogate function that decouples optimization variables from different devices. This function makes it possible to use majorization minimization techniques and reduces bundle adjustment to independent optimization subproblems that can be solved in parallel. We further apply Nesterov's acceleration and adaptive restart to improve convergence while maintaining its theoretical guarantees. Despite limited peer-to-peer communication, our method has provable convergence to first-order critical points under mild conditions. On extensive benchmarks with public datasets, our method converges much faster than decentralized baselines with similar memory usage and communication load. Compared to centralized baselines using a single device, our method, while being decentralized, yields more accurate solutions with significant speedups of up to 953.7x over Ceres and 174.6x over DeepLM. Code: https://joeaortiz.github.io/daba.

cs.CV↗
arXiv2023

Cramér distance and discretizations of circle expanding maps II: simulations

This paper presents some numerical experiments in relation with the theoretical study of the ergodic short-term behaviour of discretizations of expanding maps done in arXiv:2206.07991 [math.DS]. Our aim is to identify the phenomena driving the evolution of the Cramér distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the $t$-th iterate of the uniform measure on the grid of order $N$ by the discretization on this grid. Based on numerical simulations we propose some conjectures on the effects of numerical truncation from the ergodic viewpoint.

math.DS↗
arXiv2023

Cramér distance and discretizations of circle expanding maps I: theory

This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the $t$-th iterate of the uniform measure on the grid of order $N$ by the discretization on this grid, when $t$ is fixed and the order $N$ goes to infinity. This is done under some explicit genericity hypotheses on the dynamics, and the distance between measures is measured by the mean of \emph{Cramér} distance. The proof is based on a study of the corresponding linearized problem, where the problem is translated into terms of equirepartition on tori of dimension exponential in $t$. A numerical study associated to this work is presented in arXiv:2206.08000 [math.DS].

math.DS↗
arXiv2023

Theseus: A Library for Differentiable Nonlinear Optimization

We present Theseus, an efficient application-agnostic open source library for differentiable nonlinear least squares (DNLS) optimization built on PyTorch, providing a common framework for end-to-end structured learning in robotics and vision. Existing DNLS implementations are application specific and do not always incorporate many ingredients important for efficiency. Theseus is application-agnostic, as we illustrate with several example applications that are built using the same underlying differentiable components, such as second-order optimizers, standard costs functions, and Lie groups. For efficiency, Theseus incorporates support for sparse solvers, automatic vectorization, batching, GPU acceleration, and gradient computation with implicit differentiation and direct loss minimization. We do extensive performance evaluation in a set of applications, demonstrating significant efficiency gains and better scalability when these features are incorporated. Project page: https://sites.google.com/view/theseus-ai

cs.RO↗
arXiv2023

A general framework for the rigorous computation of invariant densities and the coarse-fine strategy

In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system trough a finite element reduction, by composing the associated transfer operator with a suitable finite dimensional projection (a discretization scheme) as in the well-known Ulam method. We introduce a general framework based on a list of properties (of the system and of the projection) that need to be verified so that we can take advantage of a so-called ``coarse-fine'' strategy. This strategy is a novel method in which we exploit information coming from a coarser approximation of the system to get useful information on a finer approximation, speeding up the computation. This coarse-fine strategy allows a precise estimation of invariant densities and also allows to estimate rigorously the speed of mixing of the system by the speed of mixing of a coarse approximation of it, which can easily be estimated by the computer. The estimates obtained here are rigourous, i.e., they come with exact error bounds that are guaranteed to hold and take into account both the discretiazation and the approximations induced by finite-precision arithmetic. We apply this framework to several discretization schemes and examples of invariant density computation from previous works, obtaining a remarkable reduction in computation time. We have implemented the numerical methods described here in the Julia programming language, and released our implementation publicly as a Julia package.

math.DS↗
arXiv2022

Verifiable Access Control for Augmented Reality Localization and Mapping

Localization and mapping is a key technology for bridging the virtual and physical worlds in augmented reality (AR). Localization and mapping works by creating and querying maps made of anchor points that enable the overlay of these two worlds. As a result, information about the physical world is captured in the map and naturally gives rise to concerns around who can map physical spaces as well as who can access or modify the virtual ones. This paper discusses how we can provide access controls over virtual maps as a basic building block to enhance security and privacy of AR systems. In particular, we propose VACMaps: an access control system for localization and mapping using formal methods. VACMaps defines a domain-specific language that enables users to specify access control policies for virtual spaces. Access requests to virtual spaces are then evaluated against relevant policies in a way that preserves confidentiality and integrity of virtual spaces owned by the users. The precise semantics of the policies are defined by SMT formulas, which allow VACMaps to reason about properties of access policies automatically. An evaluation of VACMaps is provided using an AR testbed of a single-family home. We show that VACMaps is scalable in that it can run at practical speeds and that it can also reason about access control policies automatically to detect potential policy misconfigurations.

cs.CR↗
arXiv2019

Existence of Noise Induced Order, a Computer Aided Proof

We prove the existence of Noise Induced Order in the Matsumoto-Tsuda model, where it was originally discovered in 1983 by numerical simulations. This is a model of the famous Belosouv-Zabotinsky reaction, a chaotic chemical reaction, and consists of a one dimensional random dynamical system with additive noise. The simulations showed that an increase in amplitude of the noise causes the Lyapunov exponent to decrease from positive to negative; we give a mathematical proof of the existence of this transition. The method we use relies on some computer aided estimates providing a certified approximation of the stationary measure in the $L^{1}$ norm. This is realized by explicit functional analytic estimates working together with an efficient algorithm. The method is general enough to be adapted to any piecewise differentiable dynamical system on the unit interval with additive noise. We also prove that the stationary measure of the system varies in a Lipschitz way if the system is perturbed and that the Lyapunov exponent of the system varies in a Hölder way when the noise amplitude increases.

math.DS↗
arXiv2013

Answer to a question on $A$-groups, arisen from the study of Steinitz classes

In this short note we answer to a question of group theory from arXiv:0910.5080. In that paper the author describes the set of realizable Steinitz classes for so-called $A'$-groups of odd order, obtained iterating some direct and semidirect products. It is clear from the definition that $A'$-groups are solvable $A$-groups, but the author left as an open question whether the converse is true. In this note we prove the converse when only two prime numbers divide the order of the group, but we show it to be false in general, producing a family of counterexamples which are metabelian and with exactly three primes dividing the order. Steinitz classes which are realizable for such groups in the family are computed and verified to form a group.

math.GR↗
arXiv2011

A family of Eisenstein polynomials generating totally ramified extensions, identification of extensions and construction of class fields

Let $K$ be a local field with finite residue field, we define a normal form for Eisenstein polynomials depending on the choice of a uniformizer $π_K$ and of residue representatives. The isomorphism classes of extensions generated by the polynomials in the family exhaust all totally ramified extensions, and the multiplicity with which each isomorphism class $L/K$ appears is always smaller than the number of conjugates of $L$ over $K$. An algorithm to recover the set of all special polynomials generating the extension determined by a general Eisenstein polynomial is described. We also give a criterion to quickly establish that a polynomial generates a different extension from that generated by a set of special polynomials, such criterion does not only depend on the usual distance on the set of Eisenstein polynomials considered by Krasner and others. We conclude with an algorithm for the construction of the unique special equation determining a totally ramified class field in general degree, given a suitable representation of a group of norms.

math.NT↗
arXiv2011

Generation of the Symmetric Field by Newton Polynomials in prime Characteristic

Let $N_m = x^m + y^m$ be the $m$-th Newton polynomial in two variables, for $m \geq 1$. Dvornicich and Zannier proved that in characteristic zero three Newton polynomials $N_a, N_b, N_c$ are always sufficient to generate the symmetric field in $x$ and $y$, provided that $a,b,c$ are distinct positive integers such that $(a,b,c)=1$. In the present paper we prove that in case of prime characteristic $p$ the result still holds, if we assume additionally that $a,b,c,a-b,a-c,b-c$ are prime with $p$. We also provide a counterexample in the case where one of the hypotheses is missing. The result follows from the study of the factorization of a generalized Vandermonde determinant in three variables, that under general hypotheses factors as the product of a trivial Vandermonde factor and an irreducible factor. On the other side, the counterexample is connected to certain cases where the Schur polynomials factor as a product of linear factors.

math.AC↗
arXiv2011

An equivalent of Kronecker's Theorem for powers of an Algebraic Number and Structure of Linear Recurrences of fixed length

After defining a notion of $ε$-density, we provide for any real algebraic number $α$ an estimate of the smallest $ε$ such that for each $m>1$ the set of vectors of the form $(t,tα,...,tα^{m-1})$ for $t\in\R$ is $ε$-dense modulo 1, in terms of the multiplicative Mahler measure $M(A(x))$ of the minimal integral polynomial $A(x)$ of $α$, and independently of $m$. In particular, we show that if $α$ has degree $d$ it is possible to take $ε= 2^{[d/2]}/M(A(x))$. On the other hand using asymptotic estimates for Toeplitz determinants we show that for sufficiently large $m$ we cannot have $ε$-density if $ε$ is a fixed number strictly smaller than $1/M(A(x))$. As a byproduct of the proof we obtain a result of independent interest about the structure of the $\Z$-module of integral linear recurrences of fixed length determined by a non-monic polynomial.

math.NT↗
arXiv2011

On perfect hashing of numbers with sparse digit representation via multiplication by a constant

Consider the set of vectors over a field having non-zero coefficients only in a fixed sparse set and multiplication defined by convolution, or the set of integers having non-zero digits (in some base $b$) in a fixed sparse set. We show the existence of an optimal (resp. almost-optimal in the latter case) `magic' multiplier constant that provides a perfect hash function which transfers the information from the given sparse coefficients into consecutive digits. Studying the convolution case we also obtain a result of non-degeneracy for Schur functions as polynomials in the elementary symmetric functions in positive characteristic.

math.NT↗
arXiv2011

Determination of the number of isomorphism classes of extensions of a $\kp$-adic field

We deduce a formula enumerating the isomorphism classes of extensions of a $\kp$-adic field $K$ with given ramification $e$ and inertia $f$. The formula follows from a simple group-theoretic lemma, plus the Krasner formula and an elementary class field theory computation. It shows that the number of classes only depends on the ramification and inertia of the extensions $K/\Q_p$, and $K(ζ_{p^m})/K$ obtained adding the $p^m$-th roots of 1, for all $p^m$ dividing $e$.

math.NT↗
arXiv2011

A characterization of Eisenstein polynomials generating cyclic extensions of degree $p^2$ and $p^3$ over an unramified $\kp$-adic field

Let $p\neq2$ be a prime. We show a technique based on local class field theory and on the expansions of certain resultants which allows to recover very easily Lbekkouri's characterization of Eisenstein polynomials generating cyclic wild extensions of degree $p^2$ over $\Q_p$, and to extend it to the case of the base field $K$ being an unramified extension of $\Q_p$. Furthermore, when a polynomial satisfies only some of the stated conditions, we show that the first unsatisfied condition gives information about the Galois group of the normal closure. This permits to give a complete classification of Eisenstein polynomials of degree $p^2$ whose splitting field is a $p$-extension, providing a full description of the Galois group and its higher ramification subgroups. We then apply the same methods to give a characterization of Eisenstein polynomials of degree $p^3$ generating a cyclic extension. In the last section we deduce a combinatorial interpretation of the monomial symmetric function evaluated in the roots of the unity which appear in certain expansions.

math.NT↗