arXiv subjects

Xavier Martin

Publications and source records attributed to Xavier Martin.

16 recordsLinked to original sources

arXiv2019

Moulding Humans: Non-parametric 3D Human Shape Estimation from Single Images

In this paper, we tackle the problem of 3D human shape estimation from single RGB images. While the recent progress in convolutional neural networks has allowed impressive results for 3D human pose estimation, estimating the full 3D shape of a person is still an open issue. Model-based approaches can output precise meshes of naked under-cloth human bodies but fail to estimate details and un-modelled elements such as hair or clothing. On the other hand, non-parametric volumetric approaches can potentially estimate complete shapes but, in practice, they are limited by the resolution of the output grid and cannot produce detailed estimates. In this work, we propose a non-parametric approach that employs a double depth map to represent the 3D shape of a person: a visible depth map and a "hidden" depth map are estimated and combined, to reconstruct the human 3D shape as done with a "mould". This representation through 2D depth maps allows a higher resolution output with a much lower dimension than voxel-based volumetric representations. Additionally, our fully derivable depth-based model allows us to efficiently incorporate a discriminator in an adversarial fashion to improve the accuracy and "humanness" of the 3D output. We train and quantitatively validate our approach on SURREAL and on 3D-HUMANS, a new photorealistic dataset made of semi-synthetic in-house videos annotated with 3D ground truth surfaces.

cs.CV↗

arXiv2018

Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra

The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey-Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey-Wilson algebra generated by twisted primitive elements of $\mathfrak U_q(sl(2))$. The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey-Wilson algebra into $\mathfrak U_q(sl(2))$.

math.QA↗

arXiv2017

Learning from Synthetic Humans

Estimating human pose, shape, and motion from images and videos are fundamental challenges with many applications. Recent advances in 2D human pose estimation use large amounts of manually-labeled training data for learning convolutional neural networks (CNNs). Such data is time consuming to acquire and difficult to extend. Moreover, manual labeling of 3D pose, depth and motion is impractical. In this work we present SURREAL (Synthetic hUmans foR REAL tasks): a new large-scale dataset with synthetically-generated but realistic images of people rendered from 3D sequences of human motion capture data. We generate more than 6 million frames together with ground truth pose, depth maps, and segmentation masks. We show that CNNs trained on our synthetic dataset allow for accurate human depth estimation and human part segmentation in real RGB images. Our results and the new dataset open up new possibilities for advancing person analysis using cheap and large-scale synthetic data.

cs.CV↗

arXiv2016

Human Action Localization with Sparse Spatial Supervision

We introduce an approach for spatio-temporal human action localization using sparse spatial supervision. Our method leverages the large amount of annotated humans available today and extracts human tubes by combining a state-of-the-art human detector with a tracking-by-detection approach. Given these high-quality human tubes and temporal supervision, we select positive and negative tubes with very sparse spatial supervision, i.e., only one spatially annotated frame per instance. The selected tubes allow us to effectively learn a spatio-temporal action detector based on dense trajectories or CNNs. We conduct experiments on existing action localization benchmarks: UCF-Sports, J-HMDB and UCF-101. Our results show that our approach, despite using sparse spatial supervision, performs on par with methods using full supervision, i.e., one bounding box annotation per frame. To further validate our method, we introduce DALY (Daily Action Localization in YouTube), a dataset for realistic action localization in space and time. It contains high quality temporal and spatial annotations for 3.6k instances of 10 actions in 31 hours of videos (3.3M frames). It is an order of magnitude larger than existing datasets, with more diversity in appearance and long untrimmed videos.

cs.CV↗

arXiv2015

A bispectral q-hypergeometric basis for a class of quantum integrable models

For the class of quantum integrable models generated from the $q-$Onsager algebra, a basis of bispectral multivariable $q-$orthogonal polynomials is exhibited. In a first part, it is shown that the multivariable Askey-Wilson polynomials with $N$ variables and $N+3$ parameters introduced by Gasper and Rahman [1] generate a family of infinite dimensional modules for the $q-$Onsager algebra, whose fundamental generators are realized in terms of the multivariable $q-$difference and difference operators proposed by Iliev [2]. Raising and lowering operators extending those of Sahi [3] are also constructed. In a second part, finite dimensional modules are constructed and studied for a certain class of parameters and if the $N$ variables belong to a discrete support. In this case, the bispectral property finds a natural interpretation within the framework of tridiagonal pairs. In a third part, eigenfunctions of the $q-$Dolan-Grady hierarchy are considered in the polynomial basis. In particular, invariant subspaces are identified for certain conditions generalizing Nepomechie's relations. In a fourth part, the analysis is extended to the special case $q=1$. This framework provides a $q-$hypergeometric formulation of quantum integrable models such as the open XXZ spin chain with generic integrable boundary conditions ($q\neq 1$).

math-ph↗

arXiv2009

Coupled currents in cosmic strings

We first examine the microstructure of a cosmic string endowed with two simple Abelian currents. This microstructure depends on two state parameters. We then provide the macroscopic description of such a string and show that it depends on an additional Lorentz-invariant state parameter that relates the two currents. We find that in most of the parameter space, the two-current string is essentially equivalent to the single current-carrying string, i.e., only one field condenses onto the defect. In the regions where two currents are present, we find that as far as stability is concerned, one can approximate the dynamics with good accuracy using an analytic model based on either a logarithmic (on the electric side, i.e., for timelike currents) or a rational (on the magnetic side, i.e., for spacelike currents) worldsheet Lagrangian.

hep-ph↗

arXiv2009

Simulation of a scalar field on a fuzzy sphere

The phi^4 real scalar field theory on a fuzzy sphere is studied numerically. We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a disordered phase, and a non-uniform ordered phase where the spatial SO(3) symmetry of the round sphere is spontaneously broken and which has no classical equivalent. The three coexistence lines between these phases, which meet at a triple point, are carefully located with particular attention paid to the one between the two ordered phases and the triple point itself. In the neighbourhood of the triple point all phase boundaries are well approximated by straight lines which, surprisingly, have the same scaling. We argue that unless an additional term is added to enhance the effect of the kinetic term the infinite matrix limit of this model will not correspond to a real scalar field on the commutative sphere or plane.

hep-lat↗

arXiv2006

Simulating the scalar field on the fuzzy sphere

The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three different phases: uniform and disordered phases, as in the usual commutative scalar field theory, and a non-uniform ordered phase related to UV-IR mixing like non-commutative effects. We have determined the coexistence lines between phases, their triple point and their scaling.

hep-lat↗

arXiv2004

The Random Walk in Generalized Quantum Theory

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a certain condition of ``strong positivity'', the most general Markovian, translationally invariant ``decoherence functional'' with nearest neighbor transitions.

gr-qc↗

arXiv2004

A matrix phase for the phi^4 scalar field on the fuzzy sphere

The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is also one of the simplest examples of a non commutative space to study field theory on. Aside from the usual disordered and uniform phases present in the commutative scalar field theory, we find and discuss in detail a new phase with spontaneously broken rotational invariance, called matrix phase because the geometry of the fuzzy sphere, as expressed by the kinetic term, becomes negligible there. This gives some further insight on the effect of UV-IR mixing, the unusual behaviour which arises naturally when taking the commutative limit of a non commutative field theory.

hep-th↗

arXiv2004

Fuzzy Orbifolds

A family of fuzzy orbifolds are generated by looking at sub-algebras of the fuzzy sphere. One of them is actually commutative and can be mapped exactly onto a lattice. The others are fuzzy approximations of S^2/Z_N where Z_N is the cyclic group of rotations of angle 2pi/N and provides the first example of the ``fuzzification'' of a space with singularities (at the poles). This construction can easily be generalised to other fuzzy spaces.

hep-th↗

arXiv2003

Dynamical instability criterion for circular (vorton) string loops

Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium (i.e. vorton) state of a closed string loop it is shown that the fundamental axisymmetric ($n=0$) and lowest order ($n=1$) nonaxisymmetric perturbation modes can never be unstable. However, stability for modes of higher order ($n\geq 2$) is found to be non-trivially dependent on the values of the characteristic propagation velocity, $c$ say, of longitudinal perturbations and of the corresponding extrinsic perturbation velocity, $v$ say. For each mode number the criterion for instability is the existence of nonreal roots for a certain cubic eigenvalue equation for the corresponding mode frequency. A very simple sufficient but not necessary condition for reality of the roots and therefore absence of instability is that the characteristic velocity ratio, $c/v$ be greater than or equal to unity. Closer examination of the low velocity (experimentally accessible) nonrelativistic regime shows that in that limit the criterion for instability is just that the dimensionless characteristic ratio $c/v$ be less than a critical value $χ_c$ whose numerical value is approximately $1\over 2$. In the relativistic regime that is relevant to superconducting cosmic strings the situation is rather delicate, calling for more detailed investigation that is postponed for future work.

hep-th↗

arXiv2002

Current-carrying cosmic string loops 3D simulation: towards a reduction of the vorton excess problem

The dynamical evolution of superconducting cosmic string loops with specific equations of state describing timelike and spacelike currents is studied numerically. This analysis extends previous work in two directions: first it shows results coming from a fully three dimensional simulation (as opposed to the two dimensional case already studied), and it now includes fermionic as well as bosonic currents. We confirm that in the case of bosonic currents, shocks are formed in the magnetic regime and kinks in the electric regime. For a loop endowed with a fermionic current with zero-mode carriers, we show that only kinks form along the string worldsheet, therefore making these loops slightly more stable against charge carrier radiation, the likely outcome of either shocks or kinks. All these combined effects tend to reduce the number density of stable loops and contribute to ease the vorton excess problem. As a bonus, these effects also may provide new ways of producing high energy cosmic rays.

hep-ph↗

arXiv2000

Dynamics of Cosmic Necklaces

We perform numerical simulations of cosmic necklaces (systems of monopoles connected to two strings each) and investigate the conditions under which monopoles annihilate. When the total monopole energy is large compared to the string energy, we find that the string motion is no longer periodic, and thus the strings will be chopped up by self intersection. When the total monopole energy is much smaller than the string energy, the string motion is periodic, but that of the monopoles is not, and thus the monopoles travel along the string and annihilate with each other.

astro-ph↗

arXiv1997

High Energy Particles from Monopoles Connected by Strings

Monopole-antimonopole pairs connected by strings and monopole-string networks with $N>2$ strings attached to each monopole can be formed at phase transitions in the early universe. In such hybrid defects, monopoles accelerate under the string tension and can reach ultrarelativistic Lorentz factors, $γ\gg 1$. We study the radiation of gauge quanta by accelerating monopoles. For monopoles with a chromomagnetic charge, we also discuss the high-energy hadron production through emission of virtual gluons and their subsequent fragmentation into hadrons. The relevant parameter for gauge boson radiation is $M/a$, where $M$ is the boson mass and $a$ is the proper acceleration of the monopole. For $M\ll a$, the gauge bosons can be considered as massless and the typical energy of the emitted quanta is $E\simγa$. In the opposite limit, $M\gg a$, the radiation power is exponentially suppressed and gauge quanta are emitted with a typical energy $E\simγM$ in a narrow range $ΔE/E\sim (a/M)^{1/2}$. Cosmological monopole-string networks can produce photons and hadrons of extremely high energies. For a wide range of parameters these energies can be much greater than the Planck scale.

astro-ph↗

arXiv1997

Gravitational wave background from hybrid topological defects

We investigate the spectrum of stochastic gravitational wave background generated by hybrid topological defects: domain walls bounded by strings and monopoles connected by strings. Such defects typically decay early in the history of the universe, and their mass scale is not subject to the constraints imposed by microwave background and millisecond pulsar observations. Nonetheless, the intensity of the gravitational wave background from hybrid defects can be quite high at frequencies above $10^{-8} Hz$, and in particular in the frequency range of LIGO, VIRGO and LISA detectors.

astro-ph↗