arXiv subjects

Pietro Tortella

Publications and source records attributed to Pietro Tortella.

6 recordsLinked to original sources

arXiv2020

Light3DPose: Real-time Multi-Person 3D PoseEstimation from Multiple Views

We present an approach to perform 3D pose estimation of multiple people from a few calibrated camera views. Our architecture, leveraging the recently proposed unprojection layer, aggregates feature-maps from a 2D pose estimator backbone into a comprehensive representation of the 3D scene. Such intermediate representation is then elaborated by a fully-convolutional volumetric network and a decoding stage to extract 3D skeletons with sub-voxel accuracy. Our method achieves state of the art MPJPE on the CMU Panoptic dataset using a few unseen views and obtains competitive results even with a single input view. We also assess the transfer learning capabilities of the model by testing it against the publicly available Shelf dataset obtaining good performance metrics. The proposed method is inherently efficient: as a pure bottom-up approach, it is computationally independent of the number of people in the scene. Furthermore, even though the computational burden of the 2D part scales linearly with the number of input views, the overall architecture is able to exploit a very lightweight 2D backbone which is orders of magnitude faster than the volumetric counterpart, resulting in fast inference time. The system can run at 6 FPS, processing up to 10 camera views on a single 1080Ti GPU.

cs.CV↗

arXiv2017

Moduli spaces of $Λ$-modules on abelian varieties

We study the moduli space $\mathbf{M}_X(Λ, n)$ of semistable $Λ$-modules of vanishing Chern classes over an abelian variety $X$, where $Λ$ belongs to a certain subclass of $D$-algebras. In particular, for $Λ= \mathcal{D}_X$ (resp. $Λ= \mathrm{Sym}^\bullet \mathcal{T}X$) we obtain a description of the moduli spaces of flat connections (resp. Higgs bundles). We give a description of $\mathbf{M}_X(Λ, n)$ in terms of a symmetric product of a certain fibre bundle over the dual abelian variety $\hat{X}$. We also give a moduli interpretation to the associated Hilbert scheme as the classifying space of $Λ$-modules with extra structure. Finally, we study the non-abelian Hodge theory associated to these new moduli spaces.

math.AG↗

arXiv2015

Representations of Atiyah algebroids and logarithmic connections

In this paper, we investigate representations of $\operatorname{At}(N)$, the Atiyah algebroids of a holomorphic line bundles $N$ over a complex manifold $Y$. In particular, we relate $\operatorname{At}(N)$-modules with logarithmic connections through two functors. On the one hand, we use these functors to the define invariants (monodromy) for representations of Atiyah algebroids. On the other hand, this opens the way to use the theory of Lie algebroids to study problems about logarithmic connections; we will give an example of this by showing that the existence of Deligne's extensions of flat connections and the Riemann-Hilbert correspondence for regular flat meromorphic connections may be obtained as pull-back of similar results for $\operatorname{At}(N)$-modules, and, at this level, these results are a direct consequence of the second theorem of Lie.

math.AG↗

arXiv2014

Nonabelian holomorphic Lie algebroid extensions

We classify nonabelian extensions of Lie algebroids in the holomorphic category. Moreover we study a spectral sequence associated to any such extension. This spectral sequence generalizes the Hochschild-Serre spectral sequence for Lie algebras to the holomorphic Lie algebroid setting. As an application, we show that the hypercohomology of the Atiyah algebroid of a line bundle has a natural Hodge structure.

math.SG↗

arXiv2012

$Λ$-modules and holomorphic Lie algebroid connections

Let $X$ be a complex smooth projective variety, and $\mathcal{G}$ a locally free sheaf on $X$. We show that there is a 1-to-1 correspondence between pairs $(Λ,Ξ)$, where $Λ$ is a sheaf of almost polynomial filtered algebras over $X$ satisfying Simpson's axioms and $Ξ: \GrΛ\rightarrow \Sym^\bullet_{\corO_X} \mathcal{G}$ is an isomorphism, and pairs $(\mathcal{L},Σ)$, where $\mathcal{L}$ is a holomorphic Lie algebroid structure on $\mathcal{G}$ and $Σ$ is a class in $F^1H^2(\mathcal{L},\C)$, the first Hodge filtration piece of the second cohomology of $\bella$. As an application, we construct moduli spaces of semistable flat $\mathcal{L}$-connections for any holomorphic Lie algebroid $\mathcal{L}$. Particular examples of these are given by generalized holomorphic bundles for any generalized complex structure associated to a holomorphic Poisson manifold.

math.AG↗

arXiv2010

Representations of the Heisenberg algebra and moduli spaces of framed sheaves

We give a `geometrical' construction of an action of a Heisenberg algebra on the homology of the moduli spaces of torsion free sheaves on a complex smooth connected projective surface, framed along a smooth connected genus zero curve. This result generalizes Nakajima's construction for the Hilbert schemes of points.

math.AG↗