Elliptic Genus Derivation of 4d Holomorphic Blocks

We study elliptic vortices on $\mathbb{C}\times T^2$ by considering the 2d quiver gauge theory describing their moduli spaces. The elliptic genus of these moduli spaces is the elliptic version of vortex partition function of the 4d theory. We focus on two examples: the first is a $\mathcal{N}=1$, $\mathrm{U}(N)$ gauge theory with fundamental and anti-fundamental matter; the second is a $\mathcal{N}=2$, $\mathrm{U}(N)$ gauge theory with matter in the fundamental representation. The results are instances of 4d "holomorphic blocks" into which partition functions on more complicated surfaces factorize. They can also be interpreted as free-field representations of elliptic Virasoro algebrae.Comment: 15 pages, 2 figure

Supersymmetric Wilson loops in two dimensions and duality

We classify bosonic $\mathcal{N}=(2,2)$ supersymmetric Wilson loops on arbitrary backgrounds with vector-like R-symmetry. These can be defined on any smooth contour and come in two forms which are universal across all backgrounds. We show that these Wilson loops, thanks to their cohomological properties, are all invariant under smooth deformations of their contour. At genus zero they can always be mapped to local operators and computed exactly with supersymmetric localisation. Finally, we find the precise map, under two-dimensional Seiberg-like dualities, of correlators of supersymmetric Wilson loops.Comment: 16 pages, 2 figures; v2: minor corrections, references added; v3: new section and appendix, references added, published versio

Guided Stereo Matching

Stereo is a prominent technique to infer dense depth maps from images, and deep learning further pushed forward the state-of-the-art, making end-to-end architectures unrivaled when enough data is available for training. However, deep networks suffer from significant drops in accuracy when dealing with new environments. Therefore, in this paper, we introduce Guided Stereo Matching, a novel paradigm leveraging a small amount of sparse, yet reliable depth measurements retrieved from an external source enabling to ameliorate this weakness. The additional sparse cues required by our method can be obtained with any strategy (e.g., a LiDAR) and used to enhance features linked to corresponding disparity hypotheses. Our formulation is general and fully differentiable, thus enabling to exploit the additional sparse inputs in pre-trained deep stereo networks as well as for training a new instance from scratch. Extensive experiments on three standard datasets and two state-of-the-art deep architectures show that even with a small set of sparse input cues, i) the proposed paradigm enables significant improvements to pre-trained networks. Moreover, ii) training from scratch notably increases accuracy and robustness to domain shifts. Finally, iii) it is suited and effective even with traditional stereo algorithms such as SGM.Comment: CVPR 201

Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 Super Chern-Simons theories

We present a complete two-loop analysis of the quantum expectation value for circular BPS Wilson loops in ABJ(M) theories. We examine in details the 1/2 BPS case, that requires non-trivial fermionic couplings with the contour, finding perfect agreement with the exact matrix model answer at zero framing. The result is obtained through a careful application of DRED regularization scheme, combined with a judicious rearrangement of the relevant perturbative contributions that reduces the computation to simple integrals. We carefully analyze the contribution of fermions that is crucial for the consistency with the localization procedure and point out the arising of pivotal evanescent terms, discussing their meaning in relation to Ward identities.Comment: 32 pages, 5 figures, Referemces adde

Computer vision for 3d perception and applications

Effective 3D perception of an observed scene greatly enriches the knowledge about the surrounding environment and is crucial to effectively develop high-level applications for various purposes [...

Real-time self-adaptive deep stereo

Deep convolutional neural networks trained end-to-end are the state-of-the-art methods to regress dense disparity maps from stereo pairs. These models, however, suffer from a notable decrease in accuracy when exposed to scenarios significantly different from the training set, e.g., real vs synthetic images, etc.). We argue that it is extremely unlikely to gather enough samples to achieve effective training/tuning in any target domain, thus making this setup impractical for many applications. Instead, we propose to perform unsupervised and continuous online adaptation of a deep stereo network, which allows for preserving its accuracy in any environment. However, this strategy is extremely computationally demanding and thus prevents real-time inference. We address this issue introducing a new lightweight, yet effective, deep stereo architecture, Modularly ADaptive Network (MADNet) and developing a Modular ADaptation (MAD) algorithm, which independently trains sub-portions of the network. By deploying MADNet together with MAD we introduce the first real-time self-adaptive deep stereo system enabling competitive performance on heterogeneous datasets.Comment: Accepted at CVPR2019 as oral presentation. Code Available https://github.com/CVLAB-Unibo/Real-time-self-adaptive-deep-stere

Learning monocular depth estimation with unsupervised trinocular assumptions

Obtaining accurate depth measurements out of a single image represents a fascinating solution to 3D sensing. CNNs led to considerable improvements in this field, and recent trends replaced the need for ground-truth labels with geometry-guided image reconstruction signals enabling unsupervised training. Currently, for this purpose, state-of-the-art techniques rely on images acquired with a binocular stereo rig to predict inverse depth (i.e., disparity) according to the aforementioned supervision principle. However, these methods suffer from well-known problems near occlusions, left image border, etc inherited from the stereo setup. Therefore, in this paper, we tackle these issues by moving to a trinocular domain for training. Assuming the central image as the reference, we train a CNN to infer disparity representations pairing such image with frames on its left and right side. This strategy allows obtaining depth maps not affected by typical stereo artifacts. Moreover, being trinocular datasets seldom available, we introduce a novel interleaved training procedure enabling to enforce the trinocular assumption outlined from current binocular datasets. Exhaustive experimental results on the KITTI dataset confirm that our proposal outperforms state-of-the-art methods for unsupervised monocular depth estimation trained on binocular stereo pairs as well as any known methods relying on other cues.Comment: 14 pages, 7 figures, 4 tables. Accepted to 3DV 201