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Amit Dekel

Publications and source records attributed to Amit Dekel.

At least 19 recordsLinked to original sources
arXiv2025

Visible Structure Retrieval for Lightweight Image-Based Relocalisation

Accurate camera pose estimation from an image observation in a previously mapped environment is commonly done through structure-based methods: by finding correspondences between 2D keypoints on the image and 3D structure points in the map. In order to make this correspondence search tractable in large scenes, existing pipelines either rely on search heuristics, or perform image retrieval to reduce the search space by comparing the current image to a database of past observations. However, these approaches result in elaborate pipelines or storage requirements that grow with the number of past observations. In this work, we propose a new paradigm for making structure-based relocalisation tractable. Instead of relying on image retrieval or search heuristics, we learn a direct mapping from image observations to the visible scene structure in a compact neural network. Given a query image, a forward pass through our novel visible structure retrieval network allows obtaining the subset of 3D structure points in the map that the image views, thus reducing the search space of 2D-3D correspondences. We show that our proposed method enables performing localisation with an accuracy comparable to the state of the art, while requiring lower computational and storage footprint.

cs.CV↗
arXiv2025

Quantifying Epistemic Uncertainty in Absolute Pose Regression

Visual relocalization is the task of estimating the camera pose given an image it views. Absolute pose regression offers a solution to this task by training a neural network, directly regressing the camera pose from image features. While an attractive solution in terms of memory and compute efficiency, absolute pose regression's predictions are inaccurate and unreliable outside the training domain. In this work, we propose a novel method for quantifying the epistemic uncertainty of an absolute pose regression model by estimating the likelihood of observations within a variational framework. Beyond providing a measure of confidence in predictions, our approach offers a unified model that also handles observation ambiguities, probabilistically localizing the camera in the presence of repetitive structures. Our method outperforms existing approaches in capturing the relation between uncertainty and prediction error.

cs.CV↗
arXiv2024

Conditional Variational Autoencoders for Probabilistic Pose Regression

Robots rely on visual relocalization to estimate their pose from camera images when they lose track. One of the challenges in visual relocalization is repetitive structures in the operation environment of the robot. This calls for probabilistic methods that support multiple hypotheses for robot's pose. We propose such a probabilistic method to predict the posterior distribution of camera poses given an observed image. Our proposed training strategy results in a generative model of camera poses given an image, which can be used to draw samples from the pose posterior distribution. Our method is streamlined and well-founded in theory and outperforms existing methods on localization in presence of ambiguities.

cs.CV↗
arXiv2023

A Probabilistic Framework for Visual Localization in Ambiguous Scenes

Visual localization allows autonomous robots to relocalize when losing track of their pose by matching their current observation with past ones. However, ambiguous scenes pose a challenge for such systems, as repetitive structures can be viewed from many distinct, equally likely camera poses, which means it is not sufficient to produce a single best pose hypothesis. In this work, we propose a probabilistic framework that for a given image predicts the arbitrarily shaped posterior distribution of its camera pose. We do this via a novel formulation of camera pose regression using variational inference, which allows sampling from the predicted distribution. Our method outperforms existing methods on localization in ambiguous scenes. Code and data will be released at https://github.com/efreidun/vapor.

cs.CV↗
arXiv2022

Semi-supervised Learning of Partial Differential Operators and Dynamical Flows

The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. Our method treats time and space separately. As a result, it successfully propagates initial conditions in continuous time steps by employing the general composition properties of the partial differential operators. Following previous work, supervision is provided at a specific time point. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.

cs.LG↗
arXiv2022

Unsupervised Disentanglement with Tensor Product Representations on the Torus

The current methods for learning representations with auto-encoders almost exclusively employ vectors as the latent representations. In this work, we propose to employ a tensor product structure for this purpose. This way, the obtained representations are naturally disentangled. In contrast to the conventional variations methods, which are targeted toward normally distributed features, the latent space in our representation is distributed uniformly over a set of unit circles. We argue that the torus structure of the latent space captures the generative factors effectively. We employ recent tools for measuring unsupervised disentanglement, and in an extensive set of experiments demonstrate the advantage of our method in terms of disentanglement, completeness, and informativeness. The code for our proposed method is available at https://github.com/rotmanmi/Unsupervised-Disentanglement-Torus.

cs.LG↗
arXiv2020

Exact D7-brane embedding in the Pilch-Warner background

A new supersymmetric D7-brane embedding in the Pilch-Warner gravitational background is found exactly, by solving the supersymmetric condition. In the dual holographic picture, our setting corresponds to adding a quenched fundamental matter sector to N=2* super Yang-Mills theory, at zero temperature. We show that previous results in the same setting are missing the Wess-Zumino term in the D-brane action, and how our results complete the picture.

hep-th↗
arXiv2020

Optimal least-squares solution to the hand-eye calibration problem

We propose a least-squares formulation to the noisy hand-eye calibration problem using dual-quaternions, and introduce efficient algorithms to find the exact optimal solution, based on analytic properties of the problem, avoiding non-linear optimization. We further present simple analytic approximate solutions which provide remarkably good estimations compared to the exact solution. In addition, we show how to generalize our solution to account for a given extrinsic prior in the cost function. To the best of our knowledge our algorithm is the most efficient approach to optimally solve the hand-eye calibration problem.

cs.CV↗
arXiv2019

Deformations of the circular Wilson loop and spectral (in)dependence

In this paper we study the expectation value of deformations of the circular Wilson loop in ${\cal N}=4$ super Yang-Mills theory. The leading order deformation, known as the Bremsstrahlung function, can be obtained exactly from supersymmetric localization, so our focus is on deformations at higher orders. We find simple expressions for the expectation values for generic deformations at the quartic order at one-loop at weak coupling and at leading order at strong coupling. We also present a very simple algorithm (not requiring integration) to evaluate the two-loop result. We find that an exact symmetry of the strong coupling sigma-model, known as the spectral-parameter independence, is an approximate symmetry at weak coupling, modifying the expectation value starting only at the sextic order in the deformation. Furthermore, we find very simple patterns for how the spectral parameter can appear in the weak coupling calculation, suggesting all-order structures.

hep-th↗
arXiv2017

The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines

We study operator insertions into the $1/2$ BPS Wilson loop in ${\cal N}=4$ SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension insertions and relies on known results for the expectation value of a smooth Wilson loop. In addition to the particular coefficients that we calculate, our study elucidates the connection between deformations of the line and operator insertions and between the vacuum expectation value of the line and the CFT data of the insertions.

hep-th↗
arXiv2016

Dual conformal transformations of smooth holographic Wilson loops

We study dual conformal transformations of minimal area surfaces in $AdS_5 \times S^5$ corresponding to holographic smooth Wilson loops and some other related observables. To act with dual conformal transformations we map the string solutions to the dual space by means of T-duality, then we apply a conformal transformation and finally T-dualize back to the original space. The transformation maps between string solutions with different boundary contours. The boundary contours of the minimal surfaces are not mapped back to the AdS boundary, and the regularized area of the surface changes.

hep-th↗
arXiv2015

Wilson Loops and Minimal Surfaces Beyond the Wavy Approximation

We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space. We use a formalism introduced recently by Kruczenski to perturbatively compute the area corresponding to boundary contours which are deformations of the circle. Our perturbative expansion is carried to high orders compared with the wavy approximation and yields new analytic results. The regularized area is invariant under a one parameter family of continuous deformations of the boundary contour which are not related to the global symmetry of the problem. We show that this symmetry of the Wilson loops breaks at weak coupling at an a priori unexpected order in the perturbative expansion. We also study the corresponding Lax operator and algebraic curve for these solutions.

hep-th↗
arXiv2014

Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.

hep-th↗
arXiv2013

Correlation Function of Circular Wilson Loops at Strong Coupling

We study the correlation function of two circular Wilson loops at strong coupling in N=4 super Yang-Mills theory. Using the AdS/CFT correspondence, the problem maps to finding the minimal surface between two circles defined on the boundary of AdS, and the fluctuations around the classical solution in AdS_5 x S^5. At the classical level, we derive the string solution in H_3 x S^1 explicitly, and focus on properties such as stability and phase transition. Furthermore, a computation of the associated algebraic curve is given. At the quantum level, the one-loop partition function is constructed by introducing quadratic bosonic and fermionic fluctuations around the classical solution, embedded in AdS_5 x S^5. We find an analytic, formal expression for the partition function in terms of an infinite product by employing the Gel'fand-Yaglom method and supersymmetric regularization. We regulate the expression and evaluate the partition function numerically.

hep-th↗
arXiv2013

Algebraic Curves for Factorized String Solutions

We show how to construct an algebraic curve for factorized string solution in the context of the AdS/CFT correspondence. We define factorized solutions to be solutions where the flat-connection becomes independent of one of the worldsheet variables by a similarity transformation with a matrix $S$ satisfying $S^{-1}d S=const$. Using the factorization property we construct a well defined Lax operator and an associated algebraic curve. The construction procedure is local and does not require the introduction of a monodromy matrix. The procedure can be applied for string solutions with any boundary conditions. We study the properties of the curve and give several examples for the application of the procedure.

hep-th↗
arXiv2011

Integrability of Green-Schwarz Sigma Models with Boundaries

We construct integrability preserving boundary conditions for Green-Schwarz sigma-models on semi-symmetric spaces. The boundary conditions are expressed as gluing conditions of the flat-connection, using an involutive metric preserving automorphism. We show that the boundary conditions preserve half of the space-time supersymmetry and an infinite set of conserved charges. We find integrable D-brane configurations for AdS_5 x S^5 and AdS_4 x CP^3 backgrounds.

hep-th↗
arXiv2011

Self-Duality of Green-Schwarz Sigma-Models

We study fermionic T-duality symmetries of integrable Green-Schwarz sigma-models on Anti-de-Sitter backgrounds with Ramond-Ramond fluxes, constructed as Z_4 supercosets of superconformal algebras. We find three algebraic conditions that guarantee self-duality of the backgrounds under fermionic T-duality, we classify those that satisfy them and construct the map of the monodromy matrix. We introduce new T-duality directions, where some of them contain no bosonic directions, along which the backgrounds are self-dual. We find that the only self-dual backgrounds are AdS_n x S^n for n=2,3,5. In addition we find that the backgrounds AdS_n x S^1 for n=2,3,5, AdS_4 x S^2 and AdS_2 x S^4 are self-dual at the level of the classical action, but have a non-trivial transformation of the dilaton.

hep-th↗