arXiv subjects

Meirav Galun

Publications and source records attributed to Meirav Galun.

At least 19 recordsLinked to original sources

arXiv2026

Learning Global Camera Poses from Noisy View-Graphs for Structure from Motion

Camera pose estimation is a key step in 3D reconstruction and view-synthesis pipelines. We present a deep, global Structure-from-Motion framework based on learned view-graph aggregation. Our method employs a permutation-equivariant, edge-conditioned graph neural network that takes noisy pairwise relative poses as input and outputs globally consistent camera extrinsics. The network is trained without ground-truth supervision, relying solely on a relative-pose consistency objective. This is followed by 3D point triangulation and robust bundle adjustment. Our approach is efficient, scalable to more than a thousand images, and robust to graph density. We evaluate our method on MegaDepth, 1DSfM, Strecha, and BlendedMVS. These experiments demonstrate that our method achieves superior rotation and translation accuracy compared to deep track-centric methods while registering more images across many scenes, and competitive results compared to state-of-the-art classical pipelines, while being much faster.

cs.CV↗

arXiv2025

GSVisLoc: Generalizable Visual Localization for Gaussian Splatting Scene Representations

We introduce GSVisLoc, a visual localization method designed for 3D Gaussian Splatting (3DGS) scene representations. Given a 3DGS model of a scene and a query image, our goal is to estimate the camera's position and orientation. We accomplish this by robustly matching scene features to image features. Scene features are produced by downsampling and encoding the 3D Gaussians while image features are obtained by encoding image patches. Our algorithm proceeds in three steps, starting with coarse matching, then fine matching, and finally by applying pose refinement for an accurate final estimate. Importantly, our method leverages the explicit 3DGS scene representation for visual localization without requiring modifications, retraining, or additional reference images. We evaluate GSVisLoc on both indoor and outdoor scenes, demonstrating competitive localization performance on standard benchmarks while outperforming existing 3DGS-based baselines. Moreover, our approach generalizes effectively to novel scenes without additional training.

cs.CV↗

arXiv2025

RESfM: Robust Deep Equivariant Structure from Motion

Multiview Structure from Motion is a fundamental and challenging computer vision problem. A recent deep-based approach utilized matrix equivariant architectures for simultaneous recovery of camera pose and 3D scene structure from large image collections. That work, however, made the unrealistic assumption that the point tracks given as input are almost clean of outliers. Here, we propose an architecture suited to dealing with outliers by adding a multiview inlier/outlier classification module that respects the model equivariance and by utilizing a robust bundle adjustment step. Experiments demonstrate that our method can be applied successfully in realistic settings that include large image collections and point tracks extracted with common heuristics that include many outliers, achieving state-of-the-art accuracies in almost all runs, superior to existing deep-based methods and on-par with leading classical (non-deep) sequential and global methods.

cs.CV↗

arXiv2025

Querying Kernel Methods Suffices for Reconstructing their Training Data

Over-parameterized models have raised concerns about their potential to memorize training data, even when achieving strong generalization. The privacy implications of such memorization are generally unclear, particularly in scenarios where only model outputs are accessible. We study this question in the context of kernel methods, and demonstrate both empirically and theoretically that querying kernel models at various points suffices to reconstruct their training data, even without access to model parameters. Our results hold for a range of kernel methods, including kernel regression, support vector machines, and kernel density estimation. Our hope is that this work can illuminate potential privacy concerns for such models.

cs.LG↗

arXiv2024

On the Reconstruction of Training Data from Group Invariant Networks

Reconstructing training data from trained neural networks is an active area of research with significant implications for privacy and explainability. Recent advances have demonstrated the feasibility of this process for several data types. However, reconstructing data from group-invariant neural networks poses distinct challenges that remain largely unexplored. This paper addresses this gap by first formulating the problem and discussing some of its basic properties. We then provide an experimental evaluation demonstrating that conventional reconstruction techniques are inadequate in this scenario. Specifically, we observe that the resulting data reconstructions gravitate toward symmetric inputs on which the group acts trivially, leading to poor-quality results. Finally, we propose two novel methods aiming to improve reconstruction in this setup and present promising preliminary experimental results. Our work sheds light on the complexities of reconstructing data from group invariant neural networks and offers potential avenues for future research in this domain.

cs.LG↗

arXiv2024

Consensus Learning with Deep Sets for Essential Matrix Estimation

Robust estimation of the essential matrix, which encodes the relative position and orientation of two cameras, is a fundamental step in structure from motion pipelines. Recent deep-based methods achieved accurate estimation by using complex network architectures that involve graphs, attention layers, and hard pruning steps. Here, we propose a simpler network architecture based on Deep Sets. Given a collection of point matches extracted from two images, our method identifies outlier point matches and models the displacement noise in inlier matches. A weighted DLT module uses these predictions to regress the essential matrix. Our network achieves accurate recovery that is superior to existing networks with significantly more complex architectures.

cs.CV↗

arXiv2024

Leveraging Image Matching Toward End-to-End Relative Camera Pose Regression

This paper proposes a generalizable, end-to-end deep learning-based method for relative pose regression between two images. Given two images of the same scene captured from different viewpoints, our method predicts the relative rotation and translation (including direction and scale) between the two respective cameras. Inspired by the classical pipeline, our method leverages Image Matching (IM) as a pre-trained task for relative pose regression. Specifically, we use LoFTR, an architecture that utilizes an attention-based network pre-trained on Scannet, to extract semi-dense feature maps, which are then warped and fed into a pose regression network. Notably, we use a loss function that utilizes separate terms to account for the translation direction and scale. We believe such a separation is important because translation direction is determined by point correspondences while the scale is inferred from prior on shape sizes. Our ablations further support this choice. We evaluate our method on several datasets and show that it outperforms previous end-to-end methods. The method also generalizes well to unseen datasets.

cs.CV↗

arXiv2024

Controlling the Inductive Bias of Wide Neural Networks by Modifying the Kernel's Spectrum

Wide neural networks are biased towards learning certain functions, influencing both the rate of convergence of gradient descent (GD) and the functions that are reachable with GD in finite training time. As such, there is a great need for methods that can modify this bias according to the task at hand. To that end, we introduce Modified Spectrum Kernels (MSKs), a novel family of constructed kernels that can be used to approximate kernels with desired eigenvalues for which no closed form is known. We leverage the duality between wide neural networks and Neural Tangent Kernels and propose a preconditioned gradient descent method, which alters the trajectory of GD. As a result, this allows for a polynomial and, in some cases, exponential training speedup without changing the final solution. Our method is both computationally efficient and simple to implement.

cs.LG↗

arXiv2023

A Kernel Perspective of Skip Connections in Convolutional Networks

Over-parameterized residual networks (ResNets) are amongst the most successful convolutional neural architectures for image processing. Here we study their properties through their Gaussian Process and Neural Tangent kernels. We derive explicit formulas for these kernels, analyze their spectra, and provide bounds on their implied condition numbers. Our results indicate that (1) with ReLU activation, the eigenvalues of these residual kernels decay polynomially at a similar rate compared to the same kernels when skip connections are not used, thus maintaining a similar frequency bias; (2) however, residual kernels are more locally biased. Our analysis further shows that the matrices obtained by these residual kernels yield favorable condition numbers at finite depths than those obtained without the skip connections, enabling therefore faster convergence of training with gradient descent.

cs.LG↗

arXiv2022

On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels

We study the properties of various over-parametrized convolutional neural architectures through their respective Gaussian process and neural tangent kernels. We prove that, with normalized multi-channel input and ReLU activation, the eigenfunctions of these kernels with the uniform measure are formed by products of spherical harmonics, defined over the channels of the different pixels. We next use hierarchical factorizable kernels to bound their respective eigenvalues. We show that the eigenvalues decay polynomially, quantify the rate of decay, and derive measures that reflect the composition of hierarchical features in these networks. Our results provide concrete quantitative characterization of over-parameterized convolutional network architectures.

cs.LG↗

arXiv2021

Deep Permutation Equivariant Structure from Motion

Existing deep methods produce highly accurate 3D reconstructions in stereo and multiview stereo settings, i.e., when cameras are both internally and externally calibrated. Nevertheless, the challenge of simultaneous recovery of camera poses and 3D scene structure in multiview settings with deep networks is still outstanding. Inspired by projective factorization for Structure from Motion (SFM) and by deep matrix completion techniques, we propose a neural network architecture that, given a set of point tracks in multiple images of a static scene, recovers both the camera parameters and a (sparse) scene structure by minimizing an unsupervised reprojection loss. Our network architecture is designed to respect the structure of the problem: the sought output is equivariant to permutations of both cameras and scene points. Notably, our method does not require initialization of camera parameters or 3D point locations. We test our architecture in two setups: (1) single scene reconstruction and (2) learning from multiple scenes. Our experiments, conducted on a variety of datasets in both internally calibrated and uncalibrated settings, indicate that our method accurately recovers pose and structure, on par with classical state of the art methods. Additionally, we show that a pre-trained network can be used to reconstruct novel scenes using inexpensive fine-tuning with no loss of accuracy.

cs.CV↗

arXiv2021

GPSfM: Global Projective SFM Using Algebraic Constraints on Multi-View Fundamental Matrices

This paper addresses the problem of recovering projective camera matrices from collections of fundamental matrices in multiview settings. We make two main contributions. First, given ${n \choose 2}$ fundamental matrices computed for $n$ images, we provide a complete algebraic characterization in the form of conditions that are both necessary and sufficient to enabling the recovery of camera matrices. These conditions are based on arranging the fundamental matrices as blocks in a single matrix, called the $n$-view fundamental matrix, and characterizing this matrix in terms of the signs of its eigenvalues and rank structures. Secondly, we propose a concrete algorithm for projective structure-from-motion that utilizes this characterization. Given a complete or partial collection of measured fundamental matrices, our method seeks camera matrices that minimize a global algebraic error for the measured fundamental matrices. In contrast to existing methods, our optimization, without any initialization, produces a consistent set of fundamental matrices that corresponds to a unique set of cameras (up to a choice of projective frame). Our experiments indicate that our method achieves state of the art performance in both accuracy and running time.

cs.CV↗

arXiv2021

Spectral Analysis of the Neural Tangent Kernel for Deep Residual Networks

Deep residual network architectures have been shown to achieve superior accuracy over classical feed-forward networks, yet their success is still not fully understood. Focusing on massively over-parameterized, fully connected residual networks with ReLU activation through their respective neural tangent kernels (ResNTK), we provide here a spectral analysis of these kernels. Specifically, we show that, much like NTK for fully connected networks (FC-NTK), for input distributed uniformly on the hypersphere $\mathbb{S}^{d-1}$, the eigenfunctions of ResNTK are the spherical harmonics and the eigenvalues decay polynomially with frequency $k$ as $k^{-d}$. These in turn imply that the set of functions in their Reproducing Kernel Hilbert Space are identical to those of FC-NTK, and consequently also to those of the Laplace kernel. We further show, by drawing on the analogy to the Laplace kernel, that depending on the choice of a hyper-parameter that balances between the skip and residual connections ResNTK can either become spiky with depth, as with FC-NTK, or maintain a stable shape.

cs.LG↗

arXiv2020

On the Similarity between the Laplace and Neural Tangent Kernels

Recent theoretical work has shown that massively overparameterized neural networks are equivalent to kernel regressors that use Neural Tangent Kernels(NTK). Experiments show that these kernel methods perform similarly to real neural networks. Here we show that NTK for fully connected networks is closely related to the standard Laplace kernel. We show theoretically that for normalized data on the hypersphere both kernels have the same eigenfunctions and their eigenvalues decay polynomially at the same rate, implying that their Reproducing Kernel Hilbert Spaces (RKHS) include the same sets of functions. This means that both kernels give rise to classes of functions with the same smoothness properties. The two kernels differ for data off the hypersphere, but experiments indicate that when data is properly normalized these differences are not significant. Finally, we provide experiments on real data comparing NTK and the Laplace kernel, along with a larger class ofγ-exponential kernels. We show that these perform almost identically. Our results suggest that much insight about neural networks can be obtained from analysis of the well-known Laplace kernel, which has a simple closed-form.

cs.LG↗

arXiv2020

Point of Care Image Analysis for COVID-19

Early detection of COVID-19 is key in containing the pandemic. Disease detection and evaluation based on imaging is fast and cheap and therefore plays an important role in COVID-19 handling. COVID-19 is easier to detect in chest CT, however, it is expensive, non-portable, and difficult to disinfect, making it unfit as a point-of-care (POC) modality. On the other hand, chest X-ray (CXR) and lung ultrasound (LUS) are widely used, yet, COVID-19 findings in these modalities are not always very clear. Here we train deep neural networks to significantly enhance the capability to detect, grade and monitor COVID-19 patients using CXRs and LUS. Collaborating with several hospitals in Israel we collect a large dataset of CXRs and use this dataset to train a neural network obtaining above 90% detection rate for COVID-19. In addition, in collaboration with ULTRa (Ultrasound Laboratory Trento, Italy) and hospitals in Italy we obtained POC ultrasound data with annotations of the severity of disease and trained a deep network for automatic severity grading.

eess.IV↗

arXiv2020

Multiview Neural Surface Reconstruction by Disentangling Geometry and Appearance

In this work we address the challenging problem of multiview 3D surface reconstruction. We introduce a neural network architecture that simultaneously learns the unknown geometry, camera parameters, and a neural renderer that approximates the light reflected from the surface towards the camera. The geometry is represented as a zero level-set of a neural network, while the neural renderer, derived from the rendering equation, is capable of (implicitly) modeling a wide set of lighting conditions and materials. We trained our network on real world 2D images of objects with different material properties, lighting conditions, and noisy camera initializations from the DTU MVS dataset. We found our model to produce state of the art 3D surface reconstructions with high fidelity, resolution and detail.

cs.CV↗

arXiv2020

Learning Algebraic Multigrid Using Graph Neural Networks

Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of AMG algorithms is the selection of the prolongation operator -- a problem-dependent sparse matrix which governs the multiscale hierarchy of the solver and is critical to its efficiency. Over many years, numerous methods have been developed for this task, and yet there is no known single right answer except in very special cases. Here we propose a framework for learning AMG prolongation operators for linear systems with sparse symmetric positive (semi-) definite matrices. We train a single graph neural network to learn a mapping from an entire class of such matrices to prolongation operators, using an efficient unsupervised loss function. Experiments on a broad class of problems demonstrate improved convergence rates compared to classical AMG, demonstrating the potential utility of neural networks for developing sparse system solvers.

cs.LG↗

arXiv2020

Averaging Essential and Fundamental Matrices in Collinear Camera Settings

Global methods to Structure from Motion have gained popularity in recent years. A significant drawback of global methods is their sensitivity to collinear camera settings. In this paper, we introduce an analysis and algorithms for averaging bifocal tensors (essential or fundamental matrices) when either subsets or all of the camera centers are collinear. We provide a complete spectral characterization of bifocal tensors in collinear scenarios and further propose two averaging algorithms. The first algorithm uses rank constrained minimization to recover camera matrices in fully collinear settings. The second algorithm enriches the set of possibly mixed collinear and non-collinear cameras with additional, "virtual cameras," which are placed in general position, enabling the application of existing averaging methods to the enriched set of bifocal tensors. Our algorithms are shown to achieve state of the art results on various benchmarks that include autonomous car datasets and unordered image collections in both calibrated and unclibrated settings.

cs.CV↗