Alex Bronstein

Tamir Shor, Tomer Weiss, Dor Noti et al.

Dynamic Magnetic Resonance Imaging (MRI) is known to be a powerful and reliable technique for the dynamic imaging of internal organs and tissues, making it a leading diagnostic tool. A major difficulty in using MRI in this setting is the relatively long acquisition time (and, hence, increased cost) required for imaging in high spatio-temporal resolution, leading to the appearance of related motion artifacts and decrease in resolution. Compressed Sensing (CS) techniques have become a common tool to reduce MRI acquisition time by subsampling images in the k-space according to some acquisition trajectory. Several studies have particularly focused on applying deep learning techniques to learn these acquisition trajectories in order to attain better image reconstruction, rather than using some predefined set of trajectories. To the best of our knowledge, learning acquisition trajectories has been only explored in the context of static MRI. In this study, we consider acquisition trajectory learning in the dynamic imaging setting. We design an end-to-end pipeline for the joint optimization of multiple per-frame acquisition trajectories along with a reconstruction neural network, and demonstrate improved image reconstruction quality in shorter acquisition times. The code for reproducing all experiments is accessible at https://github.com/tamirshor7/MultiPILOT.

Tsachi Blau, Roy Ganz, Bahjat Kawar et al.

Deep Neural Networks (DNNs) are highly sensitive to imperceptible malicious perturbations, known as adversarial attacks. Following the discovery of this vulnerability in real-world imaging and vision applications, the associated safety concerns have attracted vast research attention, and many defense techniques have been developed. Most of these defense methods rely on adversarial training (AT) -- training the classification network on images perturbed according to a specific threat model, which defines the magnitude of the allowed modification. Although AT leads to promising results, training on a specific threat model fails to generalize to other types of perturbations. A different approach utilizes a preprocessing step to remove the adversarial perturbation from the attacked image. In this work, we follow the latter path and aim to develop a technique that leads to robust classifiers across various realizations of threat models. To this end, we harness the recent advances in stochastic generative modeling, and means to leverage these for sampling from conditional distributions. Our defense relies on an addition of Gaussian i.i.d noise to the attacked image, followed by a pretrained diffusion process -- an architecture that performs a stochastic iterative process over a denoising network, yielding a high perceptual quality denoised outcome. The obtained robustness with this stochastic preprocessing step is validated through extensive experiments on the CIFAR-10 dataset, showing that our method outperforms the leading defense methods under various threat models.

Tamir Shor, Chaim Baskin, Alex Bronstein

Dynamic Magnetic Resonance Imaging (MRI) is a crucial non-invasive method used to capture the movement of internal organs and tissues, making it a key tool for medical diagnosis. However, dynamic MRI faces a major challenge: long acquisition times needed to achieve high spatial and temporal resolution. This leads to higher costs, patient discomfort, motion artifacts, and lower image quality. Compressed Sensing (CS) addresses this problem by acquiring a reduced amount of MR data in the Fourier domain, based on a chosen sampling pattern, and reconstructing the full image from this partial data. While various deep learning methods have been developed to optimize these sampling patterns and improve reconstruction, they often struggle with slow optimization and inference times or are limited to specific temporal dimensions used during training. In this work, we introduce a novel deep-compressed sensing approach that uses 3D window attention and flexible, temporally extendable acquisition trajectories. Our method significantly reduces both training and inference times compared to existing approaches, while also adapting to different temporal dimensions during inference without requiring additional training. Tests with real data show that our approach outperforms current state-of-theart techniques. The code for reproducing all experiments will be made available upon acceptance of the paper.

Elad Amrani, Leonid Karlinsky, Alex Bronstein

We present Self-Classifier -- a novel self-supervised end-to-end classification learning approach. Self-Classifier learns labels and representations simultaneously in a single-stage end-to-end manner by optimizing for same-class prediction of two augmented views of the same sample. To guarantee non-degenerate solutions (i.e., solutions where all labels are assigned to the same class) we propose a mathematically motivated variant of the cross-entropy loss that has a uniform prior asserted on the predicted labels. In our theoretical analysis, we prove that degenerate solutions are not in the set of optimal solutions of our approach. Self-Classifier is simple to implement and scalable. Unlike other popular unsupervised classification and contrastive representation learning approaches, it does not require any form of pre-training, expectation-maximization, pseudo-labeling, external clustering, a second network, stop-gradient operation, or negative pairs. Despite its simplicity, our approach sets a new state of the art for unsupervised classification of ImageNet; and even achieves comparable to state-of-the-art results for unsupervised representation learning. Code is available at https://github.com/elad-amrani/self-classifier.

Elad Amrani, Rami Ben-Ari, Daniel Rotman et al.

One of the key factors of enabling machine learning models to comprehend and solve real-world tasks is to leverage multimodal data. Unfortunately, annotation of multimodal data is challenging and expensive. Recently, self-supervised multimodal methods that combine vision and language were proposed to learn multimodal representations without annotation. However, these methods often choose to ignore the presence of high levels of noise and thus yield sub-optimal results. In this work, we show that the problem of noise estimation for multimodal data can be reduced to a multimodal density estimation task. Using multimodal density estimation, we propose a noise estimation building block for multimodal representation learning that is based strictly on the inherent correlation between different modalities. We demonstrate how our noise estimation can be broadly integrated and achieves comparable results to state-of-the-art performance on five different benchmark datasets for two challenging multimodal tasks: Video Question Answering and Text-To-Video Retrieval. Furthermore, we provide a theoretical probabilistic error bound substantiating our empirical results and analyze failure cases. Code: https://github.com/elad-amrani/ssml.

Sai Advaith Maddipatla, Nadav Bojan Sellam, Sanketh Vedula et al.

Proteins are dynamic, adopting ensembles of conformations. The nature of this conformational heterogenity is imprinted in the raw electron density measurements obtained from X-ray crystallography experiments. Fitting an ensemble of protein structures to these measurements is a challenging, ill-posed inverse problem. We propose a non-i.i.d. ensemble guidance approach to solve this problem using existing protein structure generative models and demonstrate that it accurately recovers complicated multi-modal alternate protein backbone conformations observed in certain single crystal measurements.

Elad Amrani, Leonid Karlinsky, Alex Bronstein

We introduce XTRA, a vision model pre-trained with a novel auto-regressive objective that significantly enhances both sample and parameter efficiency compared to previous auto-regressive image models. Unlike contrastive or masked image modeling methods, which have not been demonstrated as having consistent scaling behavior on unbalanced internet data, auto-regressive vision models exhibit scalable and promising performance as model and dataset size increase. In contrast to standard auto-regressive models, XTRA employs a Block Causal Mask, where each Block represents k $\times$ k tokens rather than relying on a standard causal mask. By reconstructing pixel values block by block, XTRA captures higher-level structural patterns over larger image regions. Predicting on blocks allows the model to learn relationships across broader areas of pixels, enabling more abstract and semantically meaningful representations than traditional next-token prediction. This simple modification yields two key results. First, XTRA is sample-efficient. Despite being trained on 152$\times$ fewer samples (13.1M vs. 2B), XTRA ViT-H/14 surpasses the top-1 average accuracy of the previous state-of-the-art auto-regressive model across 15 diverse image recognition benchmarks. Second, XTRA is parameter-efficient. Compared to auto-regressive models trained on ImageNet-1k, XTRA ViT-B/16 outperforms in linear and attentive probing tasks, using 7-16$\times$ fewer parameters (85M vs. 1.36B/0.63B).

Gabriele Serussi, Tamir Shor, Tom Hirshberg et al.

Multi-rotor aerial autonomous vehicles (MAVs) primarily rely on vision for navigation purposes. However, visual localization and odometry techniques suffer from poor performance in low or direct sunlight, a limited field of view, and vulnerability to occlusions. Acoustic sensing can serve as a complementary or even alternative modality for vision in many situations, and it also has the added benefits of lower system cost and energy footprint, which is especially important for micro aircraft. This paper proposes actively controlling and shaping the aircraft propulsion noise generated by the rotors to benefit localization tasks, rather than considering it a harmful nuisance. We present a neural network architecture for selfnoise-based localization in a known environment. We show that training it simultaneously with learning time-varying rotor phase modulation achieves accurate and robust localization. The proposed methods are evaluated using a computationally affordable simulation of MAV rotor noise in 2D acoustic environments that is fitted to real recordings of rotor pressure fields.

Nadav Bojan Sellam, Meital Bojan, Paul Schanda et al.

Accurate protein structures are essential for understanding biological function, yet incorporating experimental data into protein generative models remains a major challenge. Most predictors of experimental observables are non-differentiable, making them incompatible with gradient-based conditional sampling. This is especially limiting in nuclear magnetic resonance, where rich data such as chemical shifts are hard to directly integrate into generative modeling. We introduce a framework for non-differentiable guidance of protein generative models, coupling a continuous diffusion-based generator with any black-box objective via a tailored genetic algorithm. We demonstrate its effectiveness across three modalities: pairwise distance constraints, nuclear Overhauser effect restraints, and for the first time chemical shifts. These results establish chemical shift guided structure generation as feasible, expose key weaknesses in current predictors, and showcase a general strategy for incorporating diverse experimental signals. Our work points toward automated, data-conditioned protein modeling beyond the limits of differentiability.

Tamir Shor, Moti Freiman, Chaim Baskin et al.

Cardiac T1 mapping provides critical quantitative insights into myocardial tissue composition, enabling the assessment of pathologies such as fibrosis, inflammation, and edema. However, the inherently dynamic nature of the heart imposes strict limits on acquisition times, making high-resolution T1 mapping a persistent challenge. Compressed sensing (CS) approaches have reduced scan durations by undersampling k-space and reconstructing images from partial data, and recent studies show that jointly optimizing the undersampling patterns with the reconstruction network can substantially improve performance. Still, most current T1 mapping pipelines rely on static, hand-crafted masks that do not exploit the full acceleration and accuracy potential. In this work, we introduce T1-PILOT: an end-to-end method that explicitly incorporates the T1 signal relaxation model into the sampling-reconstruction framework to guide the learning of non-Cartesian trajectories, crossframe alignment, and T1 decay estimation. Through extensive experiments on the CMRxRecon dataset, T1-PILOT significantly outperforms several baseline strategies (including learned single-mask and fixed radial or golden-angle sampling schemes), achieving higher T1 map fidelity at greater acceleration factors. In particular, we observe consistent gains in PSNR and VIF relative to existing methods, along with marked improvements in delineating finer myocardial structures. Our results highlight that optimizing sampling trajectories in tandem with the physical relaxation model leads to both enhanced quantitative accuracy and reduced acquisition times. Code for reproducing all results will be made publicly available upon publication.

Tamir Shor, Ethan Fetaya, Chaim Baskin et al.

Implicit Neural Representations (INRs) have been recently garnering increasing interest in various research fields, mainly due to their ability to represent large, complex data in a compact and continuous manner. Past work further showed that numerous popular downstream tasks can be performed directly in the INR parameter-space. Doing so can substantially reduce the computational resources required to process the represented data in their native domain. A major difficulty in using modern machine-learning approaches, is their high susceptibility to adversarial attacks, which have been shown to greatly limit the reliability and applicability of such methods in a wide range of settings. In this work, we show that parameter-space models trained for classification are inherently robust to adversarial attacks -- without the need of any robust training. To support our claims, we develop a novel suite of adversarial attacks targeting parameter-space classifiers, and furthermore analyze practical considerations of attacking parameter-space classifiers.

Sanketh Vedula, Valentino Maiorca, Lorenzo Basile et al.

Aligning data from different domains is a fundamental problem in machine learning with broad applications across very different areas, most notably aligning experimental readouts in single-cell multiomics. Mathematically, this problem can be formulated as the minimization of disagreement of pair-wise quantities such as distances and is related to the Gromov-Hausdorff and Gromov-Wasserstein distances. Computationally, it is a quadratic assignment problem (QAP) that is known to be NP-hard. Prior works attempted to solve the QAP directly with entropic or low-rank regularization on the permutation, which is computationally tractable only for modestly-sized inputs, and encode only limited inductive bias related to the domains being aligned. We consider the alignment of metric structures formulated as a discrete Gromov-Wasserstein problem and instead of solving the QAP directly, we propose to learn a related well-scalable linear assignment problem (LAP) whose solution is also a minimizer of the QAP. We also show a flexible extension of the proposed framework to general non-metric dissimilarities through differentiable ranks. We extensively evaluate our approach on synthetic and real datasets from single-cell multiomics and neural latent spaces, achieving state-of-the-art performance while being conceptually and computationally simple.

Tamir Shor, Chaim Baskin, Alex Bronstein

Breast cancer is a prominent health concern worldwide, currently being the secondmost common and second-deadliest type of cancer in women. While current breast cancer diagnosis mainly relies on mammography imaging, in recent years the use of thermography for breast cancer imaging has been garnering growing popularity. Thermographic imaging relies on infrared cameras to capture body-emitted heat distributions. While these heat signatures have proven useful for computer-vision systems for accurate breast cancer segmentation and classification, prior work often relies on handcrafted feature engineering or complex architectures, potentially limiting the comparability and applicability of these methods. In this work, we present a novel algorithm for both breast cancer classification and segmentation. Rather than focusing efforts on manual feature and architecture engineering, our algorithm focuses on leveraging an informative, learned feature space, thus making our solution simpler to use and extend to other frameworks and downstream tasks, as well as more applicable to data-scarce settings. Our classification produces SOTA results, while we are the first work to produce segmentation regions studied in this paper.

Tomer Weiss, Nissim Peretz, Sanketh Vedula et al.

Multiple-input multiple-output (MIMO) radar is one of the leading depth sensing modalities. However, the usage of multiple receive channels lead to relative high costs and prevent the penetration of MIMOs in many areas such as the automotive industry. Over the last years, few studies concentrated on designing reduced measurement schemes and image reconstruction schemes for MIMO radars, however these problems have been so far addressed separately. On the other hand, recent works in optical computational imaging have demonstrated growing success of simultaneous learning-based design of the acquisition and reconstruction schemes, manifesting significant improvement in the reconstruction quality. Inspired by these successes, in this work, we propose to learn MIMO acquisition parameters in the form of receive (Rx) antenna elements locations jointly with an image neural-network based reconstruction. To this end, we propose an algorithm for training the combined acquisition-reconstruction pipeline end-to-end in a differentiable way. We demonstrate the significance of using our learned acquisition parameters with and without the neural-network reconstruction.

Judith Hermanns, Anton Tsitsulin, Marina Munkhoeva et al.

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph. In this paper, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics, and then exploits this correspondence to align nodes. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that GRASP outperforms state-of-the-art methods for graph alignment across noise levels and graph types.

Assaf Arbelle, Sivan Doveh, Amit Alfassy et al.

Nowadays, there is an abundance of data involving images and surrounding free-form text weakly corresponding to those images. Weakly Supervised phrase-Grounding (WSG) deals with the task of using this data to learn to localize (or to ground) arbitrary text phrases in images without any additional annotations. However, most recent SotA methods for WSG assume the existence of a pre-trained object detector, relying on it to produce the ROIs for localization. In this work, we focus on the task of Detector-Free WSG (DF-WSG) to solve WSG without relying on a pre-trained detector. We directly learn everything from the images and associated free-form text pairs, thus potentially gaining an advantage on the categories unsupported by the detector. The key idea behind our proposed Grounding by Separation (GbS) method is synthesizing `text to image-regions' associations by random alpha-blending of arbitrary image pairs and using the corresponding texts of the pair as conditions to recover the alpha map from the blended image via a segmentation network. At test time, this allows using the query phrase as a condition for a non-blended query image, thus interpreting the test image as a composition of a region corresponding to the phrase and the complement region. Using this approach we demonstrate a significant accuracy improvement, of up to $8.5\%$ over previous DF-WSG SotA, for a range of benchmarks including Flickr30K, Visual Genome, and ReferIt, as well as a significant complementary improvement (above $7\%$) over the detector-based approaches for WSG.

Eli Schwartz, Alex Bronstein, Raja Giryes

Nowadays, many of the images captured are `observed' by machines only and not by humans, e.g., in autonomous systems. High-level machine vision models, such as object recognition or semantic segmentation, assume images are transformed into some canonical image space by the camera \ans{Image Signal Processor (ISP)}. However, the camera ISP is optimized for producing visually pleasing images for human observers and not for machines. Therefore, one may spare the ISP compute time and apply vision models directly to RAW images. Yet, it has been shown that training such models directly on RAW images results in a performance drop. To mitigate this drop, we use a RAW and RGB image pairs dataset, which can be easily acquired with no human labeling. We then train a model that is applied directly to the RAW data by using knowledge distillation such that the model predictions for RAW images will be aligned with the predictions of an off-the-shelf pre-trained model for processed RGB images. Our experiments show that our performance on RAW images for object classification and semantic segmentation is significantly better than models trained on labeled RAW images. It also reasonably matches the predictions of a pre-trained model on processed RGB images, while saving the ISP compute overhead.

Or Litany, Emanuele Rodolà, Alex Bronstein et al.

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non-rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non-rigid multi-part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non-rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.

Jonathan Alush-Aben, Linor Ackerman-Schraier, Tomer Weiss et al.

Magnetic Resonance Imaging (MRI) has long been considered to be among the gold standards of today's diagnostic imaging. The most significant drawback of MRI is long acquisition times, prohibiting its use in standard practice for some applications. Compressed sensing (CS) proposes to subsample the k-space (the Fourier domain dual to the physical space of spatial coordinates) leading to significantly accelerated acquisition. However, the benefit of compressed sensing has not been fully exploited; most of the sampling densities obtained through CS do not produce a trajectory that obeys the stringent constraints of the MRI machine imposed in practice. Inspired by recent success of deep learning based approaches for image reconstruction and ideas from computational imaging on learning-based design of imaging systems, we introduce 3D FLAT, a novel protocol for data-driven design of 3D non-Cartesian accelerated trajectories in MRI. Our proposal leverages the entire 3D k-space to simultaneously learn a physically feasible acquisition trajectory with a reconstruction method. Experimental results, performed as a proof-of-concept, suggest that 3D FLAT achieves higher image quality for a given readout time compared to standard trajectories such as radial, stack-of-stars, or 2D learned trajectories (trajectories that evolve only in the 2D plane while fully sampling along the third dimension). Furthermore, we demonstrate evidence supporting the significant benefit of performing MRI acquisitions using non-Cartesian 3D trajectories over 2D non-Cartesian trajectories acquired slice-wise.

Amir Livne, Alex Bronstein, Ron Kimmel et al.

Some face recognition methods are designed to utilize geometric information extracted from depth sensors to overcome the weaknesses of single-image based recognition technologies. However, the accurate acquisition of the depth profile is an expensive and challenging process. Here, we introduce a novel method that learns to recognize faces from stereo camera systems without the need to explicitly compute the facial surface or depth map. The raw face stereo images along with the location in the image from which the face is extracted allow the proposed CNN to improve the recognition task while avoiding the need to explicitly handle the geometric structure of the face. This way, we keep the simplicity and cost efficiency of identity authentication from a single image, while enjoying the benefits of geometric data without explicitly reconstructing it. We demonstrate that the suggested method outperforms both existing single-image and explicit depth based methods on large-scale benchmarks, and even capable of recognize spoofing attacks. We also provide an ablation study that shows that the suggested method uses the face locations in the left and right images to encode informative features that improve the overall performance.

Moran Shkolnik, Brian Chmiel, Ron Banner et al.

Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers an alternative approach with improved tolerance to different classes of data-types and quantization policies. It opens up new exciting applications where the quantization process is not static and can vary to meet different circumstances and implementations. To address this issue, we propose a method that provides intrinsic robustness to the model against a broad range of quantization processes. Our method is motivated by theoretical arguments and enables us to store a single generic model capable of operating at various bit-widths and quantization policies. We validate our method's effectiveness on different ImageNet models.

Sivan Doveh, Eli Schwartz, Chao Xue et al.

Few-Shot Learning (FSL) is a topic of rapidly growing interest. Typically, in FSL a model is trained on a dataset consisting of many small tasks (meta-tasks) and learns to adapt to novel tasks that it will encounter during test time. This is also referred to as meta-learning. Another topic closely related to meta-learning with a lot of interest in the community is Neural Architecture Search (NAS), automatically finding optimal architecture instead of engineering it manually. In this work, we combine these two aspects of meta-learning. So far, meta-learning FSL methods have focused on optimizing parameters of pre-defined network architectures, in order to make them easily adaptable to novel tasks. Moreover, it was observed that, in general, larger architectures perform better than smaller ones up to a certain saturation point (where they start to degrade due to over-fitting). However, little attention has been given to explicitly optimizing the architectures for FSL, nor to an adaptation of the architecture at test time to particular novel tasks. In this work, we propose to employ tools inspired by the Differentiable Neural Architecture Search (D-NAS) literature in order to optimize the architecture for FSL without over-fitting. Additionally, to make the architecture task adaptive, we propose the concept of `MetAdapt Controller' modules. These modules are added to the model and are meta-trained to predict the optimal network connections for a given novel task. Using the proposed approach we observe state-of-the-art results on two popular few-shot benchmarks: miniImageNet and FC100.

Amit Boyarski, Sanketh Vedula, Alex Bronstein

Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix. In this work we interpret the DMF model through the lens of spectral geometry. This allows us to incorporate explicit regularization without breaking the DMF structure, thus enjoying the best of both worlds. In particular, we focus on matrix completion problems with underlying geometric or topological relations between the rows and/or columns. Such relations are prevalent in matrix completion problems that arise in many applications, such as recommender systems and drug-target interaction. Our contributions enable DMF models to exploit these relations, and make them competitive on real benchmarks, while exhibiting one of the first successful applications of deep linear networks.

Eyal Rozenberg, Daniel Freedman, Alex Bronstein

Localization of an object within an image is a common task in medical imaging. Learning to localize or detect objects typically requires the collection of data which has been labelled with bounding boxes or similar annotations, which can be very time consuming and expensive. A technique which could perform such learning with much less annotation would, therefore, be quite valuable. We present such a technique for localization with limited annotation, in which the number of images with bounding boxes can be a small fraction of the total dataset (e.g. less than 1%); all other images only possess a whole image label and no bounding box. We propose a novel loss function for tackling this problem; the loss is a continuous relaxation of a well-defined discrete formulation of weakly supervised learning and is numerically well-posed. Furthermore, we propose a new architecture which accounts for both patch dependence and shift-invariance, through the inclusion of CRF layers and anti-aliasing filters, respectively. We apply our technique to the localization of thoracic diseases in chest X-ray images and demonstrate state-of-the-art localization performance on the ChestX-ray14 dataset.

Stefan Sommer, Alex Bronstein

We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a weighted diffusion mean. Both methods are inspired by stochastics on manifolds and geometric statistics, and provide examples of how stochastic methods -- here horizontal frame bundle flows and non-linear bridge sampling schemes, can be used in geometric deep learning. We outline the theoretical foundation of the two methods, discuss their relation to Euclidean deep networks and existing methodology in geometric deep learning, and establish important properties of the proposed constructions.

Tomer Weiss, Ortal Senouf, Sanketh Vedula et al.

Magnetic Resonance Imaging (MRI) has long been considered to be among "the gold standards" of diagnostic medical imaging. The long acquisition times, however, render MRI prone to motion artifacts, let alone their adverse contribution to the relative high costs of MRI examination. Over the last few decades, multiple studies have focused on the development of both physical and post-processing methods for accelerated acquisition of MRI scans. These two approaches, however, have so far been addressed separately. On the other hand, recent works in optical computational imaging have demonstrated growing success of concurrent learning-based design of data acquisition and image reconstruction schemes. Such schemes have already demonstrated substantial effectiveness, leading to considerably shorter acquisition times and improved quality of image reconstruction. Inspired by this initial success, in this work, we propose a novel approach to the learning of optimal schemes for conjoint acquisition and reconstruction of MRI scans, with the optimization carried out simultaneously with respect to the time-efficiency of data acquisition and the quality of resulting reconstructions. To be of a practical value, the schemes are encoded in the form of general k-space trajectories, whose associated magnetic gradients are constrained to obey a set of predefined hardware requirements (as defined in terms of, e.g., peak currents and maximum slew rates of magnetic gradients). With this proviso in mind, we propose a novel algorithm for the end-to-end training of a combined acquisition-reconstruction pipeline using a deep neural network with differentiable forward- and back-propagation operators. We demonstrate its effectiveness on image reconstruction and image segmentation tasks, reporting substantial improvements in terms of acceleration factors as well as the quality of these tasks.

Anton Tsitsulin, Marina Munkhoeva, Davide Mottin et al.

The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data distributions focus on global data properties such as mean and covariance; in that sense, they are extrinsic and uni-scale. We develop a first-of-its-kind intrinsic and multi-scale method for characterizing and comparing data manifolds, using a lower-bound of the spectral variant of the Gromov-Wasserstein inter-manifold distance, which compares all data moments. In a thorough experimental study, we demonstrate that our method effectively discerns the structure of data manifolds even on unaligned data of different dimensionalities; moreover, we showcase its efficacy in evaluating the quality of generative models.

Elad Amrani, Rami Ben-Ari, Tal Hakim et al.

Learning an object detector or retrieval requires a large data set with manual annotations. Such data sets are expensive and time consuming to create and therefore difficult to obtain on a large scale. In this work, we propose to exploit the natural correlation in narrations and the visual presence of objects in video, to learn an object detector and retrieval without any manual labeling involved. We pose the problem as weakly supervised learning with noisy labels, and propose a novel object detection paradigm under these constraints. We handle the background rejection by using contrastive samples and confront the high level of label noise with a new clustering score. Our evaluation is based on a set of 11 manually annotated objects in over 5000 frames. We show comparison to a weakly-supervised approach as baseline and provide a strongly labeled upper bound.

Ortal Senouf, Sanketh Vedula, Tomer Weiss et al.

In the past few years, deep learning-based methods have demonstrated enormous success for solving inverse problems in medical imaging. In this work, we address the following question:\textit{Given a set of measurements obtained from real imaging experiments, what is the best way to use a learnable model and the physics of the modality to solve the inverse problem and reconstruct the latent image?} Standard supervised learning based methods approach this problem by collecting data sets of known latent images and their corresponding measurements. However, these methods are often impractical due to the lack of availability of appropriately sized training sets, and, more generally, due to the inherent difficulty in measuring the "groundtruth" latent image. In light of this, we propose a self-supervised approach to training inverse models in medical imaging in the absence of aligned data. Our method only requiring access to the measurements and the forward model at training. We showcase its effectiveness on inverse problems arising in accelerated magnetic resonance imaging (MRI).

Tomer Weiss, Sanketh Vedula, Ortal Senouf et al.

Magnetic Resonance Imaging (MRI) is considered today the golden-standard modality for soft tissues. The long acquisition times, however, make it more prone to motion artifacts as well as contribute to the relatively high costs of this examination. Over the years, multiple studies concentrated on designing reduced measurement schemes and image reconstruction schemes for MRI, however, these problems have been so far addressed separately. On the other hand, recent works in optical computational imaging have demonstrated growing success of the simultaneous learning-based design of the acquisition and reconstruction schemes manifesting significant improvement in the reconstruction quality with a constrained time budget. Inspired by these successes, in this work, we propose to learn accelerated MR acquisition schemes (in the form of Cartesian trajectories) jointly with the image reconstruction operator. To this end, we propose an algorithm for training the combined acquisition-reconstruction pipeline end-to-end in a differentiable way. We demonstrate the significance of using the learned Cartesian trajectories at different speed up rates.

Sanketh Vedula, Ortal Senouf, Grigoriy Zurakhov et al.

Medical ultrasound (US) is a widespread imaging modality owing its popularity to cost efficiency, portability, speed, and lack of harmful ionizing radiation. In this paper, we demonstrate that replacing the traditional ultrasound processing pipeline with a data-driven, learnable counterpart leads to significant improvement in image quality. Moreover, we demonstrate that greater improvement can be achieved through a learning-based design of the transmitted beam patterns simultaneously with learning an image reconstruction pipeline. We evaluate our method on an in-vivo first-harmonic cardiac ultrasound dataset acquired from volunteers and demonstrate the significance of the learned pipeline and transmit beam patterns on the image quality when compared to standard transmit and receive beamformers used in high frame-rate US imaging. We believe that the presented methodology provides a fundamentally different perspective on the classical problem of ultrasound beam pattern design.

Oshri Halimi, Or Litany, Emanuele Rodolà et al.

We introduce the first completely unsupervised correspondence learning approach for deformable 3D shapes. Key to our model is the understanding that natural deformations (such as changes in pose) approximately preserve the metric structure of the surface, yielding a natural criterion to drive the learning process toward distortion-minimizing predictions. On this basis, we overcome the need for annotated data and replace it by a purely geometric criterion. The resulting learning model is class-agnostic, and is able to leverage any type of deformable geometric data for the training phase. In contrast to existing supervised approaches which specialize on the class seen at training time, we demonstrate stronger generalization as well as applicability to a variety of challenging settings. We showcase our method on a wide selection of correspondence benchmarks, where we outperform other methods in terms of accuracy, generalization, and efficiency.

Anton Tsitsulin, Davide Mottin, Panagiotis Karras et al.

Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately, a "one-size-fits-all" solution is unattainable, as different analytical tasks may require different attention to global or local graph features. We develop SGR, the first, to our knowledge, method for learning graph representations in a self-supervised manner. Grounded on spectral graph analysis, SGR seamlessly combines all aforementioned desirable properties. In extensive experiments, we show how our approach works on large graph collections, facilitates self-supervised representation learning across a variety of application domains, and performs competitively to state-of-the-art methods without re-training.

Or Litany, Alex Bronstein, Michael Bronstein et al.

The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly non-rigidly moving) 3D object from a single or multiple partial scans has received increasing attention in recent years. In this work, we propose a novel learning-based method for the completion of partial shapes. Unlike the majority of existing approaches, our method focuses on objects that can undergo non-rigid deformations. The core of our method is a variational autoencoder with graph convolutional operations that learns a latent space for complete realistic shapes. At inference, we optimize to find the representation in this latent space that best fits the generated shape to the known partial input. The completed shape exhibits a realistic appearance on the unknown part. We show promising results towards the completion of synthetic and real scans of human body and face meshes exhibiting different styles of articulation and partiality.

Qiang Qiu, Jose Lezama, Alex Bronstein et al.

Hash codes are efficient data representations for coping with the ever growing amounts of data. In this paper, we introduce a random forest semantic hashing scheme that embeds tiny convolutional neural networks (CNN) into shallow random forests, with near-optimal information-theoretic code aggregation among trees. We start with a simple hashing scheme, where random trees in a forest act as hashing functions by setting `1' for the visited tree leaf, and `0' for the rest. We show that traditional random forests fail to generate hashes that preserve the underlying similarity between the trees, rendering the random forests approach to hashing challenging. To address this, we propose to first randomly group arriving classes at each tree split node into two groups, obtaining a significantly simplified two-class classification problem, which can be handled using a light-weight CNN weak learner. Such random class grouping scheme enables code uniqueness by enforcing each class to share its code with different classes in different trees. A non-conventional low-rank loss is further adopted for the CNN weak learners to encourage code consistency by minimizing intra-class variations and maximizing inter-class distance for the two random class groups. Finally, we introduce an information-theoretic approach for aggregating codes of individual trees into a single hash code, producing a near-optimal unique hash for each class. The proposed approach significantly outperforms state-of-the-art hashing methods for image retrieval tasks on large-scale public datasets, while performing at the level of other state-of-the-art image classification techniques while utilizing a more compact and efficient scalable representation. This work proposes a principled and robust procedure to train and deploy in parallel an ensemble of light-weight CNNs, instead of simply going deeper.

Gautam Pai, Ronen Talmon, Alex Bronstein et al.

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.

Zorah Lähner, Matthias Vestner, Amit Boyarski et al.

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We provide preliminary theoretical analysis and several interpretations of the method.

Matthias Vestner, Roee Litman, Emanuele Rodolà et al.

Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a post-processing stage in the functional correspondence framework. Such frequently used techniques implicitly make restrictive assumptions (e.g., near-isometry) on the considered shapes and in practice suffer from lack of accuracy and result in poor surjectivity. We propose an alternative recovery technique capable of guaranteeing a bijective correspondence and producing significantly higher accuracy and smoothness. Unlike other methods our approach does not depend on the assumption that the analyzed shapes are isometric. We derive the proposed method from the statistical framework of kernel density estimation and demonstrate its performance on several challenging deformable 3D shape matching datasets.

Or Litany, Tal Remez, Alex Bronstein

With the development of range sensors such as LIDAR and time-of-flight cameras, 3D point cloud scans have become ubiquitous in computer vision applications, the most prominent ones being gesture recognition and autonomous driving. Parsimony-based algorithms have shown great success on images and videos where data points are sampled on a regular Cartesian grid. We propose an adaptation of these techniques to irregularly sampled signals by using continuous dictionaries. We present an example application in the form of point cloud denoising.

Yoni Choukroun, Alon Shtern, Alex Bronstein et al.

Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field of shape analysis. To this end we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present a general optimization approach for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.

Alex Bronstein, Yoni Choukroun, Ron Kimmel et al.

The L1 norm has been tremendously popular in signal and image processing in the past two decades due to its sparsity-promoting properties. More recently, its generalization to non-Euclidean domains has been found useful in shape analysis applications. For example, in conjunction with the minimization of the Dirichlet energy, it was shown to produce a compactly supported quasi-harmonic orthonormal basis, dubbed as compressed manifold modes. The continuous L1 norm on the manifold is often replaced by the vector l1 norm applied to sampled functions. We show that such an approach is incorrect in the sense that it does not consistently discretize the continuous norm and warn against its sensitivity to the specific sampling. We propose two alternative discretizations resulting in an iteratively-reweighed l2 norm. We demonstrate the proposed strategy on the compressed modes problem, which reduces to a sequence of simple eigendecomposition problems not requiring non-convex optimization on Stiefel manifolds and producing more stable and accurate results.

Tal Remez, Or Litany, Shachar Yoseff et al.

We present a proof-of-concept end-to-end system for computational extended depth of field (EDOF) imaging. The acquisition is performed through a phase-coded aperture implemented by placing a thin wavelength-dependent optical mask inside the pupil of a conventional camera lens, as a result of which, each color channel is focused at a different depth. The reconstruction process receives the raw Bayer image as the input, and performs blind estimation of the output color image in focus at an extended range of depths using a patch-wise sparse prior. We present a fast non-iterative reconstruction algorithm operating with constant latency in fixed-point arithmetics and achieving real-time performance in a prototype FPGA implementation. The output of the system, on simulated and real-life scenes, is qualitatively and quantitatively better than the result of clear-aperture imaging followed by state-of-the-art blind deblurring.

Matthias Vestner, Roee Litman, Alex Bronstein et al.

Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a postprocessing stage in the functional correspondence framework. In this paper, we show that such frequently used techniques in practice suffer from lack of accuracy and result in poor surjectivity. We propose an alternative recovery technique guaranteeing a bijective correspondence and producing significantly higher accuracy. We derive the proposed method from a statistical framework of Bayesian inference and demonstrate its performance on several challenging deformable 3D shape matching datasets.

Or Litany, Tal Remez, Alex Bronstein

Recently, the dense binary pixel Gigavision camera had been introduced, emulating a digital version of the photographic film. While seems to be a promising solution for HDR imaging, its output is not directly usable and requires an image reconstruction process. In this work, we formulate this problem as the minimization of a convex objective combining a maximum-likelihood term with a sparse synthesis prior. We present MLNet - a novel feed-forward neural network, producing acceptable output quality at a fixed complexity and is two orders of magnitude faster than iterative algorithms. We present state of the art results in the abstract.

Or Litany, Tal Remez, Daniel Freedman et al.

We present ASIST, a technique for transforming point clouds by replacing objects with their semantically equivalent counterparts. Transformations of this kind have applications in virtual reality, repair of fused scans, and robotics. ASIST is based on a unified formulation of semantic labeling and object replacement; both result from minimizing a single objective. We present numerical tools for the efficient solution of this optimization problem. The method is experimentally assessed on new datasets of both synthetic and real point clouds, and is additionally compared to two recent works on object replacement on data from the corresponding papers.

Tal Remez, Or Litany, Alex Bronstein

The pursuit of smaller pixel sizes at ever increasing resolution in digital image sensors is mainly driven by the stringent price and form-factor requirements of sensors and optics in the cellular phone market. Recently, Eric Fossum proposed a novel concept of an image sensor with dense sub-diffraction limit one-bit pixels jots, which can be considered a digital emulation of silver halide photographic film. This idea has been recently embodied as the EPFL Gigavision camera. A major bottleneck in the design of such sensors is the image reconstruction process, producing a continuous high dynamic range image from oversampled binary measurements. The extreme quantization of the Poisson statistics is incompatible with the assumptions of most standard image processing and enhancement frameworks. The recently proposed maximum-likelihood (ML) approach addresses this difficulty, but suffers from image artifacts and has impractically high computational complexity. In this work, we study a variant of a sensor with binary threshold pixels and propose a reconstruction algorithm combining an ML data fitting term with a sparse synthesis prior. We also show an efficient hardware-friendly real-time approximation of this inverse operator.Promising results are shown on synthetic data as well as on HDR data emulated using multiple exposures of a regular CMOS sensor.

Qiang Qiu, Guillermo Sapiro, Alex Bronstein

Hash codes are a very efficient data representation needed to be able to cope with the ever growing amounts of data. We introduce a random forest semantic hashing scheme with information-theoretic code aggregation, showing for the first time how random forest, a technique that together with deep learning have shown spectacular results in classification, can also be extended to large-scale retrieval. Traditional random forest fails to enforce the consistency of hashes generated from each tree for the same class data, i.e., to preserve the underlying similarity, and it also lacks a principled way for code aggregation across trees. We start with a simple hashing scheme, where independently trained random trees in a forest are acting as hashing functions. We the propose a subspace model as the splitting function, and show that it enforces the hash consistency in a tree for data from the same class. We also introduce an information-theoretic approach for aggregating codes of individual trees into a single hash code, producing a near-optimal unique hash for each class. Experiments on large-scale public datasets are presented, showing that the proposed approach significantly outperforms state-of-the-art hashing methods for retrieval tasks.

Yonathan Aflalo, Alex Bronstein, Ron Kimmel

We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly-stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n^2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic.

Alex Bronstein, Pablo Sprechmann, Guillermo Sapiro

We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal splitting method for the iterative solution of hierarchical sparse coding problems, and show an efficient feed forward architecture derived from its iteration. This architecture faithfully approximates the exact structured sparse codes with a fraction of the complexity of the standard optimization methods. We also show that by using different training objective functions, learnable sparse encoders are no longer restricted to be mere approximants of the exact sparse code for a pre-given dictionary, as in earlier formulations, but can be rather used as full-featured sparse encoders or even modelers. A simple implementation shows several orders of magnitude speedup compared to the state-of-the-art at minimal performance degradation, making the proposed framework suitable for real time and large-scale applications.