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A large differentiated oligopoly yields inefficient market equilibria. An authority with imprecise information about the primitives of the market aims to design tax/subsidy interventions that increase efficiency robustly, i.e., with high probability. We identify a condition on demand that guarantees the existence of such interventions, and we show how to construct them using noisy estimates of demand complementarities and substitutabilities across products. The analysis works by deriving a novel description of the incidence of market interventions in terms of spectral statistics of a Slutsky matrix. Our notion of recoverable structure ensures that parts of the spectrum that are useful for the design of interventions are statistically recoverable from noisy demand estimates.

A crucial question in active patient care is determining if a treatment is having the desired effect, especially when changes are subtle over short periods. We propose using inter-patient data to train models that can learn to detect these fine-grained changes within a single patient. Specifically, can a model trained on multi-patient scans predict subtle changes in an individual patient's scans? Recent years have seen increasing use of deep learning (DL) in predicting diseases using biomedical imaging, such as predicting COVID-19 severity using lung ultrasound (LUS) data. While extensive literature exists on successful applications of DL systems when well-annotated large-scale datasets are available, it is quite difficult to collect a large corpus of personalized datasets for an individual. In this work, we investigate the ability of recent computer vision models to learn fine-grained differences while being trained on data showing larger differences. We evaluate on an in-house LUS dataset and a public ADNI brain MRI dataset. We find that models pre-trained on clips from multiple patients can better predict fine-grained differences in scans from a single patient by employing contrastive learning., Comment: Under review at ISBI 2025 conference

In their celebrated paper of 1976, Rothschild and Stein prove a lifting procedure that locally reduces to a free nilpotent Lie algebra any family of smooth vector fields $X_1,\dots,X_q$, over a manifold $M$. Then, a large class of differential operators can be lifted, and fundamental solutions on the lifted space can be re-projected to fundamental solutions of the given operators on $M$. In case that the Lie algebra $\mathfrak g=\mbox{Lie}(X_1,\dots,X_q)$ is finite dimensional but not nilpotent, this procedure could introduce a strong tilting of the space. In this paper we represent a global construction of a Lie group $G$ associated to $\mathfrak g$ that avoid this tilting problem. In particular $\mbox{Lie}(G)\cong\mathfrak g$ and a right $G$-action exists over $M$, faithful and transitive, inducing a natural projection $E\colon G\to M$. We represent the group $G$ as a direct product $M\times G^z$ where the model fiber $G^z$ has a group structure. We prove that for any simply connected manifold $M$ -- and a vast class of non-simply connected manifolds -- a fundamental solution for a differential operator $L=\sum_{\alpha\in\mathbb N^q} r_\alpha\cdot X^\alpha$ of finite degree over $M$ can be obtained, via a saturation method, from a fundamental solution for the associated lifted operator over the group $G$. This is a generalization of Biagi and Bonfiglioli analogous result for homogeneous vector fields over $M=\mathbb R^n$., Comment: 22 pages

Accurate and interpretable diagnostic models are crucial in the safety-critical field of medicine. We investigate the interpretability of our proposed biomarker-based lung ultrasound diagnostic pipeline to enhance clinicians' diagnostic capabilities. The objective of this study is to assess whether explanations from a decision tree classifier, utilizing biomarkers, can improve users' ability to identify inaccurate model predictions compared to conventional saliency maps. Our findings demonstrate that decision tree explanations, based on clinically established biomarkers, can assist clinicians in detecting false positives, thus improving the reliability of diagnostic models in medicine., Comment: Accepted at BIAS 2023 Conference

The Extreme Universe Space Observatory on a Super Pressure Balloon 1 (EUSO-SPB1) was launched in 2017 April from Wanaka, New Zealand. The plan of this mission of opportunity on a NASA super pressure balloon test flight was to circle the southern hemisphere. The primary scientific goal was to make the first observations of ultra-high-energy cosmic-ray extensive air showers (EASs) by looking down on the atmosphere with an ultraviolet (UV) fluorescence telescope from suborbital altitude (33~km). After 12~days and 4~hours aloft, the flight was terminated prematurely in the Pacific Ocean. Before the flight, the instrument was tested extensively in the West Desert of Utah, USA, with UV point sources and lasers. The test results indicated that the instrument had sensitivity to EASs of approximately 3 EeV. Simulations of the telescope system, telescope on time, and realized flight trajectory predicted an observation of about 1 event assuming clear sky conditions. The effects of high clouds were estimated to reduce this value by approximately a factor of 2. A manual search and a machine-learning-based search did not find any EAS signals in these data. Here we review the EUSO-SPB1 instrument and flight and the EAS search., Comment: 18 pages, 19 figures

Segmenting a moving needle in ultrasound images is challenging due to the presence of artifacts, noise, and needle occlusion. This task becomes even more demanding in scenarios where data availability is limited. In this paper, we present a novel approach for needle segmentation for 2D ultrasound that combines classical Kalman Filter (KF) techniques with data-driven learning, incorporating both needle features and needle motion. Our method offers three key contributions. First, we propose a compatible framework that seamlessly integrates into commonly used encoder-decoder style architectures. Second, we demonstrate superior performance compared to recent state-of-the-art needle segmentation models using our novel convolutional neural network (CNN) based KF-inspired block, achieving a 15\% reduction in pixel-wise needle tip error and an 8\% reduction in length error. Third, to our knowledge we are the first to implement a learnable filter to incorporate non-linear needle motion for improving needle segmentation., Comment: 7 pages, 4 figures, accepted at ISBI 2024

Due to its importance and widespread use in industry, automated testing of REST APIs has attracted major interest from the research community in the last few years. However, most of the work in the literature has been focused on black-box fuzzing. Although existing fuzzers have been used to automatically find many faults in existing APIs, there are still several open research challenges that hinder the achievement of better results (e.g., in terms of code coverage and fault finding). For example, under-specified schemas are a major issue for black-box fuzzers. Currently, EvoMaster is the only existing tool that supports white-box fuzzing of REST APIs. In this paper, we provide a series of novel white-box heuristics, including for example how to deal with under-specified constrains in API schemas, as well as under-specified schemas in SQL databases. Our novel techniques are implemented as an extension to our open-source, search-based fuzzer EvoMaster. An empirical study on 14 APIs from the EMB corpus, plus one industrial API, shows clear improvements of the results in some of these APIs.

2D materials with high charge carrier mobility and tunable electronic band gaps have attracted intense research effort for their potential use as active components in nanoelectronics. 2D-conjugated polymers (2DCP) constitute a promising sub-class due to the fact that the electronic band structure can be manipulated by varying the molecular building blocks, while at the same time preserving the key features of 2D materials such as Dirac cones and high charge mobility. The major challenge for their use in technological applications is to fabricate mesoscale ordered 2DCP networks since current synthetic routes yield only small domains with a high density of defects. Here we demonstrate the synthesis of a mesoscale ordered 2DCP with semiconducting properties and Dirac cone structures via Ullmann coupling on Au(111). This material has been obtained by combining rigid azatriangulene precursors and a hot dosing approach which favours molecular diffusion and reduces the formation of voids in the network. These results open opportunities for the synthesis of 2DCP Dirac cone materials and their integration into devices., Comment: 21 pages, 3 figures

In this paper, we present a novel deep-learning model for deformable registration of ultrasound images and an unsupervised approach to training this model. Our network employs recurrent all-pairs field transforms (RAFT) and a spatial transformer network (STN) to generate displacement fields at online rates (apprx. 30 Hz) and accurately track pixel movement. We call our approach unsupervised recurrent all-pairs field transforms (U-RAFT). In this work, we use U-RAFT to track pixels in a sequence of ultrasound images to cancel out respiratory motion in lung ultrasound images. We demonstrate our method on in-vivo porcine lung videos. We show a reduction of 76% in average pixel movement in the porcine dataset using respiratory motion compensation strategy. We believe U-RAFT is a promising tool for compensating different kinds of motions like respiration and heartbeat in ultrasound images of deformable tissue.

This paper presents a deep-learning model for deformable registration of ultrasound images at online rates, which we call U-RAFT. As its name suggests, U-RAFT is based on RAFT, a convolutional neural network for estimating optical flow. U-RAFT, however, can be trained in an unsupervised manner and can generate synthetic images for training vessel segmentation models. We propose and compare the registration quality of different loss functions for training U-RAFT. We also show how our approach, together with a robot performing force-controlled scans, can be used to generate synthetic deformed images to significantly expand the size of a femoral vessel segmentation training dataset without the need for additional manual labeling. We validate our approach on both a silicone human tissue phantom as well as on in-vivo porcine images. We show that U-RAFT generates synthetic ultrasound images with 98% and 81% structural similarity index measure (SSIM) to the real ultrasound images for the phantom and porcine datasets, respectively. We also demonstrate that synthetic deformed images from U-RAFT can be used as a data augmentation technique for vessel segmentation models to improve intersection-over-union (IoU) segmentation performance

Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model of computation. This model exhibits the same symmetry as finite Turing computation in universes constructible from a set of ordinals, but that statement is independent of von Neumann-G\"odel-Bernays class theory.

We present a theoretical framework for a stereo vision method via optimal transport tools. We consider two aligned optical systems and we develop the matching between the two pictures line by line. By considering a regularized version of the optimal transport, we can speed up the computation and obtain a very accurate disparity function evaluation. Moreover, via this same method we can approach successfully the case of images with occluded regions., Comment: 18 pages, 12 figures

Contemporary artificial neural networks (ANN) are trained end-to-end, jointly learning both features and classifiers for the task of interest. Though enormously effective, this paradigm imposes significant costs in assembling annotated task-specific datasets and training large-scale networks. We propose to decouple feature learning from downstream lung ultrasound tasks by introducing an auxiliary pre-task of visual biomarker classification. We demonstrate that one can learn an informative, concise, and interpretable feature space from ultrasound videos by training models for predicting biomarker labels. Notably, biomarker feature extractors can be trained from data annotated with weak video-scale supervision. These features can be used by a variety of downstream Expert models targeted for diverse clinical tasks (Diagnosis, lung severity, S/F ratio). Crucially, task-specific expert models are comparable in accuracy to end-to-end models directly trained for such target tasks, while being significantly lower cost to train.

Receptive profiles of V1 cortical cells are very heterogeneous and act by differentiating the stimulus image as operators changing from point to point. A lightness and color constancy image can be reconstructed as the solution of the associated inverse problem, that is a Poisson equation with heterogeneous differential operators. At the neural level the weights of short range connectivity constitute the fundamental solution of the Poisson problem adapted point by point. A first demonstration of convergence of the result towards homogeneous reconstructions is proposed by means of homogenisation techniques., Comment: 34 pages, 13 figures

Compilation of papers presented by the JEM-EUSO Collaboration at the 37th International Cosmic Ray Conference (ICRC), held on July 12-23, 2021 (online) in Berlin, Germany., Comment: html page with links to the JEM-EUSO Collaboration papers presented at ICRC-2021, Berlin, Germany

We propose using a pre-trained segmentation model to perform diagnostic classification in order to achieve better generalization and interpretability, terming the technique reverse-transfer learning. We present an architecture to convert segmentation models to classification models. We compare and contrast dense vs sparse segmentation labeling and study its impact on diagnostic classification. We compare the performance of U-Net trained with dense and sparse labels to segment A-lines, B-lines, and Pleural lines on a custom dataset of lung ultrasound scans from 4 patients. Our experiments show that dense labels help reduce false positive detection. We study the classification capability of the dense and sparse trained U-Net and contrast it with a non-pretrained U-Net, to detect and differentiate COVID-19 and Pneumonia on a large ultrasound dataset of about 40k curvilinear and linear probe images. Our segmentation-based models perform better classification when using pretrained segmentation weights, with the dense-label pretrained U-Net performing the best., Comment: Published in 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) \copyright 2021 IEEE

In this paper, we study the significance of the pleura and adipose tissue in lung ultrasound AI analysis. We highlight their more prominent appearance when using high-frequency linear (HFL) instead of curvilinear ultrasound probes, showing HFL reveals better pleura detail. We compare the diagnostic utility of the pleura and adipose tissue using an HFL ultrasound probe. Masking the adipose tissue during training and inference (while retaining the pleural line and Merlin's space artifacts such as A-lines and B-lines) improved the AI model's diagnostic accuracy., Comment: Published in MICCAI 2021 workshop on Lessons Learned from the development and application of medical imaging-based AI technologies for combating COVID-19 (LL-COVID19). The first two authors contributed equally to this work

With the onset of the COVID-19 pandemic, ultrasound has emerged as an effective tool for bedside monitoring of patients. Due to this, a large amount of lung ultrasound scans have been made available which can be used for AI based diagnosis and analysis. Several AI-based patient severity scoring models have been proposed that rely on scoring the appearance of the ultrasound scans. AI models are trained using ultrasound-appearance severity scores that are manually labeled based on standardized visual features. We address the challenge of labeling every ultrasound frame in the video clips. Our contrastive learning method treats the video clip severity labels as noisy weak severity labels for individual frames, thus requiring only video-level labels. We show that it performs better than the conventional cross-entropy loss based training. We combine frame severity predictions to come up with video severity predictions and show that the frame based model achieves comparable performance to a video based TSM model, on a large dataset combining public and private sources., Comment: Under Review for MIDL 2022 conference

Suppliers of differentiated goods make simultaneous pricing decisions, which are strategically linked. Because of market power, the equilibrium is inefficient. We study how a policymaker should target a budget-balanced tax-and-subsidy policy to increase welfare. A key tool is a certain basis for the goods space, determined by the network of interactions among suppliers. It consists of eigenbundles -- orthogonal in the sense that a tax on any eigenbundle passes through only to its own price -- with pass-through coefficients determined by associated eigenvalues. Our basis permits a simple characterization of optimal interventions. A planner maximizing consumer surplus should tax eigenbundles with low pass-through and subsidize ones with high pass-through. The Pigouvian leverage of the system -- the gain in consumer surplus achievable by an optimal tax scheme -- depends only on the dispersion of the eigenvalues of the matrix of strategic interactions. We interpret these results in terms of the network structure of the market.

Advanced resuscitative technologies, such as Extra Corporeal Membrane Oxygenation (ECMO) cannulation or Resuscitative Endovascular Balloon Occlusion of the Aorta (REBOA), are technically difficult even for skilled medical personnel. This paper describes the core technologies that comprise a teleoperated system capable of granting femoral vascular access, which is an important step in both of these procedures and a major roadblock in their wider use in the field. These technologies include a kinematic manipulator, various sensing modalities, and a user interface. In addition, we evaluate our system on a surgical phantom as well as in-vivo porcine experiments. These resulted in, to the best of our knowledge, the first robot-assisted arterial catheterizations; a major step towards our eventual goal of automatic catheter insertion through the Seldinger technique., Comment: 6 pages, 5 figures, 1 table, submitted (but not accepted yet) to ISMR

Researchers and practitioners have designed and implemented various automated test case generators to support effective software testing. Such generators exist for various languages (e.g., Java, C#, or Python) and for various platforms (e.g., desktop, web, or mobile applications). Such generators exhibit varying effectiveness and efficiency, depending on the testing goals they aim to satisfy (e.g., unit-testing of libraries vs. system-testing of entire applications) and the underlying techniques they implement. In this context, practitioners need to be able to compare different generators to identify the most suited one for their requirements, while researchers seek to identify future research directions. This can be achieved through the systematic execution of large-scale evaluations of different generators. However, the execution of such empirical evaluations is not trivial and requires a substantial effort to collect benchmarks, setup the evaluation infrastructure, and collect and analyse the results. In this paper, we present our JUnit Generation benchmarking infrastructure (JUGE) supporting generators (e.g., search-based, random-based, symbolic execution, etc.) seeking to automate the production of unit tests for various purposes (e.g., validation, regression testing, fault localization, etc.). The primary goal is to reduce the overall effort, ease the comparison of several generators, and enhance the knowledge transfer between academia and industry by standardizing the evaluation and comparison process. Since 2013, eight editions of a unit testing tool competition, co-located with the Search-Based Software Testing Workshop, have taken place and used and updated JUGE. As a result, an increasing amount of tools (over ten) from both academia and industry have been evaluated on JUGE, matured over the years, and allowed the identification of future research directions.

Class labels used for machine learning are relatable to each other, with certain class labels being more similar to each other than others (e.g. images of cats and dogs are more similar to each other than those of cats and cars). Such similarity among classes is often the cause of poor model performance due to the models confusing between them. Current labeling techniques fail to explicitly capture such similarity information. In this paper, we instead exploit the similarity between classes by capturing the similarity information with our novel confidence labels. Confidence labels are probabilistic labels denoting the likelihood of similarity, or confusability, between the classes. Often even after models are trained to differentiate between classes in the feature space, the similar classes' latent space still remains clustered. We view this type of clustering as valuable information and exploit it with our novel projective loss functions. Our projective loss functions are designed to work with confidence labels with an ability to relax the loss penalty for errors that confuse similar classes. We use our approach to train neural networks with noisy labels, as we believe noisy labels are partly a result of confusability arising from class similarity. We show improved performance compared to the use of standard loss functions. We conduct a detailed analysis using the CIFAR-10 dataset and show our proposed methods' applicability to larger datasets, such as ImageNet and Food-101N.

Consider a coordination game played on a network, where agents prefer taking actions closer to those of their neighbors and to their own ideal points in action space. We explore how the welfare outcomes of a coordination game depend on network structure and the distribution of ideal points throughout the network. To this end, we imagine a benevolent or adversarial planner who intervenes, at a cost, to change ideal points in order to maximize or minimize utilitarian welfare subject to a constraint. A complete characterization of optimal interventions is obtained by decomposing interventions into principal components of the network's adjacency matrix. Welfare is most sensitive to interventions proportional to the last principal component, which focus on local disagreement. A welfare-maximizing planner optimally works to reduce local disagreement, bringing the ideal points of neighbors closer together, whereas a malevolent adversary optimally drives neighbors' ideal points apart to decrease welfare. Such welfare-maximizing/minimizing interventions are very different from ones that would be done to change some traditional measures of discord, such as the cross-sectional variation of equilibrium actions. In fact, an adversary sowing disagreement to maximize her impact on welfare will minimize her impact on global variation in equilibrium actions, underscoring a tension between improving welfare and increasing global cohesion of equilibrium behavior.

We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of randomly realisable statements is closed under intuitionistic first-order logic, but (ii) different from the set of realisable statements, that (iii) "realisability with probability 1" is the same as realisability and (iv) that the axioms of bounded Heyting's arithmetic are randomly realisable, but some instances of the full induction scheme fail to be randomly realisable.

Ultrasound image quality has continually been improving. However, when needles or other metallic objects are operating inside the tissue, the resulting reverberation artifacts can severely corrupt the surrounding image quality. Such effects are challenging for existing computer vision algorithms for medical image analysis. Needle reverberation artifacts can be hard to identify at times and affect various pixel values to different degrees. The boundaries of such artifacts are ambiguous, leading to disagreement among human experts labeling the artifacts. We propose a weakly- and semi-supervised, probabilistic needle-and-reverberation-artifact segmentation algorithm to separate the desired tissue-based pixel values from the superimposed artifacts. Our method models the intensity decay of artifact intensities and is designed to minimize the human labeling error. We demonstrate the applicability of the approach and compare it against other segmentation algorithms. Our method is capable of differentiating between the reverberations from artifact-free patches as well as of modeling the intensity fall-off in the artifacts. Our method matches state-of-the-art artifact segmentation performance and sets a new standard in estimating the per-pixel contributions of artifact vs underlying anatomy, especially in the immediately adjacent regions between reverberation lines. Our algorithm is also able to improve the performance downstream image analysis algorithms.

Ultrasound imaging has been improving, but continues to suffer from inherent artifacts that are challenging to model, such as attenuation, shadowing, diffraction, speckle, etc. These artifacts can potentially confuse image analysis algorithms unless an attempt is made to assess the certainty of individual pixel values. Our novel confidence algorithms analyze pixel values using a directed acyclic graph based on acoustic physical properties of ultrasound imaging. We demonstrate unique capabilities of our approach and compare it against previous confidence-measurement algorithms for shadow-detection and image-compounding tasks., Comment: 5 pages, conference

Ultrasound 3D compounding is important for volumetric reconstruction, but as of yet there is no consensus on best practices for compounding. Ultrasound images depend on probe direction and the path sound waves pass through, so when multiple intersecting B-scans of the same spot from different perspectives yield different pixel values, there is not a single, ideal representation for compounding (i.e. combining) the overlapping pixel values. Current popular methods inevitably suppress or altogether leave out bright or dark regions that are useful, and potentially introduce new artifacts. In this work, we establish a new algorithm to compound the overlapping pixels from different view points in ultrasound. We uniquely leverage Laplacian and Gaussian Pyramids to preserve the maximum boundary contrast without overemphasizing noise and speckle. We evaluate our algorithm by comparing ours with previous algorithms, and we show that our approach not only preserves both light and dark details, but also somewhat suppresses artifacts, rather than amplifying them., Comment: Int J CARS (2021)

Identifying landmarks in the femoral area is crucial for ultrasound (US) -based robot-guided catheter insertion, and their presentation varies when imaged with different scanners. As such, the performance of past deep learning-based approaches is also narrowly limited to the training data distribution; this can be circumvented by fine-tuning all or part of the model, yet the effects of fine-tuning are seldom discussed. In this work, we study the US-based segmentation of multiple classes through transfer learning by fine-tuning different contiguous blocks within the model, and evaluating on a gamut of US data from different scanners and settings. We propose a simple method for predicting generalization on unseen datasets and observe statistically significant differences between the fine-tuning methods while working towards domain generalization., Comment: Machine Learning for Health (ML4H) at NeurIPS 2020 - Extended Abstract

We introduce a realisability semantics for infinitary intuitionistic set theory that is based on Ordinal Turing Machines (OTMs). We show that our notion of OTM-realisability is sound with respect to certain systems of infinitary intuitionistic logic, and that all axioms of infinitary Kripke-Platek set theory are realised. Finally, we use a variant of our notion of realisability to show that the propositional admissible rules of (finitary) intuitionistic Kripke-Platek set theory are exactly the admissible rules of intuitionistic propositional logic.

We present W-Net, a novel Convolution Neural Network (CNN) framework that employs raw ultrasound waveforms from each A-scan, typically referred to as ultrasound Radio Frequency (RF) data, in addition to the gray ultrasound image to semantically segment and label tissues. Unlike prior work, we seek to label every pixel in the image, without the use of a background class. To the best of our knowledge, this is also the first deep-learning or CNN approach for segmentation that analyses ultrasound raw RF data along with the gray image. International patent(s) pending [PCT/US20/37519]. We chose subcutaneous tissue (SubQ) segmentation as our initial clinical goal since it has diverse intermixed tissues, is challenging to segment, and is an underrepresented research area. SubQ potential applications include plastic surgery, adipose stem-cell harvesting, lymphatic monitoring, and possibly detection/treatment of certain types of tumors. A custom dataset consisting of hand-labeled images by an expert clinician and trainees are used for the experimentation, currently labeled into the following categories: skin, fat, fat fascia/stroma, muscle and muscle fascia. We compared our results with U-Net and Attention U-Net. Our novel \emph{W-Net}'s RF-Waveform input and architecture increased mIoU accuracy (averaged across all tissue classes) by 4.5\% and 4.9\% compared to regular U-Net and Attention U-Net, respectively. We present analysis as to why the Muscle fascia and Fat fascia/stroma are the most difficult tissues to label. Muscle fascia in particular, the most difficult anatomic class to recognize for both humans and AI algorithms, saw mIoU improvements of 13\% and 16\% from our W-Net vs U-Net and Attention U-Net respectively., Comment: The paper is currently under review for publication in a peer-reviewed journal

Bagaria and V\"a\"an\"anen developed a framework for studying the large cardinal strength of downwards L\"owenheim-Skolem theorems and related set theoretic reflection properties. The main tool was the notion of symbiosis, originally introduced by the third author. Symbiosis provides a way of relating model theoretic properties of strong logics to definability in set theory. In this paper we continue the systematic investigation of symbiosis and apply it to upwards L\"owenheim-Skolem theorems and reflection principles. To achieve this, we need to adapt the notion of symbiosis to a new form, called bounded symbiosis. As one easy application, we obtain upper and lower bounds for the large cardinal strength of upwards L\"owenheim-Skolem-type principles for second order logic.

We introduce a model for image morphing in the primary visual cortex V1 to perform completion of missing images in time. We model the output of simple cells through a family of Gabor filters and the propagation of the neural signal accordingly to the functional geometry induced by horizontal connectivity. Then we model the deformation between two images as a path relying two different outputs. This path is obtained by optimal transport considering the Wasserstein distance geodesics associated to some probability measures naturally induced by the outputs on V1. The frame of Gabor filters allows to project back the output path, therefore obtaining an associated image stimulus deformation. We perform a numerical implementation of our cortical model, assessing its ability in reconstructing rigidi motions of simple shapes., Comment: 25 pages, 6 figures