Publications

2025

1. J. Med. Imaging

   Self-Supervision Enhances Instance-based Multiple Instance Learning Methods in Digital Pathology: A Benchmark Study

   Ali Mammadov, Loic Le Folgoc, Julien Adam, Anne Buronfosse, Gilles Hayem, Guillaume Hocquet, and Pietro Gori

   Journal of Medical Imaging, 2025

   Abstract Paper Code

   Multiple Instance Learning (MIL) has emerged as the best solution for Whole Slide Image (WSI) classification. It consists of dividing each slide into patches, which are treated as a bag of instances labeled with a global label. MIL includes two main approaches: instance-based and embedding-based. In the former, each patch is classified independently, and then the patch scores are aggregated to predict the bag label. In the latter, bag classification is performed after aggregating patch embeddings. Even if instance-based methods are naturally more interpretable, embedding-based MILs have usually been preferred in the past due to their robustness to poor feature extractors. However, recently, the quality of feature embeddings has drastically increased using self-supervised learning (SSL). Nevertheless, many authors continue to endorse the superiority of embedding-based MIL. To investigate this further, we conduct 710 experiments across 4 datasets, comparing 10 MIL strategies, 6 self-supervised methods with 4 backbones, 4 foundation models, and various pathology-adapted techniques. Furthermore, we introduce 4 instance-based MIL methods never used before in the pathology domain. Through these extensive experiments, we show that with a good SSL feature extractor, simple instance-based MILs, with very few parameters, obtain similar or better performance than complex, state-of-the-art (SOTA) embedding-based MIL methods, setting new SOTA results on the BRACS and Camelyon16 datasets. Since simple instance-based MIL methods are naturally more interpretable and explainable to clinicians, our results suggest that more effort should be put into well-adapted SSL methods for WSI rather than into complex embedding-based MIL methods.

2. J. Imaging Informatics

   Revisiting Anatomy of Anorectal Malformations with a Symbolic AI Segmentation Method Applied on Diffusion MRI: The Lumbosacral Plexus Development and Microarchitecture Is Different in High and Low Types

   J. Goulin, G. La Barbera, A. Delmonte, E. Bonnot, L. Berteloot, C. Lozach, S. Beaudoin, T. Blanc, C. Cretolle, C. O. Muller, P. Meignan, Q. Peyrot, E. Mille, J. B. Marret, M. Zerah, N. Boddaert, Pietro Gori, I. Bloch, and S. Sarnacki

   Journal of Imaging Informatics in Medicine, 2025

   Abstract Paper

   Anorectal malformations (ARMs) are congenital anomalies of the distal part of the hindgut often associated with sacral and/or spinal anomalies. We investigated anatomical and microstructural properties of the lumbosacral plexus of ARM patients from imaging data. Twenty-five patients (16 males), median age 4 months (2–49), 13 high and 12 low ARM, underwent 3 Tesla magnetic resonance imaging with diffusion tensor sequences (dMRI) before repair. A 3D model was built from manual segmentation and used to guide novel AI algorithms for the segmentation of the nervous pelvic network. Volume and diffusion parameters were obtained for each root (L5 to S4) and compared among patients with high and low ARMs using a nonparametric Wilcoxon test. Comparison was also made between the groups with (n = 9) or without (n = 16) sacral and/or spinal cord anomalies. When compared with low ARMS, high ARMs exhibited the following: a smaller volume of S1, S2, and S3 roots and of S1 and S3 for patients without sacral and/or spinal cord abnormalities; an overall significant alteration of the roots micro-architecture reflected by a diminution of the fractional anisotropy and an increase of the axial diffusivity and radial diffusivity measures. This first analysis of the lumbosacral plexus from dMRI in children with ARMs shows differences in the development and microarchitecture of the lumbosacral nerve roots between high and low ARMs. This observation supports the hypothesis that high ARMs may result from a more regional developmental abnormality than low ARMs and open new ways to visualize and assess the lumbosacral plexus in children and adults.

3. IEEE ISBI

   Guiding the classification of hepatocellular carcinoma on 3D CT-scans using deep and handcrafted radiological features

   E. Sarfati, A. Bone, M.-M. Rohe, C. Aube, M. Ronot, Pietro Gori, and I. Bloch

   In IEEE International Symposium on Biomedical Imaging (ISBI), 2025

   Abstract Paper

   Hepatocellular carcinoma is the most spread primary liver cancer across the world. The gold standard for HCC diagnosis is liver biopsy. However, in the clinical routine, expert radiologists provide a visual diagnosis by interpreting hepatic CT-scans according to a standardized protocol, the LI-RADS, which uses five radiological criteria with an associated decision tree. In this paper, we propose an automatic approach to predict histology-proven HCC from CT images in order to reduce radiologists’ inter-variability. We first show that standard deep learning methods fail to accurately predict HCC from CT-scans on a challenging database, and propose a two-step approach inspired by the LI-RADS system to improve the performance. We achieve improvements from 6 to 18 points of AUC with respect to deep learning baselines trained with different architectures. We also provide clinical validation of our method, achieving results that outperform non-expert radiologists and are on par with expert ones.

4. Braz. J. Psy.

   White matter hyperintensities and their role in major depressive episodes: a cross-sectional study in adults under 65

   Édouard Baudouin, Emmanuelle Corruble, Pietro Gori, Isabelle Bloch, Laurent Becquemont, Emmanuelle Duron, and Romain Colle

   Brazilian Journal of Psychiatry, 2025

   Abstract Paper

   Objective: White matter hyperintensities (WMH) are associated with Major Depressive Episodes (MDE) in individuals aged 65 and over. WMH are prevalent in adults under 65, yet the association between their volume and MDE in this population remains uncertain. This study aimed to assess the association between WMH volume and MDE and its severity in patients < 65. Methods: This cross-sectional study included subjects under the age of 65, 69 patients with MDE and 32 healthy controls (HCs). Severity was assessed with the Hamilton Rating Scale and WMH were quantified by 2 experts. Post-hoc mediation analyses were conducted if associations were found between independent variables and WMH. Results: Mean was 34.5 (12.4) years old. There was no difference in WMH between patients and HCs. Higher WMH volume were observed in extremely severe MDE (2170.2 (3767.9) mm3 vs 416.6 (594.9) mm3 (r = 0.218; p < 0.05)), which completely mediated the effect of age on severity. Conclusions: In adults under 65, this study failed to identify higher WMH volume in MDE compared to HCs. However, WMH may act as a mediator of the association between age and MDE severity. This finding suggests that WMH could contribute to more severe depression in late-life.

2024

1. ICLR

   Separating common from salient patterns with Contrastive Representation Learning

   Robin Louiset, Edouard Duchesnay, Antoine Grigis, and Pietro Gori

   In International Conference on Learning Representations (ICLR), 2024

   Abstract Paper Code

   Contrastive Analysis is a sub-field of Representation Learning that aims at separating common factors of variation between two datasets, a background (i.e., healthy subjects) and a target (i.e., diseased subjects), from the salient factors of variation, only present in the target dataset. Despite their relevance, current models based on Variational Auto-Encoders have shown poor performance in learning semantically-expressive representations. On the other hand, Contrastive Representation Learning has shown tremendous performance leaps in various applications (classification, clustering, etc.). In this work, we propose to leverage the ability of Contrastive Learning to learn semantically expressive representations well adapted for Contrastive Analysis. We reformulate it under the lens of the InfoMax Principle and identify two Mutual Information terms to maximize and one to minimize. We decompose the first two terms into an Alignment and a Uniformity term, as commonly done in Contrastive Learning. Then, we motivate a novel Mutual Information minimization strategy to prevent information leakage between common and salient distributions. We validate our method, called SepCLR, on three visual datasets and three medical datasets, specifically conceived to assess the pattern separation capability in Contrastive Analysis.

2. Under Review

   Automatic Discovery of Disease Subgroups by Contrasting with Healthy Controls.

   Robin Louiset, Eduouard Duchesnay, Benoit Dufumier, Antoine Grigis, and Pietro Gori

   Under Review, 2024
3. AISTATS

   Double InfoGAN for Contrastive Analysis

   Florence Carton, Robin Louiset, and Pietro Gori

   In International Conference on Artificial Intelligence and Statistics (AISTATS), 2024

   Abstract Paper Code

   Contrastive Analysis (CA) deals with the discovery of what is common and what is distinctive of a target domain compared to a background one. This is of great interest in many applications, such as medical imaging. Current state-of-the-art (SOTA) methods are latent variable models based on VAE (CAVAEs). However, they all either ignore important constraints or they don’t enforce fundamental assumptions. This may lead to suboptimal solutions where distinctive factors are mistaken for common ones (or viceversa). Furthermore, the generated images have a rather poor quality, typical of VAEs, decreasing their interpretability and usefulness. Here, we propose Double InfoGAN, the first GAN based method for CA that leverages the high-quality synthesis of GAN and the separation power of InfoGAN. Experimental results on four visual datasets, from simple synthetic examples to complex medical images, show that the proposed method outperforms SOTA CA-VAEs in terms of latent separation and image quality. Datasets and code are available online1.

4. MIDL

   SepVAE: a contrastive VAE to separate pathological patterns from healthy ones

   Robin Louiset, Edouard Duchesnay, Antoine Grigis, Benoit Dufumier, and Pietro Gori

   In Medical Imaging with Deep Learning (MIDL), 2024

   Abstract Paper Code

   Contrastive Analysis VAEs (CA-VAEs) are a family of Variational auto-encoders (VAEs) that aims at separating the common factors of variation between a background dataset (BG) (i.e., healthy subjects) and a target dataset (TG) (i.e., patients) from the ones that only exist in the target dataset. To do so, these methods separate the latent space into a set of salient features (i.e., proper to the target dataset) and a set of common features (i.e., exist in both datasets). Currently, all models fail to prevent the sharing of information between latent spaces effectively and to capture all salient factors of variation. To this end, we introduce two crucial regularization losses: a disentangling term between common and salient representations and a classification term between background and target samples in the salient space. We show a better performance than previous CA-VAEs methods on three medical applications and a natural images dataset (CelebA).

5. IEEE ISBI

   Supervised diagnosis prediction from cortical sulci: toward the discovery of neurodevelopmental biomarkers in mental disorders

   Pierre Auriau, Antoine Grigis, Benoit Dufumier, Robin Louiset, Joel Chavas, Pietro Gori, Jean-François Mangin, and Edouard Duchesnay

   In 21st IEEE International Symposium on Biomedical Imaging (ISBI), 2024

   DOI Paper
6. IEEE ISBI

   Sparsity Constrained Linear Tangent Space Alignment Model (sLTSA) for 3D Cardiac Extracellular Volume Mapping

   Ismaël Mounime, Wonil Lee, Thibault Marin, Paul K Han, Yanis Djebra, Samira V Eslahi, Pietro Gori, Elsa Angelini, Georges El Fakhri, and Chao Ma

   In 21st IEEE International Symposium on Biomedical Imaging (ISBI), 2024

   Abstract DOI Paper

   Cardiac longitudinal relaxation time (T 1 ) and extracellular volume (ECV) are valuable bio-markers used for the quantitative characterization of cardiac tissue properties, showing great potential in many clinical applications such as diffuse fibrosis. However, cardiac T 1 and ECV mapping is difficult because of respiratory and cardiac motions. A unique challenge for post-contrast T 1 mapping is that the concentration of contrast agent also changes over time. Recently, a linear tangent space alignment (LTSA) model-based fast MRI method has been proposed to enable high-resolution, high-frame-rate dynamic MR with sparsely sampled (k, t)-space data by leveraging the intrinsic low-dimensional manifold structure of dynamic MR images, showing superior performance over the low-rank model-based methods. This work extends the LTSA method by imposing an additional sparsity constraint on the subspace alignment matrix of the LTSA model for improved image reconstruction. The performance of the proposed method is validated in 3D free-breathing, pre- and post-contrast cardiac T 1 mapping as well as ECV mapping using in vivo data acquired on healthy volunteers at 3T.

7. PATENT

   Method for characterizing an organ of a patient in a medical image

   Rebeca Vétil, Clément Abi-Nader, Alexandre Bône, Marc-Michel Rohé, Pietro Gori, and Isabelle Bloch

   2024
8. NeuroImage

   Exploring the potential of representation and transfer learning for anatomical neuroimaging: Application to psychiatry

   Benoit Dufumier, Pietro Gori, Sara Petiton, Robin Louiset, Jean-François Mangin, Antoine Grigis, and Edouard Duchesnay

   NeuroImage, 2024

   DOI Paper
9. EJC Paediatric Oncology

   Robotics and 3D modeling for precision surgery in pediatric oncology

   Nicolas Vinit, Thomas Blanc, Isabelle Bloch, Luca Pio, Rani Kassir, Giammarco La Barbera, Enzo Bonnot, Pietro Gori, Jeanne Goulin, Aurore Pire, Nathalie Boddaert, Cécile Lozach, and Sabine Sarnacki

   EJC Paediatric Oncology, 2024

   Abstract DOI Paper

   In an attempt to minimize surgical trauma in already vulnerable patients, pediatric surgeons are increasingly using minimally invasive surgery in surgical oncology, with similar outcomes as open surgery. In addition to its technical benefits, robotic surgery allows integration of technological enhancements, such as artificial-intelligence-based software or tri-dimensional (3D) modeling, into the operating room. In this article, we report our experience in robotic-assisted surgery for the resection of pediatric tumors and present current developments in 3D modeling applied to pelvic tumors. Since 2016, 149 oncology cases have been undertaken using the robotic approach. Neuroblastic tumors account for the most part, with a median hospital stay of two days [1–7 days] and very few intraoperative events. The use of robotics was mainly extended to renal tumors (predominantly Wilms tumors) and endocrine tumors, but was found of particular interest for pelvic tumors. Our experience led us to publish a first set of guidelines on robotic surgical oncology, focusing on its apparent contraindications. 3D models derived from preoperative magnetic resonance imaging have been developed for more than 150 patients with solid tumors, but the pelvic area was made a key focus because of its anatomical complexity. In addition to their educational benefits, some of these 3D models were integrated into the robotic console as a surgical aid and proved invaluable for difficult dissections or nerve plexus preservation. As evidenced by the development of robotics and 3D modeling, pediatric oncology is leaning toward ultra-precise surgical resection tailored to the patient and the tumor.

10. MICCAI-W

    Towards a foundation model for cortical folding

    Julien Laval, Joël Chavas, Vanessa Troiani, William Snyder, Marisa Patti, Mylène Moyal, Marion Plaze, Arnaud Cachia, Zhong Yi Sun, Vincent Frouin, Pietro Gori, Denis Rivière, and Jean-François Mangin

    In Machine Learning in Clinical Neuroimaging (MLCN) Workshop - MICCAI, 2024

    Paper
11. HDR

    Modeling, Learning, and Transferring Anatomical Representations in Medical Imaging using AI

    Pietro Gori

    2024

2023

1. MedIA

   Tubular structures segmentation of pediatric abdominal-visceral ceCT images with renal tumors: Assessment, comparison and improvement

   Giammarco La Barbera, Laurence Rouet, Haithem Boussaid, Alexis Lubet, Rani Kassir, Sabine Sarnacki, Pietro Gori, and Isabelle Bloch

   Medical Image Analysis, 2023

   Abstract Paper Code

   Renal tubular structures, such as ureters, arteries and veins, are very important for building a complete digital 3D anatomical model of a patient. However, they can be challenging to segment from ceCT images due to their elongated shape, diameter variation and intra- and inter-patient contrast heterogeneity. This task is even more difficult in pediatric and pathological subjects, due to high inter-subject anatomical variations, potential presence of tumors, small volume of these structures compared to the surrounding, and small available labeled datasets. Given the limited literature on methods dedicated to children, and in order to find inspirational approaches, a complete assessment of state-of-the-art methods for the segmentation of renal tubular structures on ceCT images on adults is presented. Then, these methods are tested and compared on a private pediatric and pathological dataset of 79 abdominal-visceral ceCT images with arteriovenous phase acquisitions. To the best of our knowledge, both assessment and comparison in this specific case are novel. Eventually, we also propose a new loss function which leverages for the first time the use of vesselness functions on the predicted segmentation. We show that the combination of this loss function with state-of-the-art methods improves the topological coherence of the segmented tubular structures.

2. MICCAI

   Weakly-supervised positional contrastive learning: application to cirrhosis classification

   Emma Sarfati, Alexandre Bône, Marc-Michel Rohé, Pietro Gori, and Isabelle Bloch

   In Medical Image Computing and Computer Assisted Intervention - MICCAI, 2023

   Abstract Paper Code

   Large medical imaging datasets can be cheaply and quickly annotated with low-confidence, weak labels (e.g., radiological scores). Access to high-confidence labels, such as histology-based diagnoses, is rare and costly. Pretraining strategies, like contrastive learning (CL) methods, can leverage unlabeled or weakly-annotated datasets. These methods typically require large batch sizes, which poses a difficulty in the case of large 3D images at full resolution, due to limited GPU memory. Nevertheless, volumetric positional information about the spatial context of each 2D slice can be very important for some medical applications. In this work, we propose an efficient weakly-supervised positional (WSP) contrastive learning strategy where we integrate both the spatial context of each 2D slice and a weak label via a generic kernel-based loss function. We illustrate our method on cirrhosis prediction using a large volume of weakly-labeled images, namely radiological low-confidence annotations, and small strongly-labeled (i.e., high-confidence) datasets. The proposed model improves the classification AUC by 5% with respect to a baseline model on our internal dataset, and by 26% on the public LIHC dataset from the Cancer Genome Atlas.

3. MICCAI-W

   Decoupled conditional contrastive learning with variable metadata for prostate lesion detection

   Camille Ruppli, Pietro Gori, Roberto Ardon, and Isabelle Bloch

   In MILLanD workshop (MICCAI), 2023

   Paper Code
4. MICCAI-W

   Non-Redundant Combination of Hand-Crafted and Deep Learning Radiomics: Application to the Early Detection of Pancreatic Cancer

   Rebeca Vétil, Clément Abi-Nader, Alexandre Bône, Marie-Pierre Vullierme, Marc-Michel Rohé, Pietro Gori, and Isabelle Bloch

   In CaPTion workshop (MICCAI), 2023

   Paper
5. IEEE ISBI

   Contrastive learning for regression in multi-site brain age prediction

   Carlo Alberto Barbano, Benoit Dufumier, Edouard Duchesnay, Marco Grangetto, and Pietro Gori

   In IEEE 20th International Symposium on Biomedical Imaging (ISBI), 2023

   Abstract Paper Code

   Building accurate Deep Learning (DL) models for brain age prediction is a very relevant topic in neuroimaging, as it could help better understand neurodegenerative disorders and find new biomarkers. To estimate accurate and generalizable models, large datasets have been collected, which are often multi-site and multi-scanner. This large heterogeneity negatively affects the generalization performance of DL models since they are prone to overfit site-related noise. Recently, contrastive learning approaches have been shown to be more robust against noise in data or labels. For this reason, we propose a novel contrastive learning regression loss for robust brain age prediction using MRI scans. Our method achieves state-of-the-art performance on the OpenBHB challenge, yielding the best generalization capability and robustness to site-related noise.

6. IEEE ISBI

   Learning to diagnose cirrhosis from radiological and histological labels with joint self and weakly-supervised pretraining strategies

   Emma Sarfati, Alexandre Bone, Marc-Michel Rohe, Pietro Gori, and Isabelle Bloch

   In IEEE 20th International Symposium on Biomedical Imaging (ISBI), 2023

   Abstract DOI Paper

   Identifying cirrhosis is key to correctly assess the health of the liver. However, the gold standard diagnosis of the cirrhosis needs a medical intervention to obtain the histological confirmation, e.g. the METAVIR score, as the radiological presentation can be equivocal. In this work, we propose to leverage transfer learning from large datasets annotated by radiologists, which we consider as a weak annotation, to predict the histological score available on a small annex dataset. To this end, we propose to compare different pretraining methods, namely weakly-supervised and self-supervised ones, to improve the prediction of the cirrhosis. Finally, we introduce a loss function combining both supervised and self-supervised frameworks for pretraining. This method outperforms the baseline classification of the METAVIR score, reaching an AUC of 0.84 and a balanced accuracy of 0.75, compared to 0.77 and 0.72 for a baseline classifier.

7. ICML

   Integrating Prior Knowledge in Contrastive Learning with Kernel

   Benoit Dufumier, Carlo Alberto Barbano, Robin Louiset, Edouard Duchesnay, and Pietro Gori

   In International Conference on Machine Learning (ICML), 2023

   Paper Code
8. PATENT

   Automatic generation of 3D anatomical models

   Alessandro Delmonte, Sabine Sarnacki, Isabelle Bloch, Pietro Gori, Cecile Muller, Alessio Virzi, and Giammarco La Barbera

   2023
9. ICLR

   Unbiased Supervised Contrastive Learning

   Carlo Alberto Barbano, Benoit Dufumier, Enzo Tartaglione, Marco Grangetto, and Pietro Gori

   In The Eleventh International Conference on Learning Representations (ICLR), 2023

   Abstract Paper Code

   Many datasets are biased, namely they contain easy-to-learn features that are highly correlated with the target class only in the dataset but not in the true underlying distribution of the data. For this reason, learning unbiased models from biased data has become a very relevant research topic in the last years. In this work, we tackle the problem of learning representations that are robust to biases. We first present a margin-based theoretical framework that allows us to clarify why recent contrastive losses (InfoNCE, SupCon, etc.) can fail when dealing with biased data. Based on that, we derive a novel formulation of the supervised contrastive loss ({}epsilon\-SupInfoNCE), providing more accurate control of the minimal distance between positive and negative samples. Furthermore, thanks to our theoretical framework, we also propose FairKL, a new debiasing regularization loss, that works well even with extremely biased data. We validate the proposed losses on standard vision datasets including CIFAR10, CIFAR100, and ImageNet, and we assess the debiasing capability of FairKL with {}epsilon\-SupInfoNCE, reaching state-of-the-art performance on a number of biased datasets, including real instances of biases "in the wild".

2022

1. WBIR

   Weighted Metamorphosis for Registration of Images with Different Topologies

   Anton François, Matthis Maillard, Catherine Oppenheim, Johan Pallud, Isabelle Bloch, Pietro Gori, and Joan Glaunès

   In Biomedical Image Registration (WBIR), 2022

   Abstract DOI Paper Code

   We present an extension of the Metamorphosis algorithm to align images with different topologies and/or appearances. We propose to restrict/limit the metamorphic intensity additions using a time-varying spatial weight function. It can be used to model prior knowledge about the topological/appearance changes (e.g., tumour/oedema). We show that our method improves the disentanglement between anatomical (i.e., shape) and topological (i.e., appearance) changes, thus improving the registration interpretability and its clinical usefulness. As clinical application, we validated our method using MR brain tumour images from the BraTS 2021 dataset. We showed that our method can better align healthy brain templates to images with brain tumours than existing state-of-the-art methods. Our PyTorch code is freely available here: https://github.com/antonfrancois/Demeter_metamorphosis.

2. Eurographics

   Real-time Virtual-Try-On from a Single Example Image through Deep Inverse Graphics and Learned Differentiable Renderers

   R. Kips, R. Jiang, S. Ba, B. Duke, M. Perrot, Pietro Gori, and I. Bloch

   Computer Graphics Forum, 2022

   Abstract DOI Paper

   Augmented reality applications have rapidly spread across online retail platforms and social media, allowing consumers to virtually try-on a large variety of products, such as makeup, hair dying, or shoes. However, parametrizing a renderer to synthesize realistic images of a given product remains a challenging task that requires expert knowledge. While recent work has introduced neural rendering methods for virtual try-on from example images, current approaches are based on large generative models that cannot be used in real-time on mobile devices. This calls for a hybrid method that combines the advantages of computer graphics and neural rendering approaches. In this paper, we propose a novel framework based on deep learning to build a real-time inverse graphics encoder that learns to map a single example image into the parameter space of a given augmented reality rendering engine. Our method leverages self-supervised learning and does not require labeled training data, which makes it extendable to many virtual try-on applications. Furthermore, most augmented reality renderers are not differentiable in practice due to algorithmic choices or implementation constraints to reach real-time on portable devices. To relax the need for a graphics-based differentiable renderer in inverse graphics problems, we introduce a trainable imitator module. Our imitator is a generative network that learns to accurately reproduce the behavior of a given non-differentiable renderer. We propose a novel rendering sensitivity loss to train the imitator, which ensures that the network learns an accurate and continuous representation for each rendering parameter. Automatically learning a differentiable renderer, as proposed here, could be beneficial for various inverse graphics tasks. Our framework enables novel applications where consumers can virtually try-on a novel unknown product from an inspirational reference image on social media. It can also be used by computer graphics artists to automatically create realistic rendering from a reference product image.

3. IEEE ICIP

   Is the U-Net Directional-Relationship Aware?

   Mateus Riva, Pietro Gori, Florian Yger, and Isabelle Bloch

   In International Conference on Image Processing (ICIP), 2022

   DOI Paper
4. Electronic Imaging

   Hair color digitization through imaging and deep inverse graphics

   Robin Kips, Panagiotis-Alexandros Bokaris, Matthieu Perrot, Pietro Gori, and Isabelle Bloch

   In Electronic Imaging, 2022

   Abstract DOI Paper

   Abstract Hair appearance is a complex phenomenon due to hair geometry and how the light bounces on different hair fibers. For this reason, reproducing a specific hair color in a rendering environment is a challenging task that requires manual work and expert knowledge in computer graphics to tune the result visually. While current hair capture methods focus on hair shape estimation many applications could benefit from an automated method for capturing the appearance of a physical hair sample, from augmented/virtual reality to hair dying development. Building on recent advances in inverse graphics and material capture using deep neural networks, we introduce a novel method for hair color digitization. Our proposed pipeline allows capturing the color appearance of a physical hair sample and renders synthetic images of hair with a similar appearance, simulating different hair styles and/or lighting environments. Since rendering realistic hair images requires path-tracing rendering, the conventional inverse graphics approach based on differentiable rendering is untractable. Our method is based on the combination of a controlled imaging device, a path-tracing renderer, and an inverse graphics model based on self-supervised machine learning, which does not require to use differentiable rendering to be trained. We illustrate the performance of our hair digitization method on both real and synthetic images and show that our approach can accurately capture and render hair color.

5. BMVC

   Anatomically constrained CT image translation for heterogeneous blood vessel segmentation

   Giammarco La Barbera, Haithem Boussaid, Francesco Maso, Sabine Sarnacki, Laurence Rouet, Pietro Gori, and Isabelle Bloch

   In British Machine Vision Conference (BMVC), 2022

   Abstract Paper

   Anatomical structures such as blood vessels in contrast-enhanced CT (ceCT) images can be challenging to segment due to the variability in contrast medium diffusion. The combined use of ceCT and contrast-free (CT) CT images can improve the segmentation performances, but at the cost of a double radiation exposure. To limit the radiation dose, generative models could be used to synthesize one modality, instead of acquiring it. The CycleGAN approach has recently attracted particular attention because it alleviates the need for paired data that are difficult to obtain. Despite the great performances demonstrated in the literature, limitations still remain when dealing with 3D volumes generated slice by slice from unpaired datasets with different fields of view. We present an extension of CycleGAN to generate high fidelity images, with good structural consistency, in this context. We leverage anatomical constraints and automatic region of interest selection by adapting the Self-Supervised Body Regressor. These constraints enforce anatomical consistency and allow feeding anatomically-paired input images to the algorithm. Results show qualitative and quantitative improvements, compared to stateof-the-art methods, on the translation task between ceCT and CT images (and vice versa).

6. IEEE ISBI

   A Deep Residual Learning Implementation of Metamorphosis

   Matthis Maillard, Anton François, Joan Glaunès, Isabelle Bloch, and Pietro Gori

   In 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI), 2022

   Abstract DOI Paper Code

   In medical imaging, most of the image registration methods implicitly assume a one-to-one correspondence between the source and target images (i.e., diffeomorphism). However, this is not necessarily the case when dealing with pathological medical images (e.g., presence of a tumor, lesion, etc.). To cope with this issue, the Metamorphosis model has been proposed. It modifies both the shape and the appearance of an image to deal with the geometrical and topological differences. However, the high computational time and load have hampered its applications so far. Here, we propose a deep residual learning implementation of Metamorphosis that drastically reduces the computational time at inference. Furthermore, we also show that the proposed framework can easily integrate prior knowledge of the localization of topological changes (e.g., segmentation masks) that can act as spatial regularization to correctly disentangle appearance and shape changes. We test our method on the BraTS 2021 dataset, showing that it outperforms current state-of-the-art methods in the alignment of images with brain tumors.

7. MICCAI-W

   Optimizing Transformations for Contrastive Learning in a Differentiable Framework

   Camille Ruppli, Pietro Gori, Roberto Ardon, and Isabelle Bloch

   In Medical Image Learning with Limited and Noisy Data - MILLanD (Workshop MICCAI), 2022

   Abstract DOI Paper

   Current contrastive learning methods use random transformations sampled from a large list of transformations, with fixed hyper-parameters, to learn invariance from an unannotated database. Following previous works that introduce a small amount of supervision, we propose a framework to find optimal transformations for contrastive learning using a differentiable transformation network. Our method increases performances at low annotated data regime both in supervision accuracy and in convergence speed. In contrast to previous work, no generative model is needed for transformation optimization. Transformed images keep relevant information to solve the supervised task, here classification. Experiments were performed on 34000 2D slices of brain Magnetic Resonance Images and 11200 chest X-ray images. On both datasets, with 10% of labeled data, our model achieves better performances than a fully supervised model with 100% labels.

8. MICCAI

   Learning Shape Distributions from Large Databases of Healthy Organs: Applications to Zero-Shot and Few-Shot Abnormal Pancreas Detection

   Rebeca Vétil, Clément Abi-Nader, Alexandre Bône, Marie-Pierre Vullierme, Marc-Michel Rohé, Pietro Gori, and Isabelle Bloch

   In Medical Image Computing and Computer Assisted Intervention – MICCAI, 2022

   Abstract DOI Paper

   We propose a scalable and data-driven approach to learn shape distributions from large databases of healthy organs. To do so, volumetric segmentation masks are embedded into a common probabilistic shape space that is learned with a variational auto-encoding network. The resulting latent shape representations are leveraged to derive zero-shot and few-shot methods for abnormal shape detection. The proposed distribution learning approach is illustrated on a large database of 1200 healthy pancreas shapes. Downstream qualitative and quantitative experiments are conducted on a separate test set of 224 pancreas from patients with mixed conditions. The abnormal pancreas detection AUC reached up to \\65.41}%\\65.41%in the zero-shot configuration, and \\78.97}%\\78.97%in the few-shot configuration with as few as 15 abnormal examples, outperforming a baseline approach based on the sole volume.

9. IEEE ISBI

   Improving the Automatic Segmentation of Elongated Organs Using Geometrical Priors

   Rebeca Vétil, Alexandre Bône, Marie-Pierre Vullierme, Marc-Michel Rohé, Pietro Gori, and Isabelle Bloch

   In IEEE 19th International Symposium on Biomedical Imaging (ISBI), 2022

   Abstract DOI Paper

   Deep neural networks are widely used for automated organ segmentation as they achieve promising results for clinical applications. Some organs are more challenging to delineate than others, for instance due to low contrast at their boundaries. In this paper, we propose to improve the segmentation of elongated organs thanks to Geometrical Priors that can be introduced during training, using a local Tversky loss function, or at post-processing, using local thresholds. Both strategies do not introduce additional training parameters and can be easily applied to any existing network. The proposed method is evaluated on the challenging problem of pancreas segmentation. Results show that Geometrical Priors allow us to correct the systematic under-segmentation pattern of a state-of-the-art method, while preserving the overall segmentation quality.

2021

1. MICCAI

   Contrastive Learning with Continuous Proxy Meta-data for 3D MRI Classification

   Benoit Dufumier, Pietro Gori, Julie Victor, Antoine Grigis, and Edouard Duchesnay

   In Medical Image Computing and Computer Assisted Intervention - MICCAI, 2021

   Abstract Paper Code

   Traditional supervised learning with deep neural networks requires a tremendous amount of labelled data to converge to a good solution. For 3D medical images, it is often impractical to build a large homogeneous annotated dataset for a specific pathology. Self-supervised methods offer a new way to learn a representation of the images in an unsupervised manner with a neural network. In particular, contrastive learning has shown great promises by (almost) matching the performance of fully-supervised CNN on vision tasks. Nonetheless, this method does not take advantage of available meta-data, such as participant’s age, viewed as prior knowledge. Here, we propose to leverage continuous proxy metadata, in the contrastive learning framework, by introducing a new loss called y-Aware InfoNCE loss. Specifically, we improve the positive sampling during pre-training by adding more positive examples with similar proxy meta-data with the anchor, assuming they share similar discriminative semantic features. With our method, a 3D CNN model pre-trained on \\10^4\\104multi-site healthy brain MRI scans can extract relevant features for three classification tasks: schizophrenia, bipolar diagnosis and Alzheimer’s detection. When fine-tuned, it also outperforms 3D CNN trained from scratch on these tasks, as well as state-of-the-art self-supervised methods. Our code is made publicly available here.

2. MedNeurIPS

   Conditional Alignment and Uniformity for Contrastive Learning with Continuous Proxy Labels

   Benoit Dufumier, Pietro Gori, Julie Victor, Antoine Grigis, and Edouard Duchesnay

   In MedNeurIPS, Workshop NeurIPS, 2021

   Abstract Paper

   Contrastive Learning has shown impressive results on natural and medical images, without requiring annotated data. However, a particularity of medical images is the availability of meta-data (such as age or sex) that can be exploited for learning representations. Here, we show that the recently proposed contrastive y-Aware InfoNCE loss, that integrates multi-dimensional meta-data, asymptotically optimizes two properties: conditional alignment and global uniformity. Similarly to [Wang, 2020], conditional alignment means that similar samples should have similar features, but conditionally on the meta-data. Instead, global uniformity means that the (normalized) features should be uniformly distributed on the unit hyper-sphere, independently of the meta-data. Here, we propose to define conditional uniformity, relying on the meta-data, that repel only samples with dissimilar meta-data. We show that direct optimization of both conditional alignment and uniformity improves the representations, in terms of linear evaluation, on both CIFAR-100 and a brain MRI dataset.

3. ECML/PKDD

   UCSL : A Machine Learning Expectation-Maximization Framework for Unsupervised Clustering Driven by Supervised Learning

   Robin Louiset, Pietro Gori, Benoit Dufumier, Josselin Houenou, Antoine Grigis, and Edouard Duchesnay

   In European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML/PKDD), 2021

   Abstract DOI Paper Code

   Subtype Discovery consists in finding interpretable and consistent sub-parts of a dataset, which are also relevant to a certain supervised task. From a mathematical point of view, this can be defined as a clustering task driven by supervised learning in order to uncover subgroups in line with the supervised prediction. In this paper, we propose a general Expectation-Maximization ensemble framework entitled UCSL (Unsupervised Clustering driven by Supervised Learning). Our method is generic, it can integrate any clustering method and can be driven by both binary classification and regression. We propose to construct a non-linear model by merging multiple linear estimators, one per cluster. Each hyperplane is estimated so that it correctly discriminates - or predict - only one cluster. We use SVC or Logistic Regression for classification and SVR for regression. Furthermore, to perform cluster analysis within a more suitable space, we also propose a dimension-reduction algorithm that projects the data onto an orthonormal space relevant to the supervised task. We analyze the robustness and generalization capability of our algorithm using synthetic and experimental datasets. In particular, we validate its ability to identify suitable consistent sub-types by conducting a psychiatric-diseases cluster analysis with known ground-truth labels. The gain of the proposed method over previous state-of-the-art techniques is about +1.9 points in terms of balanced accuracy. Finally, we make codes and examples available in a scikit-learn-compatible Python package. https://github.com/neurospin-projects/2021_rlouiset_ucsl/.

4. GSI

   Metamorphic Image Registration Using a Semi-lagrangian Scheme

   Anton François, Pietro Gori, and Joan Glaunès

   In Geometric Science of Information, 2021

   Abstract DOI Paper Code

   In this paper, we propose an implementation of both Large Deformation Diffeomorphic Metric Mapping (LDDMM) and Metamorphosis image registration using a semi-Lagrangian scheme for geodesic shooting. We propose to solve both problems as an inexact matching providing a single and unifying cost function. We demonstrate that for image registration the use of a semi-Lagrangian scheme is more stable than a standard Eulerian scheme. Our GPU implementation is based on PyTorch, which greatly simplifies and accelerates the computations thanks to its powerful automatic differentiation engine. It will be freely available at https://github.com/antonfrancois/Demeter_metamorphosis.

5. CVPR-W

   Deep Graphics Encoder for Real-Time Video Makeup Synthesis from Example

   Robin Kips, Ruowei Jiang, Sileye Ba, Edmund Phung, Parham Aarabi, Pietro Gori, Matthieu Perrot, and Isabelle Bloch

   In IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), 2021

   Abstract DOI Paper

   While makeup virtual-try-on is now widespread, parametrizing a computer graphics rendering engine for synthesizing images of a given cosmetics product remains a challenging task. In this paper, we introduce an inverse computer graphics method for automatic makeup synthesis from a reference image, by learning a model that maps an example portrait image with makeup to the space of rendering parameters. This method can be used by artists to automatically create realistic virtual cosmetics image samples, or by consumers, to virtually try-on a makeup extracted from their favorite reference image.

6. IEEE ISBI

   Automatic Size And Pose Homogenization With Spatial Transformer Network To Improve And Accelerate Pediatric Segmentation

   Giammarco La La Barbera, Pietro Gori, Haithem Boussaid, Bruno Belucci, Alessandro Delmonte, Jeanne Goulin, Sabine Sarnacki, Laurence Rouet, and Isabelle Bloch

   In IEEE 18th International Symposium on Biomedical Imaging (ISBI), 2021

   Abstract DOI Paper Code

   Due to a high heterogeneity in pose and size and to a limited number of available data, segmentation of pediatric images is challenging for deep learning methods. In this work, we propose a new CNN architecture that is pose and scale invariant thanks to the use of Spatial Transformer Network (STN). Our architecture is composed of three sequential modules that are estimated together during training: (i) a regression module to estimate a similarity matrix to normalize the input image to a reference one; (ii) a differentiable module to find the region of interest to segment; (iii) a segmentation module, based on the popular UNet architecture, to delineate the object. Unlike the original UNet, which strives to learn a complex mapping, including pose and scale variations, from a finite training dataset, our segmentation module learns a simpler mapping focusing on images with normalized pose and size. Furthermore, the use of an automatic bounding box detection through STN allows saving time and especially memory, while keeping similar performance. We test the proposed method in kidney and renal tumor segmentation on abdominal pediatric CT scanners. Results indicate that the estimated STN homogenization of size and pose accelerates the segmentation (25h), compared to standard data-augmentation (33h), while obtaining a similar quality for the kidney (88.01% of Dice score) and improving the renal tumor delineation (from 85.52% to 87.12%).

7. Frontiers in Neuroinformatics

   Clinica: An Open-Source Software Platform for Reproducible Clinical Neuroscience Studies

   Alexandre Routier, Ninon Burgos, Mauricio Díaz, Michael Bacci, Simona Bottani, Omar El-Rifai, Sabrina Fontanella, Pietro Gori, Jérémy Guillon, Alexis Guyot, Ravi Hassanaly, Thomas Jacquemont, Pascal Lu, Arnaud Marcoux, Tristan Moreau, Jorge Samper-González, Marc Teichmann, Elina Thibeau-Sutre, Ghislain Vaillant, Junhao Wen, Adam Wild, Marie-Odile Habert, Stanley Durrleman, and Olivier Colliot

   Frontiers in Neuroinformatics, 2021

   Abstract Paper

   We present Clinica (www.clinica.run), an open-source software platform designed to make clinical neuroscience studies easier and more reproducible. Clinica aims for researchers to (i) spend less time on data management and processing, (ii) perform reproducible evaluations of their methods, and (iii) easily share data and results within their institution and with external collaborators. The core of Clinica is a set of automatic pipelines for processing and analysis of multimodal neuroimaging data (currently, T1-weighted MRI, diffusion MRI, and PET data), as well as tools for statistics, machine learning, and deep learning. It relies on the brain imaging data structure (BIDS) for the organization of raw neuroimaging datasets and on established tools written by the community to build its pipelines. It also provides converters of public neuroimaging datasets to BIDS (currently ADNI, AIBL, OASIS, and NIFD). Processed data include image-valued scalar fields (e.g., tissue probability maps), meshes, surface-based scalar fields (e.g., cortical thickness maps), or scalar outputs (e.g., regional averages). These data follow the ClinicA Processed Structure (CAPS) format which shares the same philosophy as BIDS. Consistent organization of raw and processed neuroimaging files facilitates the execution of single pipelines and of sequences of pipelines, as well as the integration of processed data into statistics or machine learning frameworks. The target audience of Clinica is neuroscientists or clinicians conducting clinical neuroscience studies involving multimodal imaging, and researchers developing advanced machine learning algorithms applied to neuroimaging data.

2020

1. WBIR

   Nonlinear Alignment of Whole Tractograms with the Linear Assignment Problem

   Emanuele Olivetti, Pietro Gori, Pietro Astolfi, Giulia Bertó, and Paolo Avesani

   In Biomedical Image Registration (WBIR), 2020

   Abstract DOI Paper Code

   After registration of the imaging data of two brains, homologous anatomical structures are expected to overlap better than before registration. Diffusion magnetic resonance imaging (dMRI) techniques and tractography techniques provide a representation of the anatomical connections in the white matter, as hundreds of thousands of streamlines, forming the tractogram. The literature on methods for aligning tractograms is in active development and provides methods that operate either from voxel information, e.g. fractional anisotropy, orientation distribution function, T1-weighted MRI, or directly from streamline information. In this work, we align streamlines using the linear assignment problem (LAP) and propose a method to reduce the high computational cost of aligning whole brain tractograms. As further contribution, we present a comparison among some of the freely-available linear and nonlinear tractogram alignment methods, where we show that our LAP-based method outperforms all others. In discussing the results, we show that a main limitation of all streamline-based nonlinear registration methods is the computational cost and that addressing such problem may lead to further improvement in the quality of registration.

2. ECCV-W

   CA-GAN: Weakly Supervised Color Aware GAN for Controllable Makeup Transfer

   Robin Kips, Pietro Gori, Matthieu Perrot, and Isabelle Bloch

   In AIM20 (ECCV Workshop), 2020

   Abstract DOI Paper

   While existing makeup style transfer models perform an image synthesis whose results cannot be explicitly controlled, the ability to modify makeup color continuously is a desirable property for virtual try-on applications. We propose a new formulation for the makeup style transfer task, with the objective to learn a color controllable makeup style synthesis. We introduce CA-GAN, a generative model that learns to modify the color of specific objects (e.g. lips or eyes) in the image to an arbitrary target color while preserving background. Since color labels are rare and costly to acquire, our method leverages weakly supervised learning for conditional GANs. This enables to learn a controllable synthesis of complex objects, and only requires a weak proxy of the image attribute that we desire to modify. Finally, we present for the first time a quantitative analysis of makeup style transfer and color control performance.

3. GSI

   Fidelity metrics between curves and surfaces: currents, varifolds, and normal cycles

   Nicolas Charon, Benjamin Charlier, Joan Glaunès, Pietro Gori, and Pierre Roussillon

   In Riemannian Geometric Statistics in Medical Image Analysis, 2020

   Abstract DOI Paper

   This chapter provides an overview of some mathematical and computational models that have been proposed over the past few years for defining data attachment terms on shape spaces of curves or surfaces. In all these models shapes are seen as elements of a space of generalized distributions, such as currents or varifolds. Then norms are defined through reproducing kernel Hilbert spaces (RKHS), which lead to shape distances that can be conveniently computed in practice. These were originally introduced in conjunction with diffeomorphic methods in computational anatomy and have indeed proved to be very efficient in this field. We provide a basic description of these different models and their practical implementation, then discuss the respective properties and potential advantages or downsides of each of them in diffeomorphic registration problems.

4. MICCAI

   Knowledge Distillation from Multi-modal to Mono-modal Segmentation Networks

   Minhao Hu, Matthis Maillard, Ya Zhang, Tommaso Ciceri, Giammarco La Barbera, Isabelle Bloch, and Pietro Gori

   In Medical Image Computing and Computer Assisted Intervention – MICCAI, 2020

   Abstract DOI Paper

   The joint use of multiple imaging modalities for medical image segmentation has been widely studied in recent years. The fusion of information from different modalities has demonstrated to improve the segmentation accuracy, with respect to mono-modal segmentations, in several applications. However, acquiring multiple modalities is usually not possible in a clinical setting due to a limited number of physicians and scanners, and to limit costs and scan time. Most of the time, only one modality is acquired. In this paper, we propose KD-Net, a framework to transfer knowledge from a trained multi-modal network (teacher) to a mono-modal one (student). The proposed method is an adaptation of the generalized distillation framework where the student network is trained on a subset (1 modality) of the teacher’s inputs (n modalities). We illustrate the effectiveness of the proposed framework in brain tumor segmentation with the BraTS 2018 dataset. Using different architectures, we show that the student network effectively learns from the teacher and always outperforms the baseline mono-modal network in terms of segmentation accuracy.

5. Neuroinformatics

   QFib: Fast and Efficient Brain Tractogram Compression

   Corentin Mercier, S Rousseau, P Gori, I Bloch, and T Boubekeur

   Neuroinformatics, 2020

   Abstract Paper Code

   Diffusion MRI fiber tracking datasets can contain millions of 3D streamlines, and their representation can weight tens of gigabytes of memory. These sets of streamlines are called tractograms and are often used for clinical operations or research. Their size makes them difficult to store, visualize, process or exchange over the network. We propose a new compression algorithm well-suited for tractograms, by taking advantage of the way streamlines are obtained with usual tracking algorithms. Our approach is based on unit vector quantization methods combined with a spatial transformation which results in low compression and decompression times, as well as a high compression ratio. For instance, a 11.5GB tractogram can be compressed to a 1.02GB file and decompressed in 11.3 seconds. Moreover, our method allows for the compression and decompression of individual streamlines, reducing the need for a costly outof-core algorithm with heavy datasets. Last, we open a way toward on-the-fly compression and decompression for handling larger datasets without needing a load of RAM (i.e. in-core handling), faster network exchanges and faster loading times for visualization or processing.

6. ECML/PKDD-W

   Template-Based Graph Clustering

   Mateus Riva, Florian Yger, Pietro Gori, Roberto M Cesar Jr, and Isabelle Bloch

   In GEM - ECML-PKDD Workshop, 2020

   Abstract Paper Code

   We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence matching n vertices of the observed graph (to be clustered) to the k vertices of a template graph, using its edges as support information, and relaxed on the set of orthonormal matrices in order to find a k dimensional embedding. With relevant priors that encode the density of the clusters and their relationships, our method outperforms classical methods, especially for challenging cases.

7. JDI

   Comprehensive Review of 3D Segmentation Software Tools for MRI Usable for Pelvic Surgery Planning

   Alessio Virzì, Cécile Olivia Muller, Jean-Baptiste Marret, Eva Mille, Laureline Berteloot, David Grévent, Nathalie Boddaert, Pietro Gori, Sabine Sarnacki, and Isabelle Bloch

   Journal of Digital Imaging, 2020

   Abstract DOI Paper

   Patient-specific 3D modeling is the first step towards image-guided surgery, the actual revolution in surgical care. Pediatric and adolescent patients with rare tumors and malformations should highly benefit from these latest technological innovations, allowing personalized tailored surgery. This study focused on the pelvic region, located at the crossroads of the urinary, digestive, and genital channels with important vascular and nervous structures. The aim of this study was to evaluate the performances of different software tools to obtain patient-specific 3D models, through segmentation of magnetic resonance images (MRI), the reference for pediatric pelvis examination. Twelve software tools freely available on the Internet and two commercial software tools were evaluated using T2-w MRI and diffusion-weighted MRI images. The software tools were rated according to eight criteria, evaluated by three different users: automatization degree, segmentation time, usability, 3D visualization, presence of image registration tools, tractography tools, supported OS, and potential extension (i.e., plugins). A ranking of software tools for 3D modeling of MRI medical images, according to the set of predefined criteria, was given. This ranking allowed us to elaborate guidelines for the choice of software tools for pelvic surgical planning in pediatric patients. The best-ranked software tools were Myrian Studio, ITK-SNAP, and 3D Slicer, the latter being especially appropriate if nerve fibers should be included in the 3D patient model. To conclude, this study proposed a comprehensive review of software tools for 3D modeling of the pelvis according to a set of eight criteria and delivered specific conclusions for pediatric and adolescent patients that can be directly applied to clinical practice.

8. Neurosurgical Review

   Automated neurosurgical stereotactic planning for intraoperative use: a comprehensive review of the literature and perspectives

   Marc Zanello, Romain Carron, Sophie Peeters, Pietro Gori, Alexandre Roux, Isabelle Bloch, Catherine Oppenheim, and Johan Pallud

   Neurosurgical Review, 2020

   Abstract DOI Paper

   The creation of intracranial stereotactic trajectories, from entry point to target point, is still mostly done manually by the neurosurgeon. The development of automated stereotactic planning tools has been described in the literature. This systematic review aims to assess the effectiveness of stereotactic planning procedure automation and develop tools for patients undergoing neurosurgical stereotactic procedures. PubMed/MEDLINE, EMBASE, Google Scholar, CINAHL, PsycINFO, and Cochrane Register of Controlled Trials databases were searched from inception to September 1, 2019, at the exception of Google Scholar (from 1 January 2010 to September 1, 2019) in French and English. Eligible studies included all studies proposing automated stereotactic planning. A total of 1543 studies were screened. Forty-two studies were included in the systematic review, including 18 (42.9%) conference papers. The surgical procedures planned automatically were mainly deep brain stimulation (n = 14, 33.3%), stereoelectroencephalography (n = 12, 28.6%), and not specified (n = 10, 23.8%). The most frequently used surgical constraints to plan the trajectory were blood vessels (n = 32, 76.2%), cerebral sulci (n = 27, 64.3%), and cerebral ventricles (n = 23, 54.8%). The distance from blood vessels ranged from 1.96 to 4.78 mm for manual trajectories and from 2.47 to 7.0 mm for automated trajectories. At least one neurosurgeon was involved in 36 studies (85.7%). The automated stereotactic trajectory was preferred in 75.4% of the studied cases (range 30–92.9). Only 3 (7.1%) studies were multicentric. No study reported prospective use of the planning software. Stereotactic planning automation is a promising tool to provide valuable stereotactic trajectories for clinical applications.

2019

1. IEEE ISBI

   White Matter Multi-Resolution Segmentation Using Fuzzy Set Theory

   A. Delmonte, C. Mercier, J. Pallud, I. Bloch, and Pietro Gori

   In IEEE 16th International Symposium on Biomedical Imaging (ISBI), 2019

   Abstract DOI Paper Code

   The neural architecture of the white matter of the brain, obtained using tractography algorithms, can be divided into different tracts. Their function is, in many cases, still an object of study and might be affected in some syndromes or conditions. Obtaining a reproducible and correct segmentation is therefore crucial both in clinics and in research. However, it is difficult to obtain due to the huge number of fibers and high inter-subject variability. In this paper, we propose to segment and recognize tracts by directly modeling their anatomical definitions, which are usually based on relationships between structures. Since these definitions are mainly qualitative, we propose to model their intrinsic vagueness using fuzzy spatial relations and combine them into a single quantitative score mapped to each fiber. To cope with the high redundancy of tractograms and ease interpretation, we also take advantage of a simplification scheme based on a multi-resolution representation. This allows for an interactive and real-time navigation through different levels of detail. We illustrate our method using the Human Connectome Project dataset and compare it to other well-known white matter segmentation techniques.

2. MICCAI

   Fast and Scalable Optimal Transport for Brain Tractograms

   Jean Feydy, Pierre Roussillon, Alain Trouvé, and Pietro Gori

   In Medical Image Computing and Computer Assisted Intervention – MICCAI, 2019

   Abstract DOI Paper Code

   We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method enables the computation of transport plans between millions of points in a matter of minutes. We show the effectiveness of this approach on brain tractograms modeled either as bundles of fibers or as track density maps. We use the resulting smooth assignments to perform label transfer for atlas-based segmentation of fiber tractograms. The parameters – blur and reach – of our method are meaningful, defining the minimum and maximum distance at which two fibers are compared with each other. They can be set according to anatomical knowledge. Furthermore, we also propose to estimate a probabilistic atlas of a population of track density maps as a Wasserstein barycenter. Our CUDA implementation is endowed with a user-friendly PyTorch interface, freely available on the PyPi repository (pip install geomloss) and at www.kernel-operations.io/geomloss.

3. J. Pediatric Surg.

   Integrating tractography in pelvic surgery: a proof of concept

   Cécile Olivia Muller, Eva Mille, Alessio Virzi, Jean-Baptiste Marret, Quoc Peyrot, Alessandro Delmonte, Laureline Berteloot, Pietro Gori, Thomas Blanc, David Grevent, Nathalie Boddaert, Isabelle Bloch, and Sabine Sarnacki

   Journal of Pediatric Surgery Case Reports, 2019

   Abstract DOI Paper

   Objective To show the interest of tractography in pelvic surgery by a demonstrative case of neurofibroma resected by robotic assisted laparoscopy. Summary background data Although diffusion tensor magnetic resonance imaging, along with tractography algorithms, is increasingly included in image guided neurosurgery methods, it is less frequently used for the peripheral nervous system such as the pelvic sacral plexus. We report one observation demonstrating the interest of such image data for pelvic surgery. Methods A 12-years-old girl with neurofibromatosis presented with a growing left pelvic neurofibroma on repeated pelvic MRI with an increased SUV (2.83) on PET scan. A diffusion tensor pelvic MRI was performed before and after robotically assisted tumoral resection, and a tractography algorithm was applied on both images. Results The pre-operative tractogram showed the nervous nature of the tumor in close contact with the left sacral plexus. Section of a nerve trunk encased in the neurofibroma was mandatory for the resection and well documented by the 3D enhanced vision provided by the robot. Post-operatively, the patient showed a slight paresthesia and dysesthesia of the left leg calf and of the plantar vault (left S2 territory), without any motor deficit. The post-operative tractogram showed a thinning of the left S2 sacral root and the disappearance of right aberrant nervous tracts. Conclusions This clinical case validates the ability of pelvic tractography to deliver a proper imaging of the sacral nervous network and emphasizes the potential usefulness of this approach in pelvic surgery management, with perspectives of image-guided surgery.

4. GRETSI

   Appariement difféomorphique robuste de faisceaux neuronaux

   Pierre Roussillon, Jean-Marc Thiery, Isabelle Bloch, and Pietro Gori

   In GRETSI 2019, 2019

   Abstract Paper

   Dans cet article, nous nous intéressons à l’appariement difféomorphique de faisceaux du cerveau. Ce problème est complexe car deux faisceaux n’ont presque jamais le même nombre de fibres. Ces variations topologiques peuvent détériorer les déformations obtenues et fausser les interprétations cliniques. Nous proposons ici une méthode robuste aux différences topologiques, grâce à la combinaison de normes L p et de métriques à noyaux adaptées à l’espace des fibres. Les résultats sur des exemples jouets et sur des données réelles sont prometteurs. Abstract-In this article, we study the diffeomorphic matching of brain fibers bundles. This problem is complex because there is no topological correspondence between two bundles, namely two bundles do not have the same number of fibers. This strongly deteriorates the deformations obtained and can lead to a wrong clinical intepretation. We present a method that is robust to topological differences, by combining L p norms and kernel-based metrics adapted to the space of fibers. We test the effectivenes of our method on both toy examples and brain fiber bundles.

5. Radiology

   MRI Atlas of IDH Wild-Type Supratentorial Glioblastoma: Probabilistic Maps of Phenotype, Management, and Outcomes

   Alexandre Roux, Pauline Roca, Myriam Edjlali, Kanako Sato, Marc Zanello, Edouard Dezamis, Pietro Gori, Stéphanie Lion, Ariane Fleury, Frédéric Dhermain, Jean-François Meder, Fabrice Chrétien, Emmanuèle Lechapt, Pascale Varlet, Catherine Oppenheim, and Johan Pallud

   Radiology, 2019

   Abstract DOI Paper

   BackgroundTumor location is a main prognostic parameter in patients with glioblastoma. Probabilistic MRI-based brain atlases specifying the probability of tumor location associated with important demographic, clinical, histomolecular, and management data are lacking for isocitrate dehydrogenase (IDH) wild-type glioblastomas.PurposeTo correlate glioblastoma location with clinical phenotype, surgical management, and outcomes by using a probabilistic analysis in a three-dimensional (3D) MRI-based atlas.Materials and MethodsThis retrospective study included all adults surgically treated for newly diagnosed IDH wild-type supratentorial glioblastoma in a tertiary adult surgical neuro-oncology center (2006–2016). Semiautomated tumor segmentation and spatial normalization procedures to build a 3D MRI-based atlas were validated. The authors performed probabilistic analyses by using voxel-based lesion symptom mapping technology. The Liebermeister test was used for binary data, and the generalized linear model was used for continuous data.ResultsA total of 392 patients (mean age, 61 years ± 13; 233 men) were evaluated. The authors identified the preferential location of glioblastomas according to subventricular zone, age, sex, clinical presentation, revised Radiation Therapy Oncology Group-Recursive Partitioning Analysis class, Karnofsky performance status, O6-methylguanine DNA methyltransferase promoter methylation status, surgical management, and survival. The superficial location distant from the eloquent area was more likely associated with a preserved functional status at diagnosis (348 of 392 patients [89%], P \textless .05), a large surgical resection (173 of 392 patients [44%], P \textless .05), and prolonged overall survival (163 of 334 patients [49%], P \textless .05). In contrast, deep location and location within eloquent brain areas were more likely associated with an impaired functional status at diagnosis (44 of 392 patients [11%], P \textless .05), a neurologic deficit (282 of 392 patients [72%], P \textless .05), treatment with biopsy only (183 of 392 patients [47%], P \textless .05), and shortened overall survival (171 of 334 patients [51%], P \textless .05).ConclusionThe authors identified the preferential location of isocitrate dehydrogenase wild-type glioblastomas according to parameters of interest and provided an image-based integration of multimodal information impacting survival results. This suggests the role of glioblastoma location as a surrogate and multimodal parameter integrating several known prognostic factors.© RSNA, 2019Online supplemental material is available for this article.See also the editorial by Huang in this issue.

2018

1. IEEE TMI

   Double Diffeomorphism: Combining Morphometry and Structural Connectivity Analysis

   Pietro Gori, Olivier Colliot, Linda Marrakchi Kacem, Yulia Worbe, Alexandre Routier, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

   IEEE Transactions on Medical Imaging, 2018

   Abstract DOI

   The brain is composed of several neural circuits which may be seen as anatomical complexes composed of grey matter structures interconnected by white matter tracts. Grey and white matter components may be modeled as 3-D surfaces and curves, respectively. Neurodevelopmental disorders involve morphological and organizational alterations which cannot be jointly captured by usual shape analysis techniques based on single diffeomorphisms. We propose a new deformation scheme, called double diffeomorphism, which is a combination of two diffeomorphisms. The first one captures changes in structural connectivity, whereas the second one recovers the global morphological variations of both grey and white matter structures. This deformation model is integrated into a Bayesian framework for atlas construction. We evaluate it on a data-set of 3-D structures representing the neural circuits of patients with Gilles de la Tourette syndrome (GTS). We show that this approach makes it possible to localise, quantify, and easily visualise the pathological anomalies altering the morphology and organization of the neural circuits. Furthermore, results also indicate that the proposed deformation model better discriminates between controls and GTS patients than a single diffeomorphism.

2. Eurographics-W

   Progressive and Efficient Multi-Resolution Representations for Brain Tractograms

   Corentin Mercier, Pietro Gori, Damien Rohmer, Marie-Paule Cani, Tamy Boubekeur, Jean-Marc Thiery, and Isabelle Bloch

   In Eurographics Workshop VCBM, 2018

   Abstract DOI Paper Code

   Current tractography methods generate tractograms composed of millions of 3D polylines, called fibers, making visualization and interpretation extremely challenging, thus complexifying the use of this technique in a clinical environment. We propose to progressively simplify tractograms by grouping similar fibers into generalized cylinders. This produces a fine-grained multiresolution model that provides a progressive and real-time navigation through different levels of detail. This model preserves the overall structure of the tractogram and can be adapted to different measures of similarity. We also provide an efficient implementation of the method based on a Delaunay tetrahedralization. We illustrate our method using the Human Connectome Project dataset.

3. MICCAI-W

   Segmentation of Pelvic Vessels in Pediatric MRI Using a Patch-Based Deep Learning Approach

   A. Virzì, Pietro Gori, C. O. Muller, E. Mille, Q. Peyrot, L. Berteloot, N. Boddaert, S. Sarnacki, and I. Bloch

   In PIPPI MICCAI Workshop, 2018

   Abstract DOI

   In this paper, we propose a patch-based deep learning approach to segment pelvic vessels in 3D MRI images of pediatric patients. For a given T2 weighted MRI volume, a set of 2D axial patches are extracted using a limited number of user-selected landmarks. In order to take into account the volumetric information, successive 2D axial patches are combined together, producing a set of pseudo RGB color images. These RGB images are then used as input for a convolutional neural network (CNN), pre-trained on the ImageNet dataset, which results into both segmentation and vessel labeling as veins or arteries. The proposed method is evaluated on 35 MRI volumes of pediatric patients, obtaining an average segmentation accuracy in terms of Average Symmetric Surface Distance of 𝐴𝑆𝑆𝐷=0.89±0.07ASSD=0.89±0.07ASSD = 0.89 }pm 0.07 mm and Dice Index of 𝐷𝐶=0.79±0.02DC=0.79±0.02DC = 0.79 }pm 0.02.

2017

1. MedIA

   A Bayesian framework for joint morphometry of surface and curve meshes in multi-object complexes

   Pietro Gori, Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

   Medical Image Analysis, 2017

   Abstract DOI Paper

   We present a Bayesian framework for atlas construction of multi-object shape complexes comprised of both surface and curve meshes. It is general and can be applied to any parametric deformation framework and to all shape models with which it is possible to define probability density functions (PDF). Here, both curve and surface meshes are modelled as Gaussian random varifolds, using a finite-dimensional approximation space on which PDFs can be defined. Using this framework, we can automatically estimate the parameters balancing data-terms and deformation regularity, which previously required user tuning. Moreover, it is also possible to estimate a well-conditioned covariance matrix of the deformation parameters. We also extend the proposed framework to data-sets with multiple group labels. Groups share the same template and their deformation parameters are modelled with different distributions. We can statistically compare the groups’distributions since they are defined on the same space. We test our algorithm on 20 Gilles de la Tourette patients and 20 control subjects, using three sub-cortical regions and their incident white matter fiber bundles. We compare their morphological characteristics and variations using a single diffeomorphism in the ambient space. The proposed method will be integrated with the Deformetrica software package, publicly available at www.deformetrica.org.

2. MICCAI-W

   White Matter Fiber Segmentation Using Functional Varifolds

   Kuldeep Kumar, Pietro Gori, Benjamin Charlier, Stanley Durrleman, Olivier Colliot, and Christian Desrosiers

   In MFCA MICCAI Workshop, 2017

   Abstract DOI

   The extraction of fibers from dMRI data typically produces a large number of fibers, it is common to group fibers into bundles. To this end, many specialized distance measures, such as MCP, have been used for fiber similarity. However, these distance based approaches require point-wise correspondence and focus only on the geometry of the fibers. Recent publications have highlighted that using microstructure measures along fibers improves tractography analysis. Also, many neurodegenerative diseases impacting white matter require the study of microstructure measures as well as the white matter geometry. Motivated by these, we propose to use a novel computational model for fibers, called functional varifolds, characterized by a metric that considers both the geometry and microstructure measure (e.g. GFA) along the fiber pathway. We use it to cluster fibers with a dictionary learning and sparse coding-based framework, and present a preliminary analysis using HCP data.

3. PRNI

   Comparison of distances for supervised segmentation of white matter tractography

   Emanuele Olivetti, Giulia Berto, Pietro Gori, Nusrat Sharmin, and Paolo Avesani

   In International Workshop on Pattern Recognition in Neuroimaging (PRNI), 2017

   Abstract DOI

   Tractograms are mathematical representations of the main paths of axons within the white matter of the brain, from diffusion MRI data. Such representations are in the form of polylines, called streamlines, and one streamline approximates the common path of tens of thousands of axons. The analysis of tractograms is a task of interest in multiple fields, like neurosurgery and neurology. A basic building block of many pipelines of analysis is the definition of a distance function between streamlines. Multiple distance functions have been proposed in the literature, and different authors use different distances, usually without a specific reason other than invoking the “common practice”. To this end, in this work we want to test such common practices, in order to obtain factual reasons for choosing one distance over another. For these reason, in this work we compare many streamline distance functions available in the literature. We focus on the common task of automatic bundle segmentation and we adopt the recent approach of supervised segmentation from expert-based examples. Using the HCP dataset, we compare several distances obtaining guidelines on the choice of which distance function one should use for supervised bundle segmentation.

2016

1. IEEE TMI

   Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles

   Pietro Gori, Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Fabrizio De Vico Fallani, Mario Chavez, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

   IEEE Transactions on Medical Imaging, 2016

   Abstract DOI

   Fiber bundles stemming from tractography algorithms contain many streamlines. They require therefore a great amount of computer memory and computational resources to be stored, visualised and processed. We propose an approximation scheme for fiber bundles which results in a parsimonious representation of weighted prototypes. Prototypes are chosen among the streamlines and they represent groups of similar streamlines. Their weight is related to the number of approximated streamlines. Both streamlines and prototypes are modelled as weighted currents. This computational model does not need point-to-point correspondences and two streamlines are considered similar if their endpoints are close to each other and if their pathways follow similar trajectories. Moreover, the space of weighted currents is a vector space with a closed-form metric. This permits easy computation of the approximation error and the selection of the prototypes is based on the minimisation of this error. We propose an iterative algorithm which approximates independently and simultaneously all the fascicles of the bundle in a fast and accurate way. We show that the resulting representation preserves the shape of the bundle and it can be used to accurately reconstruct the original structural connectivity. We evaluate our algorithm on bundles obtained from both deterministic and probabilistic tractography algorithms. The resulting approximations use on average only 2% of the original streamlines as prototypes. This drastically reduces the computational burden of the processes where the geometry of the streamlines is considered. We demonstrate its effectiveness using as example the registration between two fiber bundles.

2. PhD thesis

   Statistical models to learn the structural organisation of neural circuits from multimodal brain images : application to Gilles de la Tourette syndrome

   Pietro Gori

   Paris 6, 2016

   Abstract Paper

   Nous proposons un cadre statistique pour analyser les anomalies morphologiques et organisationnelles altérant l’anatomie des circuits neuronaux chez les patients atteints du syndrome de Gilles de la Tourette. Les composants de chaque circuit (matière grise et blanche) sont représentés comme des maillages 3D et intégrés dans un seul complexe. Cela permet d’étudier leur organisation et surtout la connectivité structurelle. La méthode proposée est basée sur une approche statistique appelée construction d’atlas qui résulte en un template, capturant les invariants de la population, et en déformations template-vers-sujets, décrivant la variabilité morphologique. Premièrement, nous intégrons la construction d’atlas dans un cadre bayésien qui permet d’estimer automatiquement des paramètres autrement fixés. Deuxièmement, nous réduisons les ressources de calcul nécessaires au traitement de faisceaux de fibres en définissant un schéma d’approximation basée sur un nouveau modèle appelé courants pondérés. Troisièmement, nous décrivons un nouveau modèle de déformation pour la construction d’atlas qui permet de capturer les variations morphologiques et organisationnelles. On montre l’efficacité de la méthode par comparaison de deux groupes de 44 patients et 22 témoins. Les résultats soulignent des anomalies sur la forme des structures de la matière grise et sur la connectivité structurelle.

2015

1. IPMI

   Joint Morphometry of Fiber Tracts and Gray Matter Structures Using Double Diffeomorphisms

   Pietro Gori, Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Alexandre Routier, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

   In Information Processing in Medical Imaging (IPMI), 2015

   Abstract Paper

   This work proposes an atlas construction method to jointly analyse the relative position and shape of fiber tracts and gray matter structures. It is based on a double diffeomorphism which is a composition of two diffeomorphisms. The first diffeomorphism acts only on the white matter keeping fixed the gray matter of the atlas. The resulting white matter, together with the gray matter, are then deformed by the second diffeomorphism. The two diffeomorphisms are related and jointly optimised. In this way, the first diffeomorphisms explain the variability in structural connectivity within the population, namely both changes in the connected areas of the gray matter and in the geometry of the pathway of the tracts. The second diffeomorphisms put into correspondence the homologous anatomical structures across subjects. Fiber bundles are approximated with weighted prototypes using the metric of weighted currents. The atlas, the covariance matrix of deformation parameters and the noise variance of each structure are automatically estimated using a Bayesian approach. This method is applied to patients with Tourette syndrome and controls showing a variability in the structural connectivity of the left cortico-putamen circuit.

2014

1. MICCAI

   A Prototype Representation to Approximate White Matter Bundles with Weighted Currents

   Pietro Gori, Olivier Colliot, Linda Marrakchi-Kacem, Yulia Worbe, Fabrizio De Vico Fallani, Mario Chavez, Sophie Lecomte, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

   In Medical Image Computing and Computer-Assisted Intervention – MICCAI, 2014

   Abstract Paper

   Quantitative and qualitative analysis of white matter fibers resulting from tractography algorithms is made difficult by their huge number. To this end, we propose an approximation scheme which gives as result a more concise but at the same time exhaustive representation of a fiber bundle. It is based on a novel computational model for fibers, called weighted currents, characterised by a metric that considers both the pathway and the anatomical locations of the endpoints of the fibers. Similarity has therefore a twofold connotation: geometrical and related to the connectivity. The core idea is to use this metric for approximating a fiber bundle with a set of weighted prototypes, chosen among the fibers, which represent ensembles of similar fibers. The weights are related to the number of fibers represented by the prototypes. The algorithm is divided into two steps. First, the main modes of the fiber bundle are detected using a modularity based clustering algorithm. Second, a prototype fiber selection process is carried on in each cluster separately. This permits to explain the main patterns of the fiber bundle in a fast and accurate way.

2. MICCAI-W

   Evaluation of morphometric descriptors of deep brain structures for the automatic classification of patients with Alzheimer’s disease, mild cognitive impairment and elderly controls

   Alexandre Routier, Pietro Gori, Ana B. Graciano Fouquier, Sophie Lecomte, Olivier Colliot, and Stanley Durrleman

   In MICCAI Workshop, 2014

   Paper

2013

1. MICCAI

   Bayesian Atlas Estimation for the Variability Analysis of Shape Complexes

   Pietro Gori, Olivier Colliot, Yulia Worbe, Linda Marrakchi-Kacem, Sophie Lecomte, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, and Stanley Durrleman

   In Medical Image Computing and Computer-Assisted Intervention – MICCAI, 2013

   Abstract Paper

   In this paper we propose a Bayesian framework for multi-object atlas estimation based on the metric of currents which permits to deal with both curves and surfaces without relying on point correspondence. This approach aims to study brain morphometry as a whole and not as a set of different components, focusing mainly on the shape and relative position of different anatomical structures which is fundamental in neuro-anatomical studies. We propose a generic algorithm to estimate templates of sets of curves (fiber bundles) and closed surfaces (sub-cortical structures) which have the same “form” (topology) of the shapes present in the population. This atlas construction method is based on a Bayesian framework which brings to two main improvements with respect to previous shape based methods. First, it allows to estimate from the data set a parameter specific to each object which was previously fixed by the user: the trade-off between data-term and regularity of deformations. In a multi-object analysis these parameters balance the contributions of the different objects and the need for an automatic estimation is even more crucial. Second, the covariance matrix of the deformation parameters is estimated during the atlas construction in a way which is less sensitive to the outliers of the population.

2012

1. CRE

   Surface Geophysical Measurements for Locating and Mapping Ice-Wedges

   Ingeman-Nielsen T.,  Tomaškovičo vá S.,  Larsen S. H.,  Aparício S. F., and Pietro Gori

   In Cold Regions Engineering, 2012

   DOI Paper
2. ICOP

   An Optimization Algorithm For Interpreting Thermal Parameters For Frozen Soils With Significant Unfrozen Water Content

   Thomas Ingeman-Nielsen, Pietro Gori, and Sonia Tomaskovicova

   In Tenth International Conference On Permafrost, 2012

   Abstract

   In this study we develop an optimization scheme for establishing thermal parameters of permafrost soils, based on heat pulse measurements. The method is applied to measurements on a sand sample and a clayey silt sample. Acceptable fits are obtained with porosity and freezing point constrained, and all other parameters free – resulting in good reproduction of pulse amplitude and dispersion.