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Model-based clustering techniques have been widely applied to various application areas, while most studies focus on canonical mixtures with unique component distribution form. However, this strict assumption is often hard to satisfy. In this paper, we consider the more flexible Copula-Based Mixture Models (CBMMs) for clustering, which allow heterogeneous component distributions composed by flexible choices of marginal and copula forms. More specifically, we propose an adaptation of the Generalized Iterative Conditional Estimation (GICE) algorithm to identify the CBMMs in an unsupervised manner, where the marginal and copula forms and their parameters are estimated iteratively. GICE is adapted from its original version developed for switching Markov model identification with the choice of realization time. Our CBMM-GICE clustering method is then tested on synthetic two-cluster data (N=2000 samples) with discussion of the factors impacting its convergence. Finally, it is compared to the Expectation Maximization identified mixture models with unique component form on the entire MNIST database (N=70000), and on real cardiac magnetic resonance data (N=276) to illustrate its value for imaging applications.

Confidence in the results is a key ingredient to improve the adoption of machine learning methods by clinicians. Uncertainties on the results have been considered in the literature, but mostly those originating from the learning and processing methods. Uncertainty on the data is hardly challenged, as a single sample is often considered representative enough of each subject included in the analysis. In this paper, we propose a representation learning strategy to estimate local uncertainties on a physiological descriptor (here, myocardial deformation) previously obtained from medical images by different definitions or computations. We first use manifold alignment to match the latent representations associated to different high-dimensional input descriptors. Then, we formulate plausible distributions of latent uncertainties, and finally exploit them to reconstruct uncertainties on the input high-dimensional descriptors. We demonstrate its relevance for the quantification of myocardial deformation (strain) from 3D echocardiographic image sequences of the right ventricle, for which a lack of consensus exists in its definition and which directional component to use. We used a database of 100 control subjects with right ventricle overload, for which different types of strain are available at each point of the right ventricle endocardial surface mesh. Our approach quantifies local uncertainties on myocardial deformation from different descriptors defining this physiological concept. Such uncertainties cannot be directly estimated by local statistics on such descriptors, potentially of heterogeneous types. Beyond this controlled illustrative application, our methodology has the potential to be generalized to many other population analyses considering heterogeneous high-dimensional descriptors.

Anatomical landmark localization in 2D/3D images is a critical task in medical imaging. Although many general-purpose tools exist for landmark localization in classical computer vision tasks, such as pose estimation, they lack the specialized features and modularity necessary for anatomical landmark localization applications in the medical domain. Therefore, we introduce landmarker, a Python package built on PyTorch. The package provides a comprehensive, flexible toolkit for developing and evaluating landmark localization algorithms, supporting a range of methodologies, including static and adaptive heatmap regression. landmarker enhances the accuracy of landmark identification, streamlines research and development processes, and supports various image formats and preprocessing pipelines. Its modular design allows users to customize and extend the toolkit for specific datasets and applications, accelerating innovation in medical imaging. landmarker addresses a critical need for precision and customization in landmark localization tasks not adequately met by existing general-purpose pose estimation tools., Comment: 11 pages, 4 figures

Performance of deep learning segmentation models is significantly challenged in its transferability across different medical imaging domains, particularly when aiming to adapt these models to a target domain with insufficient annotated data for effective fine-tuning. While existing domain adaptation (DA) methods propose strategies to alleviate this problem, these methods do not explicitly incorporate human-verified segmentation priors, compromising the potential of a model to produce anatomically plausible segmentations. We introduce RL4Seg, an innovative reinforcement learning framework that reduces the need to otherwise incorporate large expertly annotated datasets in the target domain, and eliminates the need for lengthy manual human review. Using a target dataset of 10,000 unannotated 2D echocardiographic images, RL4Seg not only outperforms existing state-of-the-art DA methods in accuracy but also achieves 99% anatomical validity on a subset of 220 expert-validated subjects from the target domain. Furthermore, our framework's reward network offers uncertainty estimates comparable with dedicated state-of-the-art uncertainty methods, demonstrating the utility and effectiveness of RL4Seg in overcoming domain adaptation challenges in medical image segmentation., Comment: 9 pages

Conformal Predictive Systems (CPS) offer a versatile framework for constructing predictive distributions, allowing for calibrated inference and informative decision-making. However, their applicability has been limited to scenarios adhering to the Independent and Identically Distributed (IID) model assumption. This paper extends CPS to accommodate scenarios characterized by covariate shifts. We therefore propose Weighted CPS (WCPS), akin to Weighted Conformal Prediction (WCP), leveraging likelihood ratios between training and testing covariate distributions. This extension enables the construction of nonparametric predictive distributions capable of handling covariate shifts. We present theoretical underpinnings and conjectures regarding the validity and efficacy of WCPS and demonstrate its utility through empirical evaluations on both synthetic and real-world datasets. Our simulation experiments indicate that WCPS are probabilistically calibrated under covariate shift., Comment: Accepted at the 13th Symposium on Conformal and Probabilistic Prediction with Applications (COPA), 9-11 September 2024

Knowledge of the effect of interventions, known as the treatment effect, is paramount for decision-making. Approaches to estimating this treatment effect using conditional average treatment effect (CATE) meta-learners often provide only a point estimate of this treatment effect, while additional uncertainty quantification is frequently desired to enhance decision-making confidence. To address this, we introduce two novel approaches: the conformal convolution T-learner (CCT-learner) and conformal Monte Carlo (CMC) meta-learners. The approaches leverage weighted conformal predictive systems (WCPS), Monte Carlo sampling, and CATE meta-learners to generate predictive distributions of individual treatment effect (ITE) that could enhance individualized decision-making. Although we show how assumptions about the noise distribution of the outcome influence the uncertainty predictions, our experiments demonstrate that the CCT- and CMC meta-learners achieve strong coverage while maintaining narrow interval widths. They also generate probabilistically calibrated predictive distributions, providing reliable ranges of ITEs across various synthetic and semi-synthetic datasets. Code: https://github.com/predict-idlab/cct-cmc, Comment: 25 pages, 14 figures

Deep learning enables automatic and robust extraction of cardiac function descriptors from echocardiographic sequences, such as ejection fraction or strain. These descriptors provide fine-grained information that physicians consider, in conjunction with more global variables from the clinical record, to assess patients' condition. Drawing on novel transformer models applied to tabular data, we propose a method that considers all descriptors extracted from medical records and echocardiograms to learn the representation of a cardiovascular pathology with a difficult-to-characterize continuum, namely hypertension. Our method first projects each variable into its own representation space using modality-specific approaches. These standardized representations of multimodal data are then fed to a transformer encoder, which learns to merge them into a comprehensive representation of the patient through the task of predicting a clinical rating. This stratification task is formulated as an ordinal classification to enforce a pathological continuum in the representation space. We observe the major trends along this continuum on a cohort of 239 hypertensive patients, providing unprecedented details in the description of hypertension's impact on various cardiac function descriptors. Our analysis shows that i) the XTab foundation model's architecture allows to reach outstanding performance (98% AUROC) even with limited data (less than 200 training samples), ii) stratification across the population is reproducible between trainings (within 3.6% MAE), and iii) patterns emerge in descriptors, some of which align with established physiological knowledge about hypertension, while others could pave the way for a more comprehensive understanding of this pathology., Comment: 12 pages + 2 pages of supplementary material, submitted to IEEE journal

In this work, we propose a denoising diffusion generative model (DDGM) trained with healthy electrocardiogram (ECG) data that focuses on ECG morphology and inter-lead dependence. Our results show that this innovative generative model can successfully generate realistic ECG signals. Furthermore, we explore the application of recent breakthroughs in solving linear inverse Bayesian problems using DDGM. This approach enables the development of several important clinical tools. These include the calculation of corrected QT intervals (QTc), effective noise suppression of ECG signals, recovery of missing ECG leads, and identification of anomalous readings, enabling significant advances in cardiac health monitoring and diagnosis.

Understanding the target dynamics during its interaction with a relativistic ultrashort laser pulse is a challenging fundamental multi-physics problem involving at least atomic and solid-state physics, plasma physics, and laser physics. Already, the properties of the so-called pre-plasma formed as the laser pulse's rising edge ionizes the target are complicated to access in experiments and modeling, and many aspects of this laser-induced transition from solid to overdense plasma over picosecond time scales are still open questions. At the same time, applications like laser-driven ion acceleration require precise knowledge and control of the pre-plasma because the efficiency of the acceleration process itself crucially depends on the target properties at the arrival of the relativistic intensity peak of the pulse. By capturing the dynamics of the initial stage of the interaction, we report on a detailed visualization of the pre-plasma formation and evolution. Nanometer-thin diamond-like carbon foils are shown to transition from solid to plasma during the laser rising edge with intensities < 10^16 W/cm^2. Single-shot near-infrared probe transmission measurements evidence sub-picosecond dynamics of an expanding plasma with densities above 10^23 cm^-3 (about 100 times the critical plasma density). The complementarity of a solid-state interaction model and a kinetic plasma description provides deep insight into the interplay of ionization, collisions, and expansion.

We report on the properties of a non-conventional stochastic photonic source. We first describe the principle of nonlinear intensity filtering by using a modified Mach-Zehnder interferometer. The latter alters the characteristics of an input stochastic source based on Bose-Einstein emission. Computed output intensity fluctuations are compared to an analytical model. Adjusting the interferometer parameters, we show theoretically and numerically that the statistical properties of light such as its probability density function can be tailored. Depending on the parameters, the probability density may exhibit large overshoots or smoother fluctuations. We further evaluate the impact of these modified statistics on simple nonlinear processes. Compared to Bose-Einstein emitters, the yield of nonlinear phenomena varies by several orders of magnitude. We finally simulate the nonlinear interaction of such a laser source with a dielectric material (fused silica) within the framework of a more realistic model, including a statistical analysis. It confirms that the deposited energy varies over many decades and can be largely enhanced due to the properties of the presented laser source., Comment: 16 pages, 15 figures

Convolutional neural networks (CNN) have demonstrated their ability to segment 2D cardiac ultrasound images. However, despite recent successes according to which the intra-observer variability on end-diastole and end-systole images has been reached, CNNs still struggle to leverage temporal information to provide accurate and temporally consistent segmentation maps across the whole cycle. Such consistency is required to accurately describe the cardiac function, a necessary step in diagnosing many cardiovascular diseases. In this paper, we propose a framework to learn the 2D+time apical long-axis cardiac shape such that the segmented sequences can benefit from temporal and anatomical consistency constraints. Our method is a post-processing that takes as input segmented echocardiographic sequences produced by any state-of-the-art method and processes it in two steps to (i) identify spatio-temporal inconsistencies according to the overall dynamics of the cardiac sequence and (ii) correct the inconsistencies. The identification and correction of cardiac inconsistencies relies on a constrained autoencoder trained to learn a physiologically interpretable embedding of cardiac shapes, where we can both detect and fix anomalies. We tested our framework on 98 full-cycle sequences from the CAMUS dataset, which are available alongside this paper. Our temporal regularization method not only improves the accuracy of the segmentation across the whole sequences, but also enforces temporal and anatomical consistency., Comment: 12 pages, accepted for publication in IEEE TMI

This paper presents the way the joint ADBIS, TPDL and EDA 2020 conferences were organized online and the results of the participant survey conducted thereafter. We present the lessons learned from the participants' feedback., Comment: 7 pages, 16 figures

Dynamical phenomena such as infectious diseases are often investigated by following up subjects longitudinally, thus generating time to event data. The spatial aspect of such data is also of primordial importance, as many infectious diseases are transmitted from one subject to another. In this paper, a spatially correlated frailty model is introduced that accommodates for the correlation between subjects based on the distance between them. Estimates are obtained through a stochastic approximation version of the Expectation Maximization algorithm combined with a Monte-Carlo Markov Chain, for which convergence is proven. The novelty of this model is that spatial correlation is introduced for survival data at the subject level, each subject having its own frailty. This univariate spatially correlated frailty model is used to analyze spatially dependent malaria data, and its results are compared with other standard models.

A microphysics model to describe the photoionization and impact ionization processes in dielectric ablator materials like plastic has been implemented into the one-dimensional hydrodynamic code LILAC for planar and spherical targets. At present, the initial plasma formation during the early stages of a laser drive is modeled in an ad hoc manner, until the formation of a critical surface. Implementation of the physics-based models predicts higher values of electron temperature and pressure than the ad hoc model. Moreover, the numerical predictions are consistent with previous experimental observations of the shine-through mechanism in plastic ablators. For planar targets, a decompression of the rear end of the target was observed that is similar to recent experiments. An application of this model is to understand the laser-imprint mechanism that is caused by nonuniform laser irradiation due to a single beam speckle.

Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation procedures have been proposed for the fixed effects and the variances of and covariances between the random effects. Especially with an unspecified baseline hazard, i.e., the Cox model, the few available methods deal only with a specific correlation structure. In this paper, an estimation procedure, based on the integrated partial likelihood, is introduced, which can generally deal with any kind of correlation structure. The new approach, namely the maximisation of the integrated partial likelihood, combined with a stochastic estimation procedure allows also for a wide choice of distributions for the random effects. First, we demonstrate the almost sure convergence of the stochastic algorithm towards a critical point of the integrated partial likelihood. Second, numerical convergence properties are evaluated by simulation. Third, the advantage of using an unspecified baseline hazard is demonstrated through application on cancer clinical trial data.

Electron dynamics in the bulk of large band gap dielectric crystals induced by intense femtosecond laser pulses at 800 nm is studied. With laser intensities under the ablation threshold (a few 10 TW/cm\textsuperscript{2}), electrons with unexpected energies in excess of 40-50 eV are observed by using the photoemission spectroscopy. A theoretical approach based on the Boltzmann kinetic equation including state-of-the-art modeling for various particles interactions is developed to interpret these experimental observations. A direct comparison shows that both electron heating in the bulk and a further laser field acceleration after ejection from the material contribute equivalently to the final electron energy gain. The electron heating in the bulk is shown to be significantly driven by a non-collisional process, i.e. direct multiphoton transitions between sub-bands of the conduction band. This work also sheds light on the contribution of the standard electron excitation/relaxation collisional processes, providing a new baseline to study the electron dynamics in dielectric materials and associated applications as laser material structuring., Comment: 5 pages, 5 figures

Perturbations in the velocity profile of a laser-ablation-driven shock wave seeded by speckle in the spatial beam intensity (i.e., laser imprint) have been measured. Direct measurements of these velocity perturbations were recorded using a two-dimensional high-resolution velocimeter probing plastic material shocked by a 100-ps picket laser pulse from the OMEGA laser system. The measured results for experiments with one, two, and five overlapping beams incident on the target clearly demonstrate a reduction in long-wavelength ($>$25 um) perturbations with an increasing number of overlapping laser beams, consistent with theoretical expectations. These experimental measurements are crucial to validate radiation-hydrodynamics simulations of laser imprint for laser direct drive inertial confinement fusion research since they highlight the significant (factor of 3) underestimation of the level of seeded perturbation when the microphysics processes for initial plasma formation, such as multiphoton ionization are neglected., Comment: 6 pages, 5 figures

We develop a new model of laser-matter interaction based on Optical Bloch Equations, which includes photo-ionization, impact ionization, and various relaxation processes typical of dielectric materials. This approach is able to describe the temporal evolution of the electron dynamics in the conduction band driven by few-cycle laser pulses of any wavelength. Moreover, the nonlinear polarization response of both centrosymmetric and non-centrosymmetric materials can be described while ensuring the proper selection rules for the harmonics emission.

By combining analytical and numerical approaches, we theoretically investigate the effect of fabrication imperfections, e.g. roughness at metal interfaces, on nanometer metal-insulator-metal waveguides supporting slow gap-plasmon modes. Realistic devices with vapor deposition- and chemically-grown metal films are considered. We obtain quantitative predictions for the attenuations induced by absorption and by backscattering, and analytically derive how both attenuations scale with respect to the group velocity. Depending on the material parameters and fabrication quality, roughness-induced backscattering is find to be a significant additional source of attenuation for small group velocities, which is often neglected in the literature.

We analytically and numerically investigate the propagation of ultrashort tightly focused laser pulses in vacuum, with particular emphasis on Hermite-Gaussian and Laguerre-Gaussian modes. We revisit the Lax series approach for forward-propagating linearly-polarized laser pulses, in order to obtain Maxwell-consistent and symmetry-preserving analytical solutions for the propagation of all field components beyond the paraxial approximation in four-dimensional geometry (space and time). We demonstrate that our solution conserves the energy, which is set by the paraxial-level term of the series. The full solution of the wave equation towards which our series converges is calculated in the Fourier space. Three-dimensional numerical simulations of ultrashort tightly-focused pulses validate our analytical development.

We propose a method based on deep learning to perform cardiac segmentation on short axis MRI image stacks iteratively from the top slice (around the base) to the bottom slice (around the apex). At each iteration, a novel variant of U-net is applied to propagate the segmentation of a slice to the adjacent slice below it. In other words, the prediction of a segmentation of a slice is dependent upon the already existing segmentation of an adjacent slice. 3D-consistency is hence explicitly enforced. The method is trained on a large database of 3078 cases from UK Biobank. It is then tested on 756 different cases from UK Biobank and three other state-of-the-art cohorts (ACDC with 100 cases, Sunnybrook with 30 cases, RVSC with 16 cases). Results comparable or even better than the state-of-the-art in terms of distance measures are achieved. They also emphasize the assets of our method, namely enhanced spatial consistency (currently neither considered nor achieved by the state-of-the-art), and the generalization ability to unseen cases even from other databases., Comment: Accepted for publication in IEEE Transactions on Medical Imaging

We present a novel automated method to segment the myocardium of both left and right ventricles in MRI volumes. The segmentation is consistent in 3D across the slices such that it can be directly used for mesh generation. Two specific neural networks with multi-scale coarse-to-fine prediction structure are proposed to cope with the small training dataset and trained using an original loss function. The former segments a slice in the middle of the volume. Then the latter iteratively propagates the slice segmentations towards the base and the apex, in a spatially consistent way. We perform 5-fold cross-validation on the 15 cases from STACOM to validate the method. For training, we use real cases and their synthetic variants generated by combining motion simulation and image synthesis. Accurate and consistent testing results are obtained.

The formation and the interaction of multiple cavities, induced by tightly focused femtosecond laser pulses, are studied by using a developed numerical tool, including the thermo-elasto-plastic material response. Simulations are performed in fused silica in cases of one, two, and four spots of laser energy deposition. The relaxation of the heated matter, launching shock waves in the surrounding cold material, leads to cavity formation and emergence of areas where cracks may be induced. Results show that the laser-induced structure shape depends on the energy deposition configuration and demonstrate the potential of the used numerical tool to obtain the desired designed structure or technological process.

The absorbed laser energy of a femtosecond laser pulse in a transparent material induces a warm dense matter region which relaxation may lead to structural modifications in the surrounding cold matter. The modeling of the thermo-elasto-plastic material response is addressed to predict such modifications. It has been developed in a 2D plane geometry and implemented in a hydrodynamic lagrangian code. The particular case of a tightly focused laser beam in the bulk of fused silica is considered as a first application of the proposed general model. It is shown that the warm dense matter relaxation, influenced by the elasto-plastic behavior of the surrounding cold matter, generates both a strong shock and rarefaction waves. Permanent deformations appear in the surrounding solid matter if the induced stress becomes larger than the yield strength. This interaction results in the formation of a sub-micrometric cavity surrounded by an overdense area. This approach also allows one to predict regions where cracks may form. The present modeling can be used to design nano-structures induced by short laser pulses.