3.1 Research program

The recent advent of an increasing number of new microscopy techniques giving access to high throughput screenings and micro or nano-metric resolutions provides a means for quantitative imaging of biological structures and phenomena. To conduct quantitative biological studies based on these new data, it is necessary to develop non-standard specific tools. This requires using a multi-disciplinary approach. We need biologists to define experiment protocols and interpret the results, but also physicists to model the sensors, computer scientists to develop algorithms and mathematicians to model the resulting information. These different expertises are combined within the Morpheme team. This generates a fecund frame for exchanging expertise, knowledge, leading to an optimal framework for the different tasks (imaging, image analysis, classification, modeling). We thus aim at providing adapted and robust tools required to describe, explain and model fundamental phenomena underlying the morphogenesis of cellular and supra-cellular biological structures. Combining experimental manipulations, in vivo imaging, image processing and computational modeling, we plan to provide methods for the quantitative analysis of the morphological changes that occur during development. This is of key importance as the morphology and topology of mesoscopic structures govern organ and cell function. Alterations in the genetic programs underlying cellular morphogenesis have been linked to a range of pathologies.

Biological questions we will focus on include:

1. what are the parameters and the factors controlling the establishment of ramified structures? (Are they really organize to ensure maximal coverage? How are genetic and physical constraints limiting their morphology?),
2. how are newly generated cells incorporated into reorganizing tissues during development? (is the relative position of cells governed by the lineage they belong to?)

Our goal is to characterize different populations or development conditions based on the shape of cellular and supra-cellular structures, e.g. micro-vascular networks, dendrite/axon networks, tissues from 2D, 2D+t, 3D or 3D+t images (obtained with confocal microscopy, video-microscopy, photon-microscopy or micro-tomography). We plan to extract shapes or quantitative parameters to characterize the morphometric properties of different samples. On the one hand, we will propose numerical and biological models explaining the temporal evolution of the sample, and on the other hand, we will statistically analyze shapes and complex structures to identify relevant markers for classification purposes. This should contribute to a better understanding of the development of normal tissues but also to a characterization at the supra-cellular scale of different pathologies such as Alzheimer, cancer, diabetes, or the Fragile X Syndrome. In this multidisciplinary context, several challenges have to be faced. The expertise of biologists concerning sample generation, as well as optimization of experimental protocols and imaging conditions, is of course crucial. However, the imaging protocols optimized for a qualitative analysis may be sub-optimal for quantitative biology. Second, sample imaging is only a first step, as we need to extract quantitative information. Achieving quantitative imaging remains an open issue in biology, and requires close interactions between biologists, computer scientists and applied mathematicians. On the one hand, experimental and imaging protocols should integrate constraints from the downstream computer-assisted analysis, yielding to a trade-off between qualitative optimized and quantitative optimized protocols. On the other hand, computer analysis should integrate constraints specific to the biological problem, from acquisition to quantitative information extraction. There is therefore a need of specificity for embedding precise biological information for a given task. Besides, a level of generality is also desirable for addressing data from different teams acquired with different protocols and/or sensors. The mathematical modeling of the physics of the acquisition system will yield higher performance reconstruction/restoration algorithms in terms of accuracy. Therefore, physicists and computer scientists have to work together. Quantitative information extraction also has to deal with both the complexity of the structures of interest (e.g., very dense network, small structure detection in a volume, multiscale behavior, $...$) and the unavoidable defects of in vivo imaging (artifacts, missing data, $...$). Incorporating biological expertise in model-based segmentation methods provides the required specificity while robustness gained from a methodological analysis increases the generality. Finally, beyond image processing, we aim at quantifying and then statistically analyzing shapes and complex structures (e.g., neuronal or vascular networks), static or in evolution, taking into account variability. In this context, learning methods will be developed for determining (dis)similarity measures between two samples or for determining directly a classification rule using discriminative models, generative models, or hybrid models. Besides, some metrics for comparing, classifying and characterizing objects under study are necessary. We will construct such metrics for biological structures such as neuronal or vascular networks. Attention will be paid to computational cost and scalability of the developed algorithms: biological experimentations generally yield huge data sets resulting from high throughput screenings. The research of Morpheme will be developed along the following axes:

• Imaging: this includes i) definition of the studied populations (experimental conditions) and preparation of samples, ii) definition of relevant quantitative characteristics and optimized acquisition protocol (staining, imaging, $...$) for the specific biological question, and iii) reconstruction/restoration of native data to improve the image readability and interpretation.
• Feature extraction: this consists in detecting and delineating the biological structures of interest from images. Embedding biological properties in the algorithms and models is a key issue. Two main challenges are the variability, both in shape and scale, of biological structures and the huge size of data sets. Following features along time will allow to address morphogenesis and structure development.
• Classification/Interpretation: considering a database of images containing different populations, we can infer the parameters associated with a given model on each dataset from which the biological structure under study has been extracted. We plan to define classification schemes for characterizing the different populations based either on the model parameters, or on some specific metric between the extracted structures.
• Modeling: two aspects will be considered. This first one consists in modeling biological phenomena such as axon growing or network topology in different contexts. One main advantage of our team is the possibility to use the image information for calibrating and/or validating the biological models. Calibration induces parameter inference as a main challenge. The second aspect consists in using a prior based on biological properties for extracting relevant information from images. Here again, combining biology and computer science expertise is a key point.

5.1 Awards

• Luca Calatroni was awarded the Young Investigator Training Program 2020 in the occasion of the Italian biannual congress of applied mathematics SIMAI 2020+21 which took place in Parma from August 30 till September 2 2021.
• Arne Bechensteen was awarded in 2021 of the first prize of the doctoral school ED STIC mention automatic Signal and Image Processing for his PhD thesis untitled "3D fluorescence microscopy reconstruction using TIRF-MA imaging".
• Laure Blanc-Féraud has been elevated IEEE Fellow 2022, in december 2021.
• Laure Blanc-Féraud has a chair of 3IA Côte d'Azur (2019-2024).

6.1 New software

7.1 A scaled, inexact and adaptive FISTA algorithm for strongly convex optimization

Participants: Luca Calatroni.

This work has been carried out in collaboration with S. Rebegoldi (University of Florence).

In 35, we consider a variable metric and inexact version of the FISTA-type algorithm studied, e.g., by 39 for the minimization of the sum of two (possibly strongly) convex functions. The proposed algorithm is combined with an adaptive (non-monotone) backtracking strategy, which allows for the adjustment of the algorithmic step-size along the iterations in order to improve the convergence speed. We prove a linear convergence result for the function values, which depends on both the strong convexity parameters of the two functions and the upper and lower bounds on the spectrum of the variable metric operators. We validate the proposed algorithm, named Scaled Adaptive GEneralized FISTA (SAGE-FISTA), on exemplar image denoising and deblurring problems where edge-preserving Total Variation (TV) regularization is combined with Kullback-Leibler-type fidelity terms, as it is common in applications where signal-dependent Poisson noise is assumed in the data. We report the results obtained in this example in Figure 1 where convergence rates, computational times and Lipschitz constant estimations are compared both for monotone and non-monotone backtrcking.

Convergence rates in function value and Lipschitz constant estimate for strongly convex inexact FISTA with scaling and monotone (first row) and adaptive (second row) backtracking. Reference problem: TV deblurring problem with ℓ2\ell _2 fidelity.

The manuscript is currently at the second stage of review for SIAM journal on Optimization.

7.2 Efficient optimisation of Poisson-type modelling of SMLM data

Participants: Luca Calatroni, Marta Lazzaretti.

This work has been carried out in collaboration with C. Estatico (DIMA, University of Genova) and S. Rebegoldi (University of Florence).

In 25, we proposed a continuous non-convex variational model for the analysis of Single Molecule Localisation Microscopy (SMLM) data in the presence of Poisson noise. Inspired by previous work 49, 42 we consider, in particular, a variation of the Continuous Exact ${\ell }_0$ (CEL0) penalty recently introduced to relax the ${\ell }_2$-${\ell }_0$ problem where a weighted-${\ell }_2$ data fidelity is considered to model signal-dependent Poisson noise. For improving upon the numerical solution of the associated minimisation problem, we consider an iterative reweighted ${\ell }_1$ (IRL1) strategy and proposed in 28 a scaled version of the well-known FISTA algorithm is proposed. The proposed weighted-CEL0 (wCEL0) model improves the results obtained by CEL0 and the use of the scaled FISTA algorithm reduces significantly the computational efforts.

7.3 Proximal algorithms in $L^{p(·)}\left(\Omega \right)$

Participants: Luca Calatroni, Marta Lazzaretti.

This work has been carried out in collaboration with C. Estatico (DIMA, University of Genova).

In this project, we have worked on the development of forward-backward algorithm in variable exponent Lebesgue spaces ${ℒ}^{p(·)}\left(\Omega \right)$, which are spaces defined by a point-wise variable Lebesgue measurable function $p(·)>1$, used as exponent, instead of a constant exponent $p\ge 1$. These spaces are (non-Hilbertian) Banach spaces, endowed with space variant geometrical properties which are useful in adaptive regularization techniques and used for the solution of ill-posed inverse problems. We analysed, in particular, two instances (primal and dual) of proximal gradient algorithms, where the proximal step, rather than depending on the natural (non-separable) ${ℒ}^{p(·)}\left(\Omega \right)$ norm, is defined in terms of its modular function, which, thanks to its separability, allows for the efficient computation of algorithmic iterates. Convergence in function values has been proved for both algorithms, with convergence rates depending on problem/space smoothness. To show the effectiveness of the proposed modelling, some numerical tests have been carried out for exemplar deconvolution and mixed noise removal problems. Future work shall address the crucial question on how the map $p(·)$ shall be chosen in order to adapt to local signal/image prior contents. Moreover, it would be interesting to find a strategy to incorporate extrapolation/acceleration in order to improve convergence speed which, in practice, is particularly slow for primal algorithms.

The outcome of this project is the manuscript 32 which has been recently sent for publication to SIAM journal of Scientific Computing.

7.4 Residual whiteness principle for automatic parameter selection in super-resolution problems

Participants: Luca Calatroni.

In collaboration with A. Lanza, M. Pragliola, F. Sgallari (University of Bologna).

In 26, 33 we propose an automatic parameter selection strategy for the problem of image super-resolution for images corrupted by blur and additive white Gaussian noise with unknown standard deviation. The proposed approach exploits the structure of both the down-sampling and the blur operators in the frequency domain and computes the optimal regularisation parameter as the one optimising a suitable residual whiteness measure. Computationally, the proposed strategy relies on the fast solution of generalised Tikhonov ${\ell }_2$-${\ell }_2$ problems as proposed in previous works. These problems naturally appear as substeps of the Alternating Direction Method of Multipliers (ADMM) optimisation approach used to solve super-resolution problems with non-quadratic and often non-smooth, sparsity-promoting regularisers both in convex and in non-convex regimes. After detailing the theoretical properties defined in the frequency domain which allow to express the whiteness functional in a compact way, we report an exhaustive list of numerical experiments proving the effectiveness of the proposed approach for different type of problems, in comparison with well-known parameter selection strategy such as, e.g., the discrepancy principle, see, e.g., Figure 2, left, for graphical representation where the proposed whiteness measure (black line) is plotted and its minimum is compared with the one achieved by the optimisation of the standard discrepancy-principle (pink line). Analogously, in Figure 2, fight, the optimal PSNR and SSIM values are showed.

In 26, the approach is applied to ${\ell }_2$-${\ell }_2$ super-resolution problems. This work has been published to the SSVM 2021 conference proceedings. In 33, the approach is extended to non-smooth optimisation models and embedded within an ADMM optimisation strategy. This latter work is an invited submission for publication in the Journal of Mathematical Imaging and Vision.

7.5 On and beyond Total Variation regularisation in imaging: the role of space variance

Participants: Luca Calatroni.

In collaboration with A. Lanza, M. Pragliola, F. Sgallari (University of Bologna).

Over the last decades a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned in basic courses in mathematical image processing is the celebrated Rudin-Osher-Fatemi (ROF) model which relies on the minimisation of the edge-preserving Total Variation (TV) semi-norm as regularisation term. Despite its (often limiting) simplicity, this model is still very much employed in many applications and used as a benchmark for assessing the performance of modern learning-based image reconstruction approaches, thanks to its thorough analytical and numerical understanding. Among the many extensions to TV proposed over the years, a large class is based on the concept of space variance. Space-variant models can indeed overcome the intrinsic inability of TV to describe local features (strength, sharpness, directionality) by means of an adaptive mathematical modelling which accommodates local regularisation weighting, variable smoothness and anisotropy, see Figure 3 for an illustration of the many different Weighted (WTV), Weighted-$p$ variations (WTV${}_p$) and Weighted Directional TV (DTWV${}_p$) regularisers at different points. Those ideas can further be cast in the flexible Bayesian framework of generalised Gaussian distributions and combined with maximum likelihood and hierarchical optimisation approaches for efficient hyper-parameter estimation. In this work, we review and connect the major contributions in the field of space-variant TV-type image reconstruction models, focusing, in particular, on their Bayesian interpretation which paves the way to new exciting and unexplored research directions.

Weighted TV (first column), weighted TVp_p (second column) and weighted directional TVp_p penalty functions.

The outcome of this work 6 is currently under the second stage of review for SIAM Review.

7.6 ${\ell }_0$ gradient-based super-resolution for image partitioning

Participants: Luca Calatroni.

In collaboration with P. Cascarano, E. L. Piccolomini, D. Mylonopoulos (University of Bologna).

In 11, we consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic ${\ell }_0$ regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied for signal recovery problems. For the numerical realisation of the model, we propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugate-gradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several sparsity-promoting variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that thanks to the ${\ell }_0$ smoothing on the gradient, the super-resolved images can be used to improve the accuracy of standard segmentation algorithms for applications like QR codes, land-cover classification problems and cell detection as, e.g. in Figure 4. We compare the result obtained with the proposed penalised model with the ones obtained by an analogous constrained model, similarly to the one considered in 48.

Cell detection via moprhological operations from noisy and low-resolution data. a) Ground truth b) Detection from noisy and LR data c) Detection after anisotropic TV1/2^{1/2} super-resolution d) Detection after application of IRCNN e) Detection after reconstruction through dictionary learning and sparse representation SR f) Detection after ℓ0\ell _0 gradient-based SR (proposed).

This work has been published in the journal IEEE Transactions on Computational Imaging 11. A MATLAB software with well-documented guide has been sent for publication to Image Processing On Line (IPOL) and it's currently at the second stage of review.

7.7 Non-linear image osmosis for shadow removal

Participants: Luca Calatroni, Giuseppe Recupero.

In collaboration S. Morigi (University of Bologna), S. Parisotto (Fitzwilliam museum & University of Cambridge).

We studied the images osmosis model, which is a linear drift-diffusion PDE particularly useful in image processing with applications such as shadow removal, compact data representation and cloning. It is known that in shadow removal applications the osmosis model causes diffusion and is unable to preserve the underlying features in the pixels at the border of the shadow. Hence, in order to improve the results, we started developing a non-linear isotropic variation of the original osmosis model. We investigated the theoretical properties and the possible discretizations of the model showing significant improvements with respect to the standard, linear, one. In Figure 5 a comparison between linear and non-linear modelling is showed.

Ground truth	Shadowed image	Linear osmosis	Proposed

A journal paper on the outcomes of this project is being written and will be soon submitted for publication to a journal of mathematical imaging.

7.8 Local estimation of regularization parameters in inverse problems by deep learning

Participants: Rim Rekik Dit Nekhili, Luca Calatroni, Xavier Descombes.

The estimation of regularization parameters in the context of inverse problems is crucial for many different applications. More or less sophisticated and most often iterative approaches make it possible by encoding some (generally unknown) information on the data such as the noise distribution and/or the desired image to compute. For most of these approaches, the estimation is performed globally and, as such, does not take into account the different amount of regularization needed in different image regions. Deep learning approaches have proven to be very effective for many data and image analysis problems and often achieved unprecedented results in the context of digital image processing. In this project, a pixel-wise map of parameters is estimated by means of a convolutional network by considering the different patches centered in each of the pixels of the given noisy and blurry image.

In this project we have first constructed an image database by corrupting initial images with several types and levels of noise. We then tested several convolutional neural network architectures with different convolutional layers, max pooling and flattening layers and for different choices of batch-sizes, learning rates and epochs, and selected the one providing the least RMSE. The resulting CNN has a very simple architecture: one single convolutional layer followed by a max pooling and flattening layer and completed by a dense layer. By means of the proposed architecture we locally estimate the hyperparameter associated with a variationnal denoising model, the learning set being constructed by maximizing the SNR of the denoised result. The first results give a proof of concept of the deep learning approach for locally estimating parameters (see figure 6).

Next steps will consist of comparing the obtained results with statistical approaches and of addressing the case of deconvolution.

7.9 Covariance-based ${\ell }_0$ super-Resolution Microscopy with intensity Estimation and automatic parameter estimation (COL0RME)

Participants: Luca Calatroni, Laure Blanc-Féraud, Vasiliki Stergiopoulou, Sébastien Schaub.

This work has been carried out in collaboration with J. H de Goulart (INP Toulouse/IRIT).

Super-resolution light microscopy overcomes the physical barriers due to light diffraction. However, state-of-the-art approaches require specific and often demanding acquisition conditions to achieve adequate levels of both spatial and temporal resolution. Analyzing the stochastic fluctuations of the fluorescent molecules provides a solution to the aforementioned limitations. Based on this idea, we proposed COL0RME 7, 22, a method for COvariance-based ${\ell }_0$ super-Resolution Microscopy with intensity Estimation, which achieves good spatio-temporal resolution by solving a sparse optimization problem in the covariance domain, discuss automatic parameter selection strategies, estimates background and noise statistics and includes a final estimation step where intensity information is retrieved, see Figure 7 for a schematic representation. Several numerical results both on synthetic and real fluorescent microscopy images and several comparisons with state-of-the art approaches have been done. Our results show that COL0RME outperforms competing methods exploiting analogously temporal fluctuations; in particular, it achieves better localization, reduces background artifacts and avoids fine parameter tuning.

As future research directions, we are interested in the investigation of learning approaches such as, for instance, unrolled deep networks such as, e.g., the Learned SPARCOM algorithm proposed in 41. Algorithm unrolling methods connect the iterative algorithms that are widely used in image processing and the deep neural networks 47

Principles of COL0RME. (a) An overview of the two steps (Support Estimation and Intensity Estimation) by visualizing the inputs/outputs of each, as well as the interaction between them. (b) The two main outputs of COL0RME are: the support Ω⊂ℝL2\Omega \subset \mathbb {R}^{L^2} containing the locations of the fine-grid pixels with at least one fluorescent molecule, and the intensity 𝐱∈ℝL2\mathbf {x} \in \mathbb {R}^{L^2} whose non-null values are estimated only on Ω\Omega .

This appeared in the proceedings of the IEEE ISBI 2021 conference 7. A longer version of this work has been sent for publication to the Biological Imaging journal 22.

Vasiliki Stergoipoulou's work is supported by the French Government through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002.

7.10 3D-COL0RME

Participants: Luca Calatroni, Laure Blanc-Féraud, Vasiliki Stergiopoulou, Sébastien Schaub.

We proposed a 3D super-resolution approach to improve spatial resolution in Total Internal Reflectance Fluorescence (TIRF) imaging applications. Our approach, called 3D-COL0RME (3D - Covariance-based ${\ell }_0$ super-Resolution Microscopy with intensity Estimation) improves both lateral and axial resolution by combining sparsity-based modelling for precise molecule localisation and intensity estimation in the lateral plane with a 3D reconstruction procedure in the axial one using Multi-Angle TIRF (MA-TIRF). Differently from state-of-the-art approaches, 3D-COL0RME does not require the use of special equipment as it can be used with standard fluorophores. The proposed methods has been validated on simulated MA-TIRF blinking-type data and on challenging real MA-TIRF acquisitions, showing significant resolution improvements.

This appeared has been sent for publication to the proceedings of the ISBI 2022 conference 38.

Vasiliki Stergoipoulou's work is supported by the French Government through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002.

7.11 Adversarial learning for super resolution microscopy

Participants: Mayeul Cachia, Laure Blanc-Féraud, Luca Calatroni, Sébastien Schaub.

Fluorescence microscopy is a well known method to observe specific proteins, marking them with fluorescent molecules. However, the resolution of this method is limited by the diffraction of light in the optical system. In practice it is not possible to observe details below 200nm in the lateral plane.

The goal of super-resolution is to overcome this limitation. There exist many methods for super resolution but most of them are based on specific setup or molecules. The idea was to propose a numerical method both data-driven and model-based inspired from CryoGAN 44 and MSR-GAN 51 but adapted to super-resolution context. The first step was to model the direct problem of microscope acquisition and implement a reliable simulator. This component generates from a discrete distribution of sources a range of corresponding coarse images we could get from the real microscope. Since emission and absorption of photons is a random process, especially when there are only a few photons, this simulator cannot be deterministic. These simulated images should be then compared with real images from the microscope.

Computing a super-resolved image means computing a fine estimation of the distribution of sources. Thus we update the input of the simulator until the output is distributed like the real images from the microscope. This optimization process aims to minimize the distance between the real images and the simulated images depending on the input of the simulator. It can be considered as an adversarial learning problem similar to the training of a specific well-chosen generative adverse network (GAN). The idea is to train a neural net called discriminator to evaluate the simulator output. The discriminator is trained to distinguish the real images from the simulated ones while the simulator should generate images each step nearer from the real images. So these two components have conflicting goals and this kind of double optimisation is said to be adverse.

The main difficulty is to set the hyperparameters of the algorithm. It could be interesting to understand more precisely their respective influence on the results. Despite this limitation this new method for super-resolution yields promising results on both synthetic data and ostreopsis experimental images, see Figure 8. It seems to be robust enough to generalize to other data. In the general context of inverse problems it provides a new validation of the CryoGAN and MSR-GAN approach and let us suppose this approach could be easily adapted to other inverse problems.

7.12 Off-the-grid dynamic super-resolution for fluorescence microscopy

Participants: Bastien Laville, Laure Blanc-Féraud, Gilles Aubert.

Off-the-grid variational methods recover Radon measures, elements of the Banach $ℳ\left(𝒳\right)$ from a stack of noisy altered measurements on a compact $𝒳\subset {ℝ}^{2\mathrm{or}3}$. The thesis consists in the investigation and the development of new gridless methods in static or dynamic settings, with applications in biomedical imaging. As of today:

• we implemented several algorithms for off-the-grid methods taken from the literature in a efficient and user-friendly Python module;
• we developed a new gridless method in a dynamical context. Through the definition of new operator and variational problem, we worked on the localisation of spikes with time-dependent amplitude (and static position), a proxy of the SOFI problem. See Figure 9.

Ongoing project consists in investigating a new approach to extend the off-the-grid theory (right now limited to points) to the reconstruction of more exotic structures like curves, from both theoretical and numerical standpoints;

We have published a review paper in Journal of Imaging 17 and a preprint accepted in IEEE ICASSP 2022 'Off-the-grid covariance-based super-resolution fluctuation microscopy'. See 31

7.13 Correcting estimations of the copepod volume from 2-dimensional images

Participants: Cédric Dubois, Eric Debreuve.

This work was carried out in collaboration with Jean-Olivier Irisson (LOV, Villefranche-sur-mer, France).

Accurate plankton biomass estimations are essential to study marine ecological processes and biogeochemical cycles. This is particularly true for copepods, which dominate mesozooplankton. Such estimations can efficiently be computed from organism volume estimated from images. However, imaging devices only provide 2D projections of 3D objects. The classical procedures to retrieve volumes, based on the Equivalent Spherical Diameter (ESD) or the best-fitting ellipse, are biased. We developed a method to correct these biases. First a new method aims to estimate the organism body area through ellipse fitting (see Figure 10, left image). Then, the body of copepods is modeled as an ellipsoid whose 2D silhouette is mathematically derived. Samples of copepod bodies are simulated with realistic shapes/sizes and random orientations. Their total volume is estimated from their silhouettes using the two classical methods and a correction factor is computed, relative to the known, total, volume. On real data, individual orientations and volumes are unknown but the correction factor still holds for the total volume of a large number of organisms. The correction is around -20% for the ESD method and +10% for the ellipse method. When applied to a database of $\sim$150,000 images of copepods captured by the Underwater Vision Profiler, the corrections decreased the gap between the two methods by a factor of 54 (see Figure 10, right image). Additionally, the same procedure is used to evaluate the consequence of the bias in the estimation of individual volumes on the slopes of Normalized Biovolume Size Spectra (NBSS) and show that they are not sensitive to the bias. This work is being reviewed by the journal “Limnology and Oceanography: Methods” (Wiley).

7.14 Graphical User Interface for the image processing pipeline of the NutriMorph project

Participants: Thissas Benkaroun, Eric Debreuve.

This work was made in collaboration with Clara Sanchez and Carole Rovère, IPMC, Sophia Antipolis, France.

Overweight and obesity are major public health issues affecting respectively 39% and 13% of the world population (From World Health Organization, 2016). They constitute prominent risks for numerous chronic diseases, including diabetes, cardiovascular diseases, and cancer. Studies in animal models and humans reveal that excess fat diets promote both a peripheral chronic inflammation and a hypothalamic neuroinflammation, which possibly leads to feeding behavior deregulation. Ascertaining whether the inhibition of early activation of two major brain cells involved in feeding behavior (glial cells, more specifically astrocytes and microglia) in the hypothalamus could prevent obesity would offer new prospects for therapeutic treatments. To understand the mechanisms pertaining to obesity-related neuroinflammatory response, we developed a fully automated algorithm, NutriMorph. Although some algorithms were developed in the past decade to detect and segment neural cells, they are highly specific, not fully automatic, and do not provide the desired morphological analysis. Our algorithm cope with these issues and performs the analysis of cells images (here, microglia of the hypothalamic arcuate nucleus), and the morphological clustering of these cells through statistical analysis and machine learning. However, graphical user interfaces at key steps of the pipeline are actually helpful to tune the parameters of the algorithm on a couple of images before running the analyses in batch mode on a whole dataset. Therefore, we developed such an interface for the soma detection task, allowing to check and select the cells for further analysis (see Figure 11).

7.15 Dynamic analysis framework to detect cell division and death events in live-cell imaging without specific event markers

Participants: Asma Chalabi, Eric Debreuve.

This work was made in collaboration with Jérémie Roux, Ircan, Nice, France.

The detection of cell division and death events is essential for the understanding of tumor cells responses to cancer therapeutics and to obtain robust metrics of pharmacodynamics. Knowing precisely when these events occur in a live-cell experiment allows to study the relative contribution of different drug effects, such as cytotoxic or cytostatic effects, on a cell population. Yet, classical methods require event-specific dyes (or markers) and measure cell viability as an end-point assay with whole population counts where the proliferation rates can only be estimated when both viable and dead cells are labeled simultaneously. As an alternative, we are developing a dynamic analysis framework for detecting single cell events in marker-free time-lapse microscopy experiments of drug pharmacological profiling. Cell tracking is performed using a basic approach which has been adapted to account for cell divisions. Cell divisions are detected topologically on the tree-shaped cell trajectories produced by the tracking step. A pattern matching procedure is then applied to the cell intensity entropy to filter out spurious divisions arising from debris tracking after cell death. Cell death are detected topologically as trajectories ending before the last time-lapse frame, or using pattern matching on cell intensity entropy (see Figure 12).

7.16 Optimal transport for classification

Participants: Sarah Laroui, Eric Debreuve, Xavier Descombes.

This work was carried out in collaboration with Aurelia Vernay (Bayer) as part of a contract with Bayer.

We have developed an alternative classification approach based on optimal transport whose strength lies in its ability to consider the geometry of the sample distribution. We proposed to transform the data so they follow a simple model (in practice a Gaussian model), the complexity of the data then being "hidden" in the transport transformation. This approach also offers an original way to estimate the probability density function (PDF) underlying a population sample. For that, we used optimal transport (OT) to transform one distribution into another at a lower cost. In our case, we transform the starting data into data that follows a normal distribution. Thus, for each class, we generate a Gaussian with the same Mean and variance as the starting distribution. We learn the transport between source and target samples. Then we transport the samples via the learned transport, and we calculate source sample PDF values using the position of the transported samples and the parameters (mean and variance) of the class distribution. An extrapolation function is then learned based on the class samples and the recovered PDFs. Finally, we obtain for each class, a model that gives the PDFs of any sample (see figure 13.)

7.17 Fungus growth model

Participants: Sarah Laroui, Eric Debreuve, Xavier Descombes.

This work is made in collaboration with Aurelia Vernay (Bayer) as part of a contract with Bayer.

To model the growth of the Botrytis cinerea fungus, we consider a fungus as a tree structure whose growth is an iterative process for which some events must be defined, and the probability of their occurrence computed. We first acquired several microscopy time lapses of growing fungi. The first step is to segment the fungi. We used a Canny-based procedure. After segmentation, we corrected the masks according to an inclusion hypothesis (fungi do not move and can only grow). Then, the fungi are tracked over time using the classical overlapping hypothesis. Finally, we extracted the fungi skeletons, converted them to a graph, and computed three parameters per fungus: the total length of the skeleton and the number of primary and terminal branches. From these data, we studied the length parameter evolution over time, and chose an exponential law as the length evolution model. The law coefficients were estimated independently for each fungus using the least square method, and their respective distribution was computed. This allows to generate realistic random length evolutions. We also studied the branch creation events over time. We concluded that this event occurrences do not exhibit any particular trend. The proposed fungus growth simulator represents a fungus by a tree graph whose first node corresponds to the initial spore. A branch is composed of one or more edges. The fungus growth is generated by successive creations of edges without thickness notion. At each time (or iteration), the graph branches lengthen by an additional edge. Additionally, a new branch can be created, either from a terminal node (split at the ending point of a branch) or from the initial (spore) node, by adding a new edge according to a Bernoulli law. Each of these additions of edges relies on two parameters: a length and an angle. The length depends on coefficients drawn according to the distributions previously estimated in the exponential law context, and on the number of edges to be created. The angle is drawn randomly within fixed intervals (see Figure 14).

7.18 Parametric shapes segmentation using deep learning

Participants: Oumaima Laguili, Sarah Laroui, Xavier Descombes.

In this project, we aim at identifying parametric objects in an image using a deep learning approach. The goal is to detect and segment a collection of objects. In first step, we have simulated a database of noisy images containing disks or ellipses. We first have considered a circle detection CNN architecture on an image containing one disk. We have then applied a transfer learning scheme where the convolutional layers were frozen to generalize the network to the ellipse case. The next step is to address a collection of objects. We considered the Faster RCNN network to draw a bounding box around each object. We can see that the Faster RCNN is able to desambiguate clusters of objects by drawing a bounding box around each individual oject, preventing the use of non overlapping prior (see figure 15). We then extract the image patch corresponding to each bounding box and compare two strategies. First we segment the ellipse using the ellipse detection CNN and we compare the result with an ellipse fitting algorithm. This two steps framework extract clustered objects model by ellipses from images. The next work will consist in a transfer learning step to address real data.

7.19 Uveitis detection from OCT using deep learning

Participants: Youness Mellak, Xavier Descombes.

This work has been carried out in collaboration with Prof. Alin Achim from Bristol university.

Uveitis is an inflammatory disease that affect the eye and is considered a leading cause of vision loss in young and old people around the world. Experts confirm that early and accurate detection of vitreous inflammation can potentially reduce the rate of blindness. In this work, we have defined a CNN-based approach that allows the detection of the disease, even in early stages, i.e. retinas in day 2 of the development of the disease (see figure 16), furthermore we applied an explainable AI method (Grad-CAM) to help the clinicians to know where the disease is located and why the algorithm gives a prediction. The performances obtained are of the order of 80% in distinguishing whether the 2D image corresponds to an inflamated retina, on the different phases of the disease.

Often in clinical routine, specialists need statistical tools that can quantify the distribution of particles in diseased eyes. Since the particles size is small and annotating them with bounding boxes or masks is costly in terms of time and money, we present an automatic method to segment small particles based on a weak annotation (points). It is based on FCN8 architecture with a loss function containing 4 terms written as follows:

These terms include an image term which tends to put objects on bright areas, a consistency term between the annotations and the detected points, a consistency term between the watershed segmentation obtained from the markers given respectively by the annotations and by the detection and a last term preventing from false detections.

After having detected the particles, we consider their localization with respect to the retina and analyze their distribution using the K-Ripley function. We thus show a clustering effect that may reflect a local inflammation of the retina near the optical nerve(see figure 17). Further work will consist of grading the pathology.

7.20 Simultaneous vascular network segmentation and classification using a multi-tasks semi-supervised neural network

Participants: Rudan Xiao, Xavier Descombes.

This work was carried out in collaboration with Damien Ambrosetti, Nice CHU.

Vascular network analysis is crucial to define the tumoral architecture and then diagnose the Renal Cell Carcinoma (RCC) subtypes. However, automatic vascular network segmentation from histopathological images is still a challenge due to the background complexity. We propose a method that reduces reliance on labeled data through semi-supervised learning (SSL). Additionally, considering the correlation between tumor classification and vascular segmentation, we propose a multi-task learning (MTL) model, shown in Fig. 18, which can simultaneously segment the vascular network using SSL and predict the tumor class in a supervised context. This multi-task learning procedure offers an end-to-end machine learning solution to jointly perform vascular network segmentation and tumor classification. We computed the ratio of miss-detected vessels (MV), the ratio of falsely detected vessels (FV) and the global performance index (IV) to evaluate our segmentation results. Fig. 19 shows the segmentation results of the proposed MTL and Tab. 1 gives a quantitative evaluation.

Proposed multi-task learning model architecture.

Segmentation results of the proposed model.

7.21 RCC classification using a deep neural decision tree

Participants: Xavier Descombes.

This work was carried out in collaboration with Francesco Ponzio from Politechnico di Torino (Italy) and Damien Ambrosetti from Nice CHU.

Renal cell carcinoma (RCC), which typically emerges from the renal tubules, is currently categorized into five main histological sub-types: clear cell, papillary, chromophobe, collecting duct, and unclassified RCC. Among them, the three most common RCCs types are clear cell, papillary, and chromophobe, including 70% to 80%, 14% to 17%, and 4% to 8% of all RCCs, respectively. Collecting duct carcinoma is the most uncommon class of RCC (1%), and unclassified RCCs gathers those alien types which do not fit, morphologically or cytogenetically, into any of the above four sub-types. The CNN (Convolutional Neural Network) appears to be a successful approach for image classification purposes. However it leads to data-hungry supervised algorithms, requiring ten of thousands of annotated images to be proficiently trained. This aspect is still an open issue that limits CNN usability in the everyday clinical setting. Transfer learning (TL), which leverages knowledge from related domains (called source domains) to facilitate the learning in a new domain (called target domain), is known to be a good solution to this problem. Originally defined as a research problem in machine learning that focuses on storing knowledge gained while solving one problem and applying it to a different but related problem, TL was initially considered capable of shifting and reusing knowledge between two similar/related domains of interest. For instance, using features embedding extracted from a nudity detection model into a new facial recognition task. Nonetheless, debate continues about the practicability of TL-based embedding in contexts distant from the original training domain, or in presence of a limited number of annotated samples. In this regard, the term negative transfer (NT) specifically refers to situations where the source knowledge can have a negative impact on the target learner, causing reduced learning performance in the target domain.

In this study, we applied several TL-based and full-trained state-of-the-art CNNs in the RCC sub-typing task. We show how both these learning paradigms failed, and, specifically, how TL led to NT, producing not satisfactory performance in the target domain. As a matter of fact, RCC sub-typing task includes those conditions known to be cumbersome even for TL-based solutions: a complex classification task, well-known to be arduous also for skilled pathologists showing a limited number of annotated samples. Our results proved on the one hand that canonical TL from general propose images, and even from other histological source domains, fail, inducing NT. We proposed a hybrid approach, leveraging a combination of TL and expert knowledge, that we named as DeepRCCTree, which was able to outperform several state-of-the-art CNNs in subtyping the RCC cancer (see figure 20). The different binary classification tasks, included in this decision tree, are directly inspired by the histopathologist practice.

Expert-based decision tree based for histopathological image classification.

7.22 Analysis and characterization of the tissue structure of the epidermis from confocal imaging

Participants: Imane Lboukili, Xavier Descombes.

This work was carried out in collaboration with Georgios Stamatas (Johnson & Johnson Consumer Health R&D) as part of a collaboration contract with Johnson & Johnson.

We propose an automated approach to identify cells on a Reflectance Confocal Microscopy (RCM) image of skin. The study of RCM images provides information on the topological and geometrical properties of the epidermis. These properties change in each layer of the epidermis, with age and with certain skin conditions. RCM can also reveal dynamic changes to the epidermis structure in response to stimuli, as it enables repetitive sampling of the skin without damaging the tissue. Studying RCM images requires manual identification of each cell to derive geometrical and topological information, which is time-consuming and subject to human error. More insights could be derived from these data if not for the tediousness of their manual segmentation, highlighting the need for an automated cell identification method. Our automated method of cell identification on RCM images follows three general steps, (1) identifying the region of interest on the RCM image by removing any areas not containing cells, (2) identifying cells within the region of interest using different filters, and (3) rebuilding the identified cells. Pre-processing is required before each one of these steps. Accuracy assessment is complicated on real RCM images as an absolute ground truth doesn’t exist due to inter-expert variability. To assess the accuracy of our results more accurately and guide parametrization we create synthetic images similar to RCM images in their elements and noise. The obtained segmentation results show that identification of cells on RCM images is possible (see Figure 21).

A patent has been submitted for this work.

Synthetic RCM image (left) and obtained automatic cells detection of its cells (right).

7.23 Classification of particle trajectories of the left-right organizer (LRO) in the zebrafish embryo

Participants: Morgane Fierville, Xavier Descombes.

This project has been conducted in collaboration with M. Fürthauer (iBV) and supported by an UCA Academy 2 project.

In this project we study the laterality of organs in the zebrafish embryo and more particularly the breaking of the right-left symmetry. This phenomenon occurs in a cavity called the Kupffer vesicle (KV) which contains particles moving in a flow. We can observe that in mutant embryos (Myo1D gene mutation), we have a disturbance of the flow in the cavity, which generates a defect of the laterality of the organs.

This year we first created velocity maps to validate the orientation of the flow in the cavity (circular in anti-clockwise). We recovered trajectory positions that were obtained through the semi-automatic tracking of exogenous particles (fluorescent beads) developed last year(see Morpheme 2020 activity report). We extrapolated the trajectories using the sliding window principle to obtain velocities at all points of the KV. We then considered a diffusion model using these velocity maps to estimate the associated parameters. This model is then used to simulate trajectories inside the cavity. These simulations lead to a reliable estimate of the density of particles in the different angular sectors of the KV and of the distribution of hitting points on the cavity membrane.

We then develop an automatic pipeline to accurately detect and track endogenous particles to avoid the injection of fluorescent beads which is invasive and can disturb the cavity flow (see Fig. 22). We first removed the heterogeneous non-stationary background from the images by substracting a local time mean. Then, we projected the image sequences into a $(\alpha ,\rho )$ space to observe the trajectories as tubular structures. We enhanced the contrast of linear structures (Gabor and Sato filters) in this representation. Finally, we thresholded, skeletonized and projected back the images in the initial plane to obtain the position of the trajectories over time.

Endogenous particles trajectories are sparse motivating the use of simulated additional trajectories to compute the particle density statistics.

Image processing pipeline for endogenous particle detection. a) 3D image sequences; b) KV outlined; c) image after deletions of the KV background; d) transformations in (ρ,α,z)(\rho , \alpha , z); e) visualization of linear structures in (α,z)(\alpha , z) ; f) directional filtering with Gabor (frequency = 0.2, θ=45o\theta = 45^{o}); g) filtering with Sato 2D (σ∈[5,20])(\sigma \in [5, 20]) ; h) binarization with Yen method ; i) 3D skeletonization; j) transformation into (x,y,z)(x, y, z) and maximum intensity projection (MIP) of trajectories; k) visualization of the manually detected trajectories; l) diagram for the transformation into (ρ,α,z)(\rho , \alpha , z).

7.24 Robust plant cell tracking

Participants: Grégoire Malandain.

This work was carried out in collaboration with Manuel Petit, Guillaume Cerutti and Christophe Godin from Mosaic Inria team, within the IPL Naviscope (section 9.3.5).

Automatic tracking of cell deformation during development using time-lapse confocal microscopy is a challenging task. In plant cell tissues, large deformations and several division cycles can occur between two consecutive time-points making the image registration and tracking procedure particularly difficult. Here, we propose an iterative approach where an initial registration transformation and cell-to-cell mapping are alternatively refined using high-confidence associations selected on the basis of a geometric context preservation score. The method, evaluated on a long time-lapse series of floral meristem, clearly demonstrates its superiority over a non-iterative approach. In addition, we show that the geometric context preservation score can be used to define a lineage quality assessment metric that makes it possible for an expert to provide locally nudges to finalize the lineage detection if necessary in a semi-automatic way.

7.25 Ascidian embryo cell naming

Participants: Grégoire Malandain.

This work has been carried out in collaboration with Killian Biasuz, Benjamin Gallean and Patrick Lemaire from CRBM, Montpellier, within the ANR Cell Whisper (section 9.3.4).

Since the pioneering work of Conklin 40, it is admitted that ascidian exhibited a stereotyped development in the first stages of their embryogenesis. As a consequence, embryo cells can be unambiguously canonically named after their fate: this provides a common reference space into which population of inviduals can be projected and compared (see Fig. 23). Moreover, this stereotypy also provides a means to name a new sequence from already named ones.

Two ascidian embryos with cells colored according to their name: this emphasize the development stereotypy.

In 5, we proposed a pipeline to segment and track the embryo cells over several generations from a temporal sequence of light-sheet microscopy 3D images. This provides not only the cell segmentations and lineage but also numerous quantitative measurements (volume, contact surfaces). This work resulted in 10 developing embryos almost entirely named (through visual inspection), or atlases.

We hypothetized that the development stereotypy induces cell neighborhood invariance. Thus the cell neighborhood can be viewed as a cell fingerprint. The definition of cell-to-cell as well as division-to-division distances allows then to name a newly acquired embryo from one or several atlases. As a side result, it also provides means to investigate the developmental variability at a cellular level.

7.26 Morphogenesis of the sea urchin embryo

Participants: Grégoire Malandain.

This work is made in collaboration with Barthélémy Delorme and Matteo Rauzi (iBV, Nice).

The project aims at understanding the mechanisms driving the larval gut formation in the embryo of the sea urchin Paracentrotus lividus 45.

We use the Astec pipeline (see section 6.1.1 and 5) to process several sets of data and performed targeted quantifications to improve our understanding of the archenteron formation.

The sea urchin embryo is composed of a simple epithelium – a layer of mechanically coupled cells – forming a hollow, bell-shaped organism. At a given point of the embryo - known as the vegetal pole, the epithelium folds and elongates concomitantly to form the rudiment of a tube, the archenteron (Figure 24).

One mechanism commonly found in various model systems that drives tissue folding is apical constriction: a group of cells reduce their surfaces on one side and expand on the opposite side 46. In the sea urchin embryo, a ring of apically constricted cells is indeed present during archenteron invagination (blue cluster on Figure 25 A). Nevertheless, we also imaged and analyzed a mutant that does not display archenteron invagination: the ring-shaped cluster of apically constricted cells is present too (cf Figure 25 B), with similar characteristics (number of cells and level of constriction) (cf Figure 25 C&D). Hereby we demonstrate for the first time that apical constriction is not sufficient to drive archenteron folding in the sea urchin embryo.

Various mechanisms may drive tissue elongation; nevertheless, neighbor exchange via cell intercalation is often found to be a key factor of extension in morphogenetic processes. The 3D segmentations allowed us to systematically track cell intercalation (cf Figure 26 A-D). We could thus demonstrate that, from the onset of archenteron invagination, the tissue elongates via cell intercalations mainly located in the region surrounding the vegetal pole (cf Figure 26 E).

8.1 Bilateral contracts with industry

• Bayer CropScience, Lyon: 39-month companion contract (Aug 2018 – Oct 2021) for the Cifre PhD thesis of Sarah Laroui.
• Johnson & Johnson, Santé Beauté France, Paris: 36-month companion contract (Jan 2021 – Dec 2023) for the PhD thesis of Imane Lboukili.

9.1 International initiatives

9.2 European initiatives

9.3 National initiatives

9.4 Regional initiatives

10.1 Promoting scientific activities

10.2 Teaching - Supervision - Juries

10.3 Popularization

• Rudan Xiao took part in "Fête de la Science" in Nice in October.

11.1 Major publications

• 1 articleA.Arne Bechensteen, L.Laure Blanc-Féraud and G.Gilles Aubert. A continuous relaxation of the constrained $L_2-L_0$ problem.Journal of Mathematical Imaging and VisionJanuary 2021
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• 2 articleF.Fabienne De Graeve, E.Eric Debreuve, S.Somia Rahmoun, S.Szilvia Ecsedi, A.Alia Bahri, A.Arnaud Hubstenberger, X.Xavier Descombes and F.Florence Besse. Detecting and quantifying stress granules in tissues of multicellular organisms with the Obj.MPP analysis tool.TrafficJuly 2019
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• 3 articleX.Xavier Descombes. Multiple objects detection in biological images using a marked point process framework.Methods2016
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• 4 articleG.Georgios Efthymiou, A.Agata Radwanska, A.-I.Anca-Ioana Grapa, S.Stéphanie Beghelli-de la Forest Divonne, D.Dominique Grall, S.Sébastien Schaub, M.Maurice Hattab, S.Sabrina Pisano, M.M. Poët, D. F.Didier F Pisani, L.Laurent COUNILLON, X.Xavier Descombes, L.Laure Blanc-Féraud and E.Ellen Van Obberghen-Schilling. Fibronectin Extra Domains tune cellular responses and confer topographically distinct features to fibril networks.Journal of Cell ScienceFebruary 2021
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• 5 articleL.Léo Guignard, U.-M.Ulla-Maj Fiuza, B.Bruno Leggio, J.Julien Laussu, E.Emmanuel Faure, G.Gaël Michelin, K.Kilian Biasuz, L.Lars Hufnagel, G.Grégoire Malandain, C.Christophe Godin and P.Patrick Lemaire. Contact area-dependent cell communication and the morphological invariance of ascidian embryogenesis.ScienceJuly 2020
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• 6 miscM.Monica Pragliola, L.Luca Calatroni, A.Alessandro Lanza and F.Fiorella Sgallari. On and beyond Total Variation regularisation in imaging: the role of space variance.April 2021
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• 7 miscV.Vasiliki Stergiopoulou, L.Luca Calatroni, J. H.José Henrique de M Goulart, S.Sébastien Schaub and L.Laure Blanc-Féraud. COL0RME: Super-resolution microscopy based on sparse blinking fluorophore localization and intensity estimation.August 2021
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11.2 Publications of the year

11.3 Cited publications

• 39 articleA.A. Beck and M.M. Teboulle. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems.SIAM Journal on Imaging Sciences212009, 183-202
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• 40 bookE. G.Edwin Grant Conklin. The organization and cell-lineage of the ascidian egg / by Edwin G. Conklin..Philadelphia :[Academy of Natural Sciences],1905, 182URL: http://www.biodiversitylibrary.org/item/24005
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• 41 inproceedingsG.Gili Dardikman-Yoffe and Y. C.Yonina C. Eldar. LSPARCOM: Deep Unfolded Super-Resolution Microscopy.Imaging and Applied Optics CongressOptical Society of America2020, JW5A.5URL: http://opg.optica.org/abstract.cfm?URI=AOMS-2020-JW5A.5
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• 42 inproceedingsS.Simon Gazagnes, E.Emmanuel Soubies and L.Laure Blanc-Féraud. High density molecule localization for super-resolution microscopy using CEL0 based sparse approximation.Biomedical Imaging (ISBI 2017), 2017 IEEE 14th International Symposium onIEEE2017, 28--31
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• 43 articleG.Gaby Gorsky, M. D.Mark D. Ohman, M.Marc Picheral and others. Digital zooplankton image analysis using the ZooScan integrated system.Journal of Plankton Research32303 2010, 285--303URL: https://doi.org/10.1093/plankt/fbp124
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• 44 articleH.Harshit Gupta, M. T.Michael T. McCann, L.Laurène Donati and M.Michael Unser. CryoGAN: A New Reconstruction Paradigm for Single-Particle Cryo-EM Via Deep Adversarial Learning.IEEE Transactions on Computational Imaging72021, 759-774
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• 45 articleT.Tetsuya Kominami and H.Hiromi Takata. Gastrulation in the sea urchin embryo: a model system for analyzing the morphogenesis of a monolayered epithelium..Dev Growth Differ464August 2004, 309-26
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• 46 articleA. C.Adam C Martin and B.Bob Goldstein. Apical constriction: themes and variations on a cellular mechanism driving morphogenesis..Development14110May 2014, 1987-98
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• 47 articleV.Vishal Monga, Y.Yuelong Li and Y. C.Yonina C. Eldar. Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing.IEEE Signal Processing Magazine3822021, 18-44
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• 48 articleS.Shunsuke Ono. $L_0$ Gradient Projection.IEEE Transactions on Image Processing2642017, 1554-1564
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• 49 articleE.Emmanuel Soubies, L.Laure Blanc-Féraud and G.Gilles Aubert. A Unified View of Exact Continuous Penalties for ${}_2-{}_0$ Minimization.SIAM Journal on Optimization2732017, 2034--2060
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• 50 articleJ.Jianchao Yang, J.John Wright, T. S.Thomas S. Huang and Y.Yi Ma. Image Super-Resolution Via Sparse Representation.IEEE Transactions on Image Processing19112010, 2861-2873
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• 51 inproceedingsM.Mona Zehni and Z.Zhizhen Zhao. MSR-GAN: Multi-Segment Reconstruction via Adversarial Learning.ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)2021, 5115-5119
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• 52 inproceedingsK.Kai Zhang, W.Wangmeng Zuo, S.Shuhang Gu and L.Lei Zhang. Learning Deep CNN Denoiser Prior for Image Restoration.2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)2017, 2808-2817
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