This work is made in collaboration with Simone Rebegoldi, Marco Prato and Luca Zanni are in the Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Universita di Modena e Reggio Emilia, Modena, Italy.

he DIC (differential-interference-contrast) microscopy states the problem of image phase reconstruction which is ill-posed (under-determinated) and non-convex optimization problem. We have worked on the phase reconstruction from color images by optimization of a non linear least-squares-like discrepancy term regularized with a total variation functional. We have considered two different penalties, the first one being the total variation (TV) functional which is suitable for piecewise constant images, while the second is the hypersurface (HS) potential, which is a smooth generalization of the TV able to reconstruct both sharp and smooth variations of the unknown phase. Since the latter choice leads to the minimization of a smooth functional, we developed a limited memory gradient method, in which suitable adaptive steplength parameters are chosen to improve the convergence rate of the algorithm. As concerns the TV–based model, we addressed the minimization problem by means of a recently proposed linesearch–based forward–backward method able to handle the nonsmoothness of the TV functional. Numerical tests show that in the case of smooth TV minimization funcitonal, the performance of the limited memory gradient method is much better than those of the conjugate gradient approaches proposed in the literature, in terms of number of function/gradient evaluations and, therefore, computational time. In the case of TV functional, despite the difficulties due to the presence of a nondifferentiable term, also the linesearch–based forward–backward method proposed in this case is able to provide reconstructed images with a computational cost comparable to that of the gradient methods, thus leaving to a potential user freedom to choose the desired regularizer without losing in efficiency.

This work has been done during the PhD thesis of Lola Bautista defended in June 2017 . It has been published in the journal Inverse Problems in 2017 .

We focus on the problem of minimizing the least-squares loss function under the constraint that the reconstructed signal is at maximum k-sparse. This is called the ${\ell }_2$-${\ell }_0$ constrained problem. The minimization problem is of interest in signal processing, with application to compressed sensing, source separation and super-resolution imaging.

This problem has previously been relaxed, among other methods, by using the convex ${\ell }_1$ norm instead of the ${\ell }_0$ norm, but depending on the specific problem the global minimizer may not be the same.

The goal of our work is to propose a continuous exact relaxation of the ${\ell }_2$-${\ell }_0$ constrained problem. The initial problem is non-continuous and is therefore from an algorithmic point of view difficult to minimize. A continuous exact relaxation has the same global minimizers as the initial problem, and a local minimizer of the relaxation is a local minimizer of the initial problem, with possible less local minimizers than the initial problem. Solving the initial ${\ell }_2$-${\ell }_0$ constrained problem is equivalent, in the sense of the global minimizers, to solving the continuous relaxed form. Furthermore, a continuous exact relaxation provides better properties for the objective function in terms of minimization, because of the continuity and the number of local minimizers.

Based on the recent works of Marcus Carlson we propose a continuous exact relaxation of the ${\ell }_2$-${\ell }_0$ constrained problem $S_{\gamma }$, with an algorithm to minimize the function.

In order to increase the quality of the optimization, we have to chose “the best” exact relaxation. Inspired by the work by Emmanuel Soubies we have computed the convex hull of the initial problem for a special case. The penalty term obtain, $f_{cr}$ may be a continuous relaxation with respect to the initial problem, with fewer local minimizers than the initial problem and the relaxation $S_{\gamma }$ (see figure ). This has to be proven.

The work will be presented at Mathematical Image Analysis 2018 conference in Berlin on the form of a poster.

This work takes place within the ANR PhaseQuant.

In microscopy imaging, a trade-off has to be made between a high resolution, that enables to see details, and the width of the field of view, that enables to see many objects. Such a trade-off is avoided by mosaicing, which consists in the acquisition of several images, say $N\times N$, with a small overlap between images. This way, an image with a $N$ larger field of view can be reconstructed with the same resolution than a single microscopic image.

Such an imaging protocol is available on many microscopy software. Basically, displacements of the table on which lies the material to be imaged are programmed, and used to reconstruct the mosaic. However, it appears (at the overlapping areas), that a residual offset is still present. The cause of this has not be identified so far: this may be due to small geometric mis-alignement in the imaging device, or to the command of the micrometer table.

We thus investigate the stability of this residual offset with respect to time and to the image position within the mosaic.

This work is made in collaboration with Pascal Thérond, Tamas Matusek and Caterina Novelli (iBV). It is supported by the ANR project HMOVE.

Cellular communication is one of the most important processes for understanding and controlling morphogenesis (the set of laws that determine the structure of tissues and organs during embryonic development) necessary for the development of an organism. This is an important issue in the field of developmental biology and it has recently been shown that the exchange of information between cells is controlled by long cellular extensions called "cytonemes".

Due to the amount of information to be processed and the time required to study this information, it is essential to be able to provide image processing tools through which reliable, automatic and effective methods are proposed for these studies. In this work we have developped a pipeline for membrane extension and vesicles detection from in vivo data obtained by confocal microscopy. The vesicles are detected using a marked point process modeling. The cell extension detection embed the membrane detection using active contours and the filament detection using a tophat operator, the Frangi filter and Dijkstra algorithm. With this detection tool (exemplified in Figure ), we have characterized a mutant population compared to a wild population of drosophila wings with respect to Hedgehog signalization. Interestingly we have shown that a significative difference appears in the cytonemes length but not in their number.

Our work is motivated by the study of developmental axonal remodeling, a genetically-controlled process characterized by a degeneration step followed by a rapid regrowth of axons. Here, we focus our interest on the axonal regrowth phase, which can be studied during brain development, using the fruit fly, Drosophila melanogaster, as a model system.

During the regrowth, small dynamical branches can be observed: they emanate from long stable branches and have generally a short lifetime. Such small branches may contribute to rebuild the axon connectivity during the adult stage. A better knowledge of the mechanisms controlling the dynamic of these branches may contribute to a better understanding of neuronal morphogenesis. In this work, we are particularly interested in the quantification of this process, for which the extraction of both the main and second branches is required.

Neuron tracing is still a challenge in neuroinformatics. Despite the huge progresses made during the last decades, this problem is still an open question. This is exacerbated with the development of new imaging techniques, that produce more and more images with improved quality and/or resolution. Among these, live-imaging techniques are more and more prominent. Indeed, acquisitions of 3D image sequences over long periods of time, in particular, have enabled neurobiologists to follow complex processes such as the development of neuronal populations. However, they produce time series of 3D volumes, for which there does not exist dedicated tracing approach.

Apart slight movements, the dynamic changes of axons are due to growing or retracting branches. Thus, we designed a topologically constrained tracking method that first ensures that the tree structure of the axon and its branches is preserved through the time sequence, and second enables a slight displacement of the axon (within an user-specified extend), while mimicing both the retraction and the growth of branches. Results are presented in figure .

This work is made in collaboration with Frédéric Bost, Stephan Clavel, Aurélie Charazac, Celia Decondé le Butor (C3M).

We consider in this project a high content microscopy based screening focused on the effects of endocrine disruptors on prostatic cancer cells metabolism. Specifically, we developed our automatic computational tool to detect and classify mitochondrial network morphology from microscopy acquired images. The first step consists in binarizing the image and the binary pattern representing the mitochondrial network is classified in a second step. To binarize the mitochondrial network we consider the different level sets in the original image. A score is computed on each connected component of the level set pyramid depending on the contrast between the component and the neighboring background and on a shape criteria. We thus select the best scored component considering a compromise between the component contrast and a shape prior. We then run a k-mean clustering on the set defined by all the mitochondrial component extracted from the whole database. The different estimated classes are typical mitochondrial network element such as filaments or blobs. An image is then classified based on its signature defined by the number of mitochondrial element detected for each of the pre-defined classes (see Figure). This classification scheme provides a discrimination framework based on geometrical and topological mitochondrial network properties than can differentiate for example filamentous and aggregate networks. This tool will be used for automatically specifying the effect of endocrine disruptors.

This work is made in collaboration with Céline Cansell and Carole Rovere (IPMC, Sophia Antipolis).

The goal of this project is to classify 3D images of neuronal cells (astrocytes and microglia) into mice fed normally and mice fed with a high-fat diet (see Fig. ). The distinction can be made in two different areas of interest of the hypothalamus: Median Eminence (EM) and Arcuate Nucleus (ARC).

Astrocytes are perceived as networks. Our goal is to find out if there is a difference in the organization of these networks between the two areas of interest and between the two mouse models. Regarding inflammatory cells (microglias), we first segment each cell body and their extensions using a Frangi filter bank to enhance filamentous structures. This produces network pieces that must be joined to build one network per microglia. Thus, we connect filaments to soma and filaments to filaments using minimal paths (using an image-based, anisotropic metric) computed by dynamic programming. Finally, we extract geometrical and topological parameters such as the length and width of the extensions, the number of branches ... These parameters will be used for clustering microglia networks in order to identity the different populations.

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

Botrytis cinerea is a reference model of filamentous phytopathogen fungi. Some chemical treatments can lead to characteristic morphological changes, or phenotypic signatures, observable with transmitted light microscopy (see Fig. ), which could be associated with the molecule Mode of Action.

In this context, we developed a robust image analysis and classification method relying on morphometric characteristics to automatically detect fungi observed using transmitted light microscopy, and classify them into predefined phenotypes. The detection task has been implemented in a classical way using a combination of mathematical morphology operations and active contours. The classification task has been solved in a supervised learning context.

Since a fungus can be described as tubular extensions connected to a spore (a roundish “root” cell), we proposed to describe such an object by its skeleton together with the distances from the skeleton to the fungus boundary. The skeleton was then converted into a valued graph. We selected a dozen topological and morphological features such as the number of nodes, the length of the longest branch, or the average and variance of the per-branch average skeleton-to-boundary distances.

These features were used in a supervised machine learning framework. Specifically, a cascade of two classifiers was proposed, the first one based on a decision tree to reject non relevant phenotypes (spores and mycelium), the second one to actually determine the phenotypes of the fungi. This second classifier was a Random Forest learned on the provided learning set composed of sample fungi from two phenotypes. Note that the classification accuracy can be computed either in a per-fungus way, or in a per-image way. Indeed, a given image corresponds to a unique chemical treatment so that all the fungi it contains exhibit the same phenotype (up to the natural biological variations), which can therefore be associated to the image itself. This per-image phenotype can be obtained by a majority vote among the individual fungus phenotypes. It represents the answer the biologists need. For the 2-phenotype problem we worked on, we obtained an image classification accuracy of around 90%, which is more than encouraging. In order to allow for a future, deeper analysis of the features characterizing each phenotype, we also computed the influence of each feature on the classification accuracy.

As part of the ANR project RNAGRIMP Imp = IGF-II mRNA-binding protein; IGF = Insulin-like Growth Factor; mRNA = Messenger Ribonucleic Acid. (section ), two series of images have been acquired using fluorescence microscopy: one where the cell cytoplasm has been stained with GFP (Green Fluorescent Protein), the second where the nuclei have been stained with DAPI (4',6-diamidino-2-phenylindole). The first steps are detecting the nuclei on the DAPI images and learning a classification procedure into living cell or dead cell based on morphological and radiometric nuclei properties (average intensity, area, granularity, circularity...) (see Fig. ).

A specific CellProfiler http://cellprofiler.org pipeline has been developed for this, and CellProfiler Analyst http://cellprofiler.org/cp-analyst has been used to learn a decision tree for automatic nuclei (hence, cell) classification. The next step is to segment (i.e., extract automatically the region of) the cell cytoplasms on the GFP images. Indeed, the target RNP-IMP granules appear in that compartment of the cell and are visible through their GFP response. We developed an active contour-based segmentation method relying on local image contrast with an initialization provided by a marked point process detection of ellipses (see Fig. ). Then, the detection of the particles can be performed inside the segmented cytoplasms (using a method called SPADE previously developed by the team).

This work is made in collaboration with Damien Ambrosetti (MD, Pasteur Hospital, Nice).

The renal cell carcinoma is the most frequent type of kidney cancer (between 90% and 95% of all cases). Twelve classes of carcinoma can be distinguished, among which the clear cell carcinoma (CCRCC) and the papillary carcinoma (PRCC) are the two most common ones (75% and 10% of the cases, respectively). After the carcinoma has been diagnosed, the tumor is ablated and prepared for histological examination (fixation, staining, slicing, observation with a microscope) (see Fig. ).

Along with genetic tests and protein reactions, the histological study allows to classify and grade the tumor in order to make a prognosis and monitor the patient treatment. Clinically speaking, digital histology is a recent domain (routinely, histological slices are studied by MDs directly on the microscope). The classical works on digital histology deal with the automatic analysis of cells (size, density ...). However, one crucial factor for carcinoma classification is the structure of the vascular network. Coarsely, CCRCC is characterized by a "fishnet” structure while the PRCC has a tree-like structure.

In this context, we proposed to extract the vascular network from a given histological slice, compute features of the underlying graph structure, and classify the tumor into CCRCC or PRCC based on these features . Then, we started to focus on performing a higher-level analysis of the vascular graphs. It can be noted that cells that are close to the vascular network naturally tend to align with it. Thus there might be specific “cell-vascular network” arrangements for each type of carcinoma. Our plan is to look for repeated subgraph patterns using pattern matching methods on labeled graphs, where a pattern would be a combination of (i) topological features from the graph, (ii) nearby cell features, and (iii) measures characterizing the coherence between nearby cells and the network (cell-to-network distances, cell density along the network, degree of alignment with the network...). There are chances that each carcinoma type exhibits a set of patterns that appear with a high frequency, therefore being characteristic of the given type. Such patterns would then represent discriminant features for carcinoma classification.

The data used for this work are courtesy of Yassin Refahi (Sainsbury Laboratory, Cambridge university) and Ulla-Maj Fiuza (CRBM, CNRS, Montpellier 1 & 2 university).

In the context of developmental biology, 3D+t microscopy imaging allows to quantitatively study the morphogenesis at the cellular level, but requires automated segmentation methods to handle the huge quantities of data. To minimize the necessary and tedious user interaction to correct unavoidable errors (3D images may have up to thousands of cells), it is desirable to improve such segmentation methods. This, in turn, motivates the need for a comprehensive evaluation methodology that will allow to automatically compare the outputs of two segmentation methods, not only in terms of cell border accuracy, but also in terms of cell detection.

The aim of the present work is to propose such an original comprehensive segmentation comparison method that provides an objective way for multi-object segmentation comparison. This method enables to determine automatically a region-to-region correspondence map and provides asymmetric shape similarity indexes between two segmented images, with a robustness to potential region border variations. We illustrate the applicability of the proposed method with two examples in figure .

This work is made in collaboration with Julien Laussu, Patrick Lemaire (CRBM, CNRS, Montpellier 1 & 2 university), Emmanuel Faure (IRIT, CNRS, Toulouse) and Christophe Godin (Inria Virtual Plants team, Montpellier).

In developmental biology, the embryogenesis study relies in particular on image-based studies. Today, fluorescent confocal microscopy is a means for in vivo imaging of developing organisms at cell level with a high spatio-temporal resolution. To handle such 3D+$t$ image sequences, adapted computer-assisted methods are highly desirable in order to extract essential information from these data.

More specifically, for developing ascidian embryos, an existing framework called ASTEC  is used by biologists in order to extract the cell segmentation and lineage from some 3D+$t$ sequences. However, remaining issues about segmentation accuracy motivated us to propose a new framework as an alternative to ASTEC for cell segmentation and tracking. The originality of the proposed Grouped Local Automated Cell Extractor (GLACE) framework is to segment the $i$–th image of a sequence by applying locally the original 3D cell segmentation framework of  for all the regions of interest defined by the segmented cells of the $i-1$–th image of the sequence. The union of all the local reconstructions provides the segmentation of the $i$–th image of the sequence (figure ). The GLACE framework does not replace the ASTEC framework, however they provide complementary results for embryo image sequence reconstructions.

This work is made in collaboration with Julien Laussu, Patrick Lemaire (CRBM, CNRS, Montpellier 1 & 2 university) and Christophe Godin (Inria Virtual Plants team, Montpellier).

Until gastrulation, ascidian embryos have a very stereotyped and invariant development, so that it is possible to establish a cell-to-cell mapping between two developing embryos at a same developing stage. We proposed in a previous work a method for geometric registration that determines a linear (affine) transformation superimposing a test embryo into a reference one and that draws a cell-to-cell mapping up  .

In the current work, we extend this framework for the determination of cell lineage mapping between two developing ascidian embryos by propagating an initial cell-to-cell mapping to the cell descendants since the cell correspondences are inherited for the ascidian embryo (figure  (top)). To do so, we use the information provided by the 3D+$t$ sequences segmentation and lineage such as cell volume, life-span and relative position in the embryos. We experimented on real data the proposed cell lineage registration framework (figure  (bottom)).

This work is made in collaboration with Yassin Refahi (Sainsbury Laboratory, Cambridge university), Jonathan Legrand, Jan Traas (RDP, ENS Lyon, INRA, CNRS, Lyon) and Christophe Godin (Inria Virtual Plants team, Montpellier).

In developmental biology, the study of model organisms aims for the understanding of genetic mechanisms responsible of morphogenesis. Today, fluorescent confocal microscopy is a means for in vivo imaging of developing plants at cell level with a high spatio-temporal resolution.

We propose in this work some dedicated computational tools for the study of such 3D+t sequences. These methods offer the means to compare temporal sequences of flower development and to build 4D digital atlases of developing arabidposis floral meristems on which every individual can be projected (figure ), opening the avenue to the statical analysis of populations.

This work is made in collaboration with Régis Vaillant (GE-Healthcare, Buc, France) and Nicholas Ayache (Inria Asclepios team).

Percutaneous Coronary Intervention (PCI) is a minimally procedure which is used to treat coronary artery narrowing. During the guidewire navigation, the lesion is crossed and in some cases, the physician could benefit from a visual assessment of the coronary wall. The x-ray imaging interventional system used for per-operative guidance is not able to display this information mostly by lack of density resolution. On the contrary, Computed Tomography Angiography (CTA) is a modality which has the capability of capturing the characteristics of the vessel wall.

Fusing pre-operative CT angiography with per-operative angiographic and fluoroscopic images is thus considered by physicians as a potentially useful tool for improved guidance. To be adopted, this tool has required the development of tracking methods adapted to the deformations of the arteries caused by the cardiac motion. We have proposed a 3D/2D temporal tracking of one coronary vessel, based on a spline deformation, using pairings with a controlled 2D stretching or contraction along the paired curves and a preservation of the length of the 3D curve which corresponds to the anatomic propriety , . Experiments were conducted on a database of 10 vessels from 5 distinct patients, with dedicated metrics assessing both the global registration and the local coherency of the position along the vessel. The proposed results demonstrate the efficiency of the proposed method, with an average standard deviation of 2 mm for the localization of landmarks (see Fig. ).

Axons develop embedded in mechanically constrained environments. Thus, to fully understand this dynamical process, one must take into account collective mechanisms and mechanical interactions within the axonal populations. However, techniques to directly measure this from living brains are today lacking or heavy to implement. This interdisciplinary work intends to close the gap between classic in vitro experimental assumptions and real in vivo situations, where the final neuronal morphology is acquired through a dynamical and environmental-dependent process. We use as biological model Drosophila $\gamma$ axon remodeling and analyze, for the first time to our knowledge, the mechanical situation of a whole population of $\gamma$ neurons (650 individuals) growing together in a constraint space (i.e. medial lobe of the Mushroom Body).

We have designed a mathematical model of single axon growth based on Gaussian Markov Chains with two parameters, accounting for axon rigidity and attraction to the target field. We used this model to simulate the growing axons embedded in space constraint populations to test our hypothesis. We explored new branch formation mechanisms to mimic the growth of wild type $\gamma$ axons population , as well as predict different mutant phenotypes. This approach allowed also to analyze dynamical aspects of the $\gamma$ neuron collective growth process such as speed and density in function of space and time, which help to explain several characteristics of the $\gamma$ neuron morphology and behavior during development. Among the obtained results, the proposed model is able to reproduce the intra-population morphological variability. Interestingly, applying the ESA distance between trees previously developed in the team showed that real axons present shapes that showcase a compromise between collective elongation and morphological variability, essential for axonal connectivity (Figure ). Finally, we explored other branch occurrence strategies –from uniformly random to occurrence upon mechanical interactions- to contrast and validate with previously developed hypothesis on the importance of branching for axonal elongation in vivo.

Piecewise homogeneous Markov chain processes can be applied to diverse phenomena of various nature, such as genetics, physics. Recent bibliography has focused on these systems, proposing different alternatives to detect the jump points and be able to separate between different phases of the signals. The Markov chain is usually defined by its transition matrix and the change points are modeled by a hidden Markov process. In this work, we focus on the Gaussian case with a Bernoulli distribution governing the change points. We have developped two different theoretical frameworks: one Bayesian with a Bernoulli prior, and the other one statistic-oriented, proposing a test of hypothesis based on ratio of likelihoods. For both cases we provide with robust algorithms to detect the jump points and reduce the error in the estimations of the parameters of the main model. We compare both methods and investigate their limits and advantages. We finally provided practical examples to showcase the power of the proposed approach (see Figure ).