Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical. In the variational approach, the reconstructed signal is solution to an optimization problem that establishes a tradeoff between fidelity to the data and smoothness conditions via a quadratic regularization associated to a linear operator. In the statistical approach, the signal is modeled as a stationary random process defined from a Gaussian white noise and a whitening operator; one then looks for the optimal estimator in the mean-square sense. We give a generic form of the reconstructed signals for both approaches, allowing for a rigorous comparison of the two.We fully characterize the conditions under which the two formulations yield the same solution, which is a periodic spline in the case of sampling measurements. We also show that this equivalence between the two approaches remains valid on simulations for a broad class of problems. This extends the practical range of applicability of the variational method

Active Subdivision Surfaces for the Semiautomatic Segmentation of Biomedical Volumes

International audienceWe present a new family of active surfaces for the semiautomatic segmentation of volumetric objects in 3D biomedical images. We represent our deformable model by a subdivision surface encoded by a small set of control points and generated through a geometric refinement process. The subdivision operator confers important properties to the surface such as smoothness, reproduction of desirable shapes and interpolation of the control points. We deform the subdivision surface through the minimization of suitable gradient-based and region-based energy terms that we have designed for that purpose. In addition, we provide an easy way to combine these energies with convolutional neural networks. Our active subdivision surface satisfies the property of multiresolution, which allows us to adopt a coarse-tofine optimization strategy. This speeds up the computations and decreases its dependence on initialization compared to singleresolution active surfaces. Performance evaluations on both synthetic and real biomedical data show that our active subdivision surface is robust in the presence of noise and outperforms current stateof-the-art methods. In addition, we provide a software that gives full control over the active subdivision surface via an intuitive manipulation of the control points

Apprentissage profond non supervisé fondé sur l'algorithme EM pour la segmentation du mouvement

International audienceThis paper presents a CNN-based fully unsupervised method for motion segmentation from optical flow. We assume that the input optical flow can be represented as a piecewise set of parametric motion models, typically, affine or quadratic motion models. The core idea of this work is to leverage the Expectation-Maximization (EM) framework. It enables us to design in a well-founded manner the loss function and the training procedure of our motion segmentation neural network. However, in contrast to the classical iterative EM, once the network is trained, we can provide a segmentation for any unseen optical flow field in a single inference step, with no dependence on the initialization of the motion model parameters since they are not estimated in the inference stage. Our method outperforms comparable unsupervised methods and is very efficient.Cet article présente une méthode entièrement non supervisée basée sur un réseau neuronal convolutionnel pour la segmentation du mouvement à partir du flot optique. Nous supposons que le flot optique d'entrée peut être représenté par un ensemble de modèles de mouvement paramétriques, typiquement des modèles de mouvement affines ou quadratiques. L'idée centrale de ce travail est d'exploiter le cadre de l'Espérance-Maximisation (EM). Il nous permet de concevoir d'une manière bien fondée la fonction de perte et la procédure d'apprentissage de notre réseau de neurones de segmentation du mouvement. Contrairement à la méthode EM itérative classique, une fois le réseau entraîné, nous pouvons fournir une segmentation pour tout nouveau champ de flot optique en une seule étape d'inférence et sans avoir avoir à estimer de modèles de mouvement. Notre méthode surpasse les méthodes non supervisées comparables et est très efficace en temps de calcul. Mots Clés Segmentation du mouvement, flot optique, réseau de neurones, algorithme EM

Simulation of Astrocytic Calcium Dynamics in Lattice Light Sheet Microscopy Images

International audienceAstrocytes regulate neuronal information processing through a variety of spatio-temporal calcium signals. Advances in calcium imaging started to reveal astrocytic activities, but the complexity of the recorded data strongly call for computational analysis tools. Their development is hindered by the lack of reliable annotations that are essential for their evaluation and for the design of learning-based methods. To overcome the labeling problem, we present a framework to simulate realistic astrocytic calcium signals in 3D+time lattice light sheet microscopy (LLSM) images by closely modeling calcium kinetics in real astrocytes

EM-driven unsupervised learning for efficient motion segmentation

International audienceIn this paper, we present a CNN-based fully unsupervised method for motion segmentation from optical flow. We assume that the input optical flow can be represented as a piecewise set of parametric motion models, typically, affine or quadratic motion models. The core idea of our work is to leverage the Expectation-Maximization (EM) framework in order to design in a well-founded manner a loss function and a training procedure of our motion segmentation neural network that does not require either ground-truth or manual annotation. However, in contrast to the classical iterative EM, once the network is trained, we can provide a segmentation for any unseen optical flow field in a single inference step and without estimating any motion models. We investigate different loss functions including robust ones and propose a novel efficient data augmentation technique on the optical flow field, applicable to any network taking optical flow as input. In addition, our method is able by design to segment multiple motions. Our motion segmentation network was tested on four benchmarks, DAVIS2016, SegTrackV2, FBMS59, and MoCA, and performed very well, while being fast at test time

Reinforcing Interdisciplinary Collaborations to Unravel the Astrocyte “Calcium Code”

In this review article, we present the major insights from and challenges faced in the acquisition, analysis and modeling of astrocyte calcium activity, aiming at bridging the gap between those fields to crack the complex astrocyte “Calcium Code”. We then propose strategies to reinforce interdisciplinary collaborative projects to unravel astrocyte function in health and disease

Texture-driven parametric snakes for semi-automatic image segmentation

We present a texture-driven parametric snake for semi-automatic segmentation of a single and closed structure in an image. We propose a new energy functional that combines intensity and texture information. The two types of image information are balanced using Fisher’s linear discriminant analysis. The framework can be used with any filter-based texture features. The parametric representation of the snake allows for easy and friendly user interaction while the framework can be trained on-the-fly from pixel collections provided by the user. We demonstrate the efficiency of the snake through an extensive validation on synthetic as well as on real data. Additionally, we show that the proposed snake is robust to noise and that it improves the segmentation performance when compared to an intensity-only scheme

Deforming Tessellations for the Segmentation of Cell Aggregates

We present a new active contour to segment cell aggregates. We describe it by a smooth tessellation that is attracted toward the cell membranes. Our approach relies on subdivision schemes that are tightly linked to the theory of wavelets. The shape is encoded by control points grouped in tiles. The smooth and continuously defined boundary of each tile is generated by recursively applying a refinement process to its control points. We deform the smooth tessellation in a global manner using a ridge-based energy that we have designed for that purpose. By construction, cells are segmented without overlap and the tessellation structure is maintained even on dim membranes. Leakage, which afflicts usual image-processing methods (e.g., watershed), is thus prevented. We validate our framework on both synthetic and real microscopy images, showing that the proposed method is robust to membrane gaps and to high levels of noise

Simulation of Astrocytic Calcium Dynamics in Lattice Light Sheet Microscopy Images

International audienceAstrocytes regulate neuronal information processing through a variety of spatio-temporal calcium signals. Recent advances in calcium imaging have started to shine light on astrocytic activity, but the complexity and size of the recorded data strongly call for more advanced computational analysis tools. Their development is currently hindered by the lack of reliable, labeled annotations that are essential for the evaluation of algorithms and the training of learning-based methods. To solve this labeling problem, we have designed a generator of 2D/3D lattice light sheet microscopy (LLSM) sequences which realistically depict the calcium dynamics of astrocytes. By closely modeling calcium kinetics in real astrocytic ramifications, the generated datasets open the door for the deployment of convolutional neural networks in LLSM