Étienne Baudrier

Thibaut Eloy, Etienne Baudrier, Marine Laporte et al.

Single particle reconstruction has recently emerged in 3D fluorescence microscopy as a powerful technique to improve the axial resolution and the degree of fluorescent labeling. It is based on the reconstruction of an average volume of a biological particle from the acquisition multiple views with unknown poses. Current methods are limited either by template bias, restriction to 2D data, high computational cost or a lack of robustness to low fluorescent labeling. In this work, we propose a single particle reconstruction method dedicated to convolutional models in 3D fluorescence microscopy that overcome these issues. We address the joint reconstruction and estimation of the poses of the particles, which translates into a challenging non-convex optimization problem. Our approach is based on a multilevel reformulation of this problem, and the development of efficient optimization techniques at each level. We demonstrate on synthetic data that our method outperforms the standard approaches in terms of resolution and reconstruction error, while achieving a low computational cost. We also perform successful reconstruction on real datasets of centrioles to show the potential of our method in concrete applications.

Denis Fortun, Etienne Baudrier, Fabian Zwettler et al.

In this paper, we address the problem of registering multiple point clouds corrupted with high anisotropic localization noise. Our approach follows the widely used framework of Gaussian mixture model (GMM) reconstruction with an expectation-maximization (EM) algorithm. Existing methods are based on an implicit assumption of space-invariant isotropic Gaussian noise. However, this assumption is violated in practice in applications such as single molecule localization microscopy (SMLM). To address this issue, we propose to introduce an explicit localization noise model that decouples shape modeling with the GMM from noise handling. We design a stochastic EM algorithm that considers noise-free data as a latent variable, with closed-form solutions at each EM step. The first advantage of our approach is to handle space-variant and anisotropic Gaussian noise with arbitrary covariances. The second advantage is to leverage the explicit noise model to impose prior knowledge about the noise that may be available from physical sensors. We show on various simulated data that our noise handling strategy improves significantly the robustness to high levels of anisotropic noise. We also demonstrate the performance of our method on real SMLM data.

Etienne Le Quentrec, Loïc Mazo, Étienne Baudrier et al.

Preserving the topology during a digitization process is a requirement of first importance. To this end, it is classical in Digital Geometry to assume the shape borders to be par-regular. Par-regularity was proved to be equivalent to having positive reach or to belong to the class C 1,1 of curves with Lipschitz derivative. Recently, we proposed to use a larger class that encompasses polygons with obtuse angles, the locally turn-bounded curves. The aim of this technical report is to define the class of par-regular curves inside the class of locally turn-bounded curves using only the notion of turn, that is of integral curvature. To be more precise, in a previous article, we have already proved that par-regular curves are locally turn-bounded. Incidentally this proof lead us to show that the turn of par-regular curves is a Lipschitz function of their length. We call the class of curves verifying this latter property the curves with Lipschitz turn. In this technical report, we prove the converse assertion : locally turn-bounded curves with Lipschitz turn are par-regular. The equivalence is stated in Theorem 3.1 and the converse assertion is proved in Lemma 3.2. In section 1, we recall the definition of par-regularity and equivalently of sets with positive reach. In section 2, we present the notions of curves locally turn-bounded and of curves with Lipschitz turn. Throughout this latter section, some of intermediate steps (Lemmas 2.3 and 2.11) are proved just after the introduction of their related notions. The last section (section 3) is dedicated to the proof of the equivalence of the notions.