BACKGROUND: The segmentation of a 3D image is a task that can hardly be automatized in certain situations, notably when the contrast is low and/or the distance between elements is small. The existing supervised methods require a high amount of user input, e.g. delineating the domain in all planar sections. RESULTS: We present FitEllipsoid, a supervised segmentation code that allows fitting ellipsoids to 3D images with a minimal amount of interactions: the user clicks on a few points on the boundary of the object on 3 orthogonal views. The quantitative geometric results of the segmentation of ellipsoids can be exported as a csv file or as a binary image. The core of the code is based on an original computational approach to fit ellipsoids to point clouds in an affine invariant manner. The plugin is validated by segmenting a large number of 3D nuclei in tumor spheroids, allowing to analyze the distribution of their shapes. User experiments show that large collections of nuclei can be segmented with a high accuracy much faster than with more traditional 2D slice by slice delineation approaches. CONCLUSIONS: We designed a user-friendly software FitEllipsoid allowing to segment hundreds of ellipsoidal shapes in a supervised manner. It may be used directly to analyze biological samples, or to generate segmentation databases necessary to train learning algorithms. The algorithm is distributed as an open-source plugin to be used within the image analysis software Icy. We also provide a Matlab toolbox available with GitHub.

Extracting geometrical information from large 2D or 3D biomedical images is important to better understand fundamental phenomena such as morphogenesis. We address the problem of automatically analyzing spatial organization of cells or nuclei in 2D or 3D images of tissues. This problem is challenging due to the usually low quality of microscopy images as well as their typically large sizes. The structure tensor is a simple and robust descriptor that was developed to analyze textures orientation. Contrarily to segmentation methods which rely on an object based modeling of images, the structure tensor considers the sample at a macroscopic scale, like a continuous medium. We show that this tool allows quantifying two important features of nuclei in tissues: their privileged orientation as well as the ratio between the length of their main axes. A quantitative evaluation of the method is provided for synthetic and real 2D and 3D images. As an application, we analyze the nuclei orientation and anisotropy on multicellular tumor spheroids cryosections. This analysis reveals that cells are elongated in a privileged direction that is parallel to the spheroid boundary. A MATLAB toolbox and an Icy plugin are available to use the proposed method.

Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white noise setting. We recently proposed a variational algorithm to tackle this issue. In this paper, we analyze this problem from a statistical point of view and provide deterministic properties of the solutions of the associated variational problems. In the first part of this work, we demonstrate that in many practical problems, the noise can be assimilated to a colored Gaussian noise. We provide a quantitative measure of the distance between a stationary process and the corresponding Gaussian process. In the second part, we focus on the Gaussian setting and analyze denoising methods which consist in minimizing the sum of a total variation term and an $l^2$ data fidelity term. While the constrained formulation of this problem allows us to easily tune the parameters, the Lagrangian formulation can be solved more efficiently since the problem is strongly convex. Our second contribution consists in providing analytical values of the regularization parameter in order to approximately reach a given noise level.

Abstract While walking through a crowd, a pedestrian experiences a large number of interactions with his neighbors. The nature of these interactions is varied, and it has been observed that macroscopic phenomena emerge from the combination of these local interactions. Crowd models have hitherto considered collision avoidance as the unique type of interactions between individuals, few have considered walking in groups. By contrast, our paper focuses on interactions due to the following behaviors of pedestrians. Following is frequently observed when people walk in corridors or when they queue. Typical macroscopic stop‐and‐go waves emerge under such traffic conditions. Our contributions are, first, an experimental study on following behaviors, second, a numerical model for simulating such interactions, and third, its calibration, evaluation and applications. Through an experimental approach, we elaborate and calibrate a model from microscopic analysis of real kinematics data collected during experiments. We carefully evaluate our model both at the microscopic and the macroscopic levels. We also demonstrate our approach on applications where following interactions are prominent.

In human crowds as well as in many animal societies, local interactions among individuals often give rise to self-organized collective organizations that offer functional benefits to the group. For instance, flows of pedestrians moving in opposite directions spontaneously segregate into lanes of uniform walking directions. This phenomenon is often referred to as a smart collective pattern, as it increases the traffic efficiency with no need of external control. However, the functional benefits of this emergent organization have never been experimentally measured, and the underlying behavioral mechanisms are poorly understood. In this work, we have studied this phenomenon under controlled laboratory conditions. We found that the traffic segregation exhibits structural instabilities characterized by the alternation of organized and disorganized states, where the lifetime of well-organized clusters of pedestrians follow a stretched exponential relaxation process. Further analysis show that the inter-pedestrian variability of comfortable walking speeds is a key variable at the origin of the observed traffic perturbations. We show that the collective benefit of the emerging pattern is maximized when all pedestrians walk at the average speed of the group. In practice, however, local interactions between slow- and fast-walking pedestrians trigger global breakdowns of organization, which reduce the collective and the individual payoff provided by the traffic segregation. This work is a step ahead toward the understanding of traffic self-organization in crowds, which turns out to be modulated by complex behavioral mechanisms that do not always maximize the group's benefits. The quantitative understanding of crowd behaviors opens the way for designing bottom-up management strategies bound to promote the emergence of efficient collective behaviors in crowds.

A framework and an algorithm are presented in order to remove stationary noise from images. This algorithm is called variational stationary noise remover. It can be interpreted both as a restoration method in a Bayesian framework and as a cartoon+texture decomposition method. In numerous denoising applications, the white noise assumption fails. For example, structured patterns such as stripes appear in the images. The model described here addresses these cases. Applications are presented with images acquired using different modalities: scanning electron microscope, FIB-nanotomography, and an emerging fluorescence microscopy technique called selective plane illumination microscopy.

Topological asymptotic analysis provides tools to detect edges and their orientation. The purpose of this article is to show the possibilities of anisotropic topological gradient in image restoration. Previous methods based on the topological gradient used isotropic diffusion to restore images. These methods are improved here by using anisotropic diffusion and differentiating between principal and secondary edges. A texture detector is also used to increase the diffusion outside textured regions. Numerical results are presented, including a comparison with the Non-Local Means method. The algorithms presented here lead to results similar to the Non-Local Means (in terms of quality), and shorter processing times.

We discuss the reconstruction of the impedance from the local power density. This study is motivated by a new imaging principle which allows us to recover interior measurements of the energy density by a noninvasive method. We discuss the theoretical feasibility in two dimensions, and propose numerical algorithms to recover the conductivity in two and three dimensions. The efficiency of this approach is documented by several numerical simulations.