We designed a strategy for extracting the shapes of cell membranes and nuclei from time lapse confocal images taken throughout early zebrafish embryogenesis using a partial-differential-equation-based segmentation. This segmentation step is a prerequisite for an accurate quantitative analysis of cell morphodynamics during embryogenesis and it is the basis for an integrated understanding of biological processes. The segmentation of embryonic cells requires live zebrafish embryos fluorescently labeled to highlight sub-cellular structures and designing specific algorithms by adapting classical methods to image features. Our strategy includes the following steps: the signal-to-noise ratio is first improved by an edge-preserving filtering, then the cell shape is reconstructed applying a fully automated algorithm based on a generalized version of the Subjective Surfaces technique. Finally we present a procedure for the algorithm validation either from the accuracy and the robustness perspective.

In this paper we reconsider the sub-Riemannian cortical model of image completion introduced in [16,61]. This model combines two mechanisms, the sub-Riemannian diffusion and the concentration, giving rise to a diffusion driven motion by curvature. In this paper we give a formal proof of the existence of viscosity solutions of the sub-Riemannian motion by curvature. Furthermore we illustrate the sub-Riemannian finite difference scheme used to implement the model and we discuss some properties of the algorithm. Finally results of completion and enhancement on a number of natural images are shown and compared with other models.A model expressed by a system of two equations, one responsible for boundary extraction, and one for figure completion was proposed by Bertalmio, Sapiro, Caselles, and Ballester in [3]. In Sarti et al [63] the role of the observer was considered, letting evolve by curvature in the Riemannian metric associated to the image a fixed surface called point of view surface.

In this paper, we propose to model the edge information contained in natural scenes as points in the 3D space of positions and orientations. This space is equipped with a strong geometrical structure and it is identified as the rototranslation group. In this space, we compute a histogram of co-occurrence of edges from a database of natural images and show that it can be interpreted as a probability density function, expressed by the fundamental solution of a suitable Fokker-Planck equation defined in the 3D structured space. Both estimated statistics and model predictions are reconsidered and compared with the partial gestalt association fields proposed by D. J. Field, A. Hayes, and R. F. Hess (1993). Finally, parametric identification allows to estimate the variance of the co-occurrence random process in natural images.