Imaging and mathematical modelling of cell morphology and motility

In order to precisely segment and extract the cell shape from image data, we have been focusing on the past years on the theory of deformable models, also known as “active contours” techniques. The principle is to deform an initial contour placed on the image until it fits the boundary of the target cell. The deformation can be mathematically expressed as the minimization of an energy functional, which comprises several terms related either to the image data (driving the contour toward the cell boundary) or to geometrical properties of the contour (regularizing the deformation to avoid local energy minima). This energy is an essential ingredient of the method, and several of our contributions consist in adapting this energy and its implementation to meet the particular constraints of biological imaging, e.g., low signal-to-noise ratio, multiple cell-cell contacts over time, inhomogeneous cell staining, photo-bleaching, etc.. Active contours also offer a flexible formalism for efficient shape representation and quantification, allowing to compute robust statistics over large-scale cell populations. The algorithms developed for this project are currently used through collaborations for numerous applications including multi-cell segmentation, tracking, interaction and particle localization.