Optimising adjacent membrane segmentation and parameterisation in multicellular aggregates by piecewise active contours

In fluorescence microscopy imaging, the segmentation of adjacent cell membranes within cell aggregates, multicellular samples, tissue, organs, or whole organisms remains a challenging task. The lipid bilayer is a very thin membrane when compared to the wavelength of photons in the visual spectra. Fluorescent molecules or proteins used for labelling membranes provide a limited signal intensity, and light scattering in combination with sample dynamics during in vivo imaging lead to poor or ambivalent signal patterns that hinder precise localisation of the membrane sheets. In the proximity of cells, membranes approach and distance each other. Here, the presence of membrane protrusions such as blebs; filopodia and lamellipodia; microvilli; or membrane vesicle trafficking, lead to a plurality of signal patterns, and the accurate localisation of two adjacent membranes becomes difficult. Several computational methods for membrane segmentation have been introduced. However, few of them specifically consider the accurate detection of adjacent membranes. In this article we present ALPACA (ALgorithm for Piecewise Adjacent Contour Adjustment), a novel method based on 2D piecewise parametric active contours that allows: (i) a definition of proximity for adjacent contours, (ii) a precise detection of adjacent, nonadjacent, and overlapping contour sections, (iii) the definition of a polyline for an optimised shared contour within adjacent sections and (iv) a solution for connecting adjacent and nonadjacent sections under the constraint of preserving the inherent cell morphology. We show that ALPACA leads to a precise quantification of adjacent and nonadjacent membrane zones in regular hexagons and live image sequences of cells of the parapineal organ during zebrafish embryo development. The algorithm detects and corrects adjacent, nonadjacent, and overlapping contour sections within a selected adjacency distance d, calculates shared contour sections for neighbouring cells with minimum alterations of the contour characteristics, and presents piecewise active contour solutions, preserving the contour shape and the overall cell morphology. ALPACA quantifies adjacent contours and can improve the meshing of 3D surfaces, the determination of forces, or tracking of contours in combination with previously published algorithms. We discuss pitfalls, strengths, and limits of our approach, and present a guideline to take the best decision for varying experimental conditions for in vivo microscopy.