A curvicylindrical coordinate system for the visualization and segmentation of the ascidian tail

State of the art biological imaging methods, such as confocal microscopy, create 3D volumes by sampling on a cartesian grid. This cartesian coordinate system is often not convenient for visualization and analysis of multi layered organs or tissues. The ascidian embryonic tail, for example, is organized along anterioposterior (AP), dorsoventral (DV) and left-right (LR) axes that are locally orthogonal but curved in the XYZ microscope space. Here, we propose a “curvicylindrical” coordinate system for analysis of such biological structures. By extracting representative paths that traverse different tissue layers, the embryo can be visualized in a small number of 2D images (3 images in the case of the ascidian tail). As we demonstrate, this reduction of the dimensionality from 3D to 2D facilitates the initialization process for high quality segmentation of different cell types, and identification of tissue boundaries.