Segmentation of Macrophages on a Quadtree Grid Using the p4est Library

Abstract The paper proposes the numerical schemes applied in the macrophage segmentation process on a quadtree grid, generated adaptively with respect to intensity of the data. Because the data are sparse and, in general, distinctly rectangular images, to generate the mesh the library ‘p4est’ (parallel forest) has been selected. The library offers tools to connect multiple trees into a ‘forest’ (‘4est’), enabling parallel processing (‘p4est’). The segmentation methods used canbe solvedwith PDEs commonly used in image processing, the linear heat equation and the modified SUBSURF model, for which we proposed explicit and semi-implicit schemes based on the finite volume space discretisation. The choice of numerical algorithms is adapted to the way the grid elements are iterated in the environment of the library. In this paper we focus on a single quadtree. From the numerical point of view, the extension to the forest is straightforward. Description of the library’s principles with respect to the grid generation, its elements iteration, refining, coarsening and balancing the grid with the help of so-called callback functions and parallelism can be found in more detail, e.g., in [7], [8].