SEGMENTATION OF MACROPHAGES ON A QUADTREE GRID USING THE P4EST LIBRARY

Abstract

The paper proposes the numerical schemes applied in the process of segmentation of
macrophages on a quad-tree 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 more trees into ”forest” (”4est”) and applying the parallelism
is possible (”p4est”). The segmentation methods used can be solved with PDEs com-
monly 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 quad-tree. From the numerical point of view, the
extension to the forest is straightforwad.Description of the library’s principles with
respect to the grid generation, its elements iteration, refining, coarsening and balanc-
ing the grid with help of so calledcall-backfunctions and parallelism can be found in
more details, e.g., in [6],[19].