As the first step of this study we developed the algorithm of detection of neuronal clusters using the approach known in Mathematical Morphology as “distance map”. The notion of the morphological distance map is based on metric defined by erosion (see, for example, a review “Mathematical Morphology and Distance map” by R.Kimmel in “Numerical Geometry of Images” pp 75-86) and successfully used in many applications for image classification, granulometry, analysis of spatial distribution of particles etc.
Fig.1. (Above) The distance map of segmented 1 micron-resolution section. Color codes the distance, increasing from red to pink. Black regions correspond to the initial segmented image.
To illustrate the approach, we demonstrate in Fig.1 the distance map of a fragment of 1 micron-resolution section of the area 19 of human cortex, obtained using MAMBA-Image library in Python. The initial image was segmented to identify neurons using the approach described in the “Segmentation” page. After segmentation the center of each neuron was found using ultimate erosion operator, with subsequent processing of the obtained set using isotropic distance function.
Fig.2. Clusters formed at the distance “20”
The obtained map can be thresholded at different levels to reveal clusters formed at a selected distance (Fig. 2). Similarly, clusters formed by a particular number of cells can be extracted as well. As an example, clusters formed by 10 to 20 cells are extracted, outlined and superimposed on the fragment of the original section (Fig. 3).
Fig.3. Outline of clusters formed by 10 to 20 cells.