A Skeletonizing Algorithm for Granulation and Supergranuation Cell Finding

ARNALDO FLORIO ¹, FRANCESCO BERRILLI ²

In this paper we describe a new algorithm to extract the boundaries of granulation cells (GC) and supergranulation cells (SGC) from white light and Ca K images respectively. The cells edges are defined by the skeleton of dark intergranular lanes (GC) and by the skeleton of chromospheric network (SGC). The algorithm, based on a Medial Axis Transformation, uses intensity information of solar image and a cellular automaton to cut off unconnected cell boundaries. A cell filling procedure is used to calculate different geometrical properties of recognized cells.

Several numerical algorithms have been developed to define cells (Roudier and Muller 1987, Title et al. 1989, Hirzberger et al. 1997, Schrijver, Hagenar and Title 1997). The fast algorithm presented here is able to separate different cells on the basis of intensity information and to measure their geometrical properties. A simple way to analyze the structural shape of a region is to reduce it to a graph. This can be made by obtaining the skeleton, first proposed by Blum (1967), of the region. The skeleton is also called medial axis because the pixels are located at midpoints or along local symmetrical axes of the region. The skeleton of the region, that should be 1 pixel thick uniformly, may be obtained with thinning procedures applied on a binary image (a two-level image where the pixel set to '1' are representative of the region, and the background points are set to '0'). The present parallel algorithm, based on that published by Zhang and Suen (1984), obtains a skeleton that p reserve the connectivity present in the pattern. We add to the original algorithm an iterative process that modifies the binary images in order to take into account intensity information.

The procedure is applied on images that have been corrected for electronics offset, thermal dark current, flat field response and in which the spatial low frequency trends are removed.

The thinning algorithm, iteratively applied to subsequent binary images, consists of successive iterations of two basic steps, applied to the contour points, to select pixels to be deleted. A contour point is any pixel with value 1 having at least one 8-neighbour valued '0'. The algorithm uses masks in order to select pixels to be deleted. The 8 closest neighbours are numbered following a clockwise walk around the pixel P, starting at the upper edge:

P₈ P₁ P₂

P₇ P P₃

P₆ P₅ P₄

the first step flags a contour point P for deletion if the following conditions are satisfied:

S (P_i) = 1

where S(P_i) is the number of 0-1 transitions in the ordered sequence from P₁ to P₈.In the second step the flagged points P are deleted if the first two conditions and the further following conditions are satisfied:

The first binary image is obtained using a suitable dynamical threshold value. The subsequent ones are built using as starting patterns the skeletons obtained in the previous iteration and iteratively adding the pixels connected to pixels set to '1' and having an associated intensity value less or equal, for GC, or greater or equal, for SGC, of 8-neighbours intensity mean value. In this way the binary images, and therefore the resulting skeletons, take into account intensity information contained in the solar image. The iterative process stops when changes on a new skeleton became negligible to respect to the previous one.At the end of this process, when required, the unconnected cell boundaries or branches can be cut off applying successive iterations of a Cellular Automaton Filter.

Figure 1: A white light granulation field obtained at the NSO-VTT telescope. a) the original image; b) the starting binary image; c) the final skeleton superimposed on the original image; d) the different identified cells.

We define 'cell' a group of adjacent, connected pixels contained in a region whose edges are defined by the skeleton.

We develop a procedure in order to fill the cells based on region growing by pixel aggregation. After the stacking of the addresses of background pixels of the skeletonized image, the contiguous horizontal or vertical pixel of the starting one (the 'seed') is filled in if is a background pixel. The algorithm proceeds iteratively using as a new seed the pixel at the top of the stack. When the stack is empty, the algorithm terminates and we can calculate for each identified cell the following geometrical properties: the perimeter, as the number of skeleton pixel sides that border the cell; the area, as the number of pixels with the same label; the barycenter as the center of mass of the above pixels; the axes in the horizontal, vertical, and diagonal directions with respect to the barycenter; the average radius as derived from the above axes.

The proposed algorithm extracts informations on granular cells using the skeleton of dark intergranular lanes, and informations on supergranular cells using the skeleton as representative of the chromospheric network. There are several procedures to characterize the skeleton of a region that differ from each other in performance and in implementation. This algorithm has been tested on 180 Ca K 256 x 256 pixels images and the whole procedure has been completed, identifying and measuring about 60000 cells, in less than two hours using FORTRAN programs on a 200 MHz PC.

The whole procedure above described has been applied on white light images based on observations at the THEMIS-IPM (Berrilli et al. 1997), at the NSO/SP Vacuum Tower to study the cellular pattern of granulation cells (Cauzzi et al. 1998); and of Ca II K images obtained at the OAR-PSPT to study the geometrical properties of chromospheric network (Berrilli, Florio and Ermolli 1998, Berrilli et al. 1998).

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