3 Image segmentation

The identification of granular structures has been carried out as shown in Hirzberger et al. (1997) based on a Fourier filtering method developed by Roudier & Muller (1987). The constants of the Fourier filter have been tuned such that the resulting granular shapes match intensity inflection points best as calculated by the application of a Laplacian operator. Again as in Hirzberger et al. (1997) the remaining intergranular lanes outside the detected granular areas have been split into two halves, each "belonging'' to its neighbouring granule. Hence, a granular cell can be defined as a granule plus its surrounding part of the intergranular lanes, i.e. the total cell area is $A_{\rm c}=A_{\rm g}+A_{\rm ig}$.

Figure 1: Broad band image (upper panel) and granular areas obtained with the Fourier segmentation algorithm (middle panel). The lower panel shows absolute values of the horizontal intensity gradient in the broad band image. Tickmarks are at distances of $1^{\prime \prime }$.

Only the broad band images have been segmented in the above mentioned way. An example is shown in Fig. 1. The fractional granular area amounts to 47.7% of the total area. This value is strongly dependent on the applied image segmentation algorithm which has to be taken into account when interpreting the results. In the literature much smaller values (e.g. 39% by Roudier & Muller 1987) but also much larger values (e.g. 60% by Bovelet & Wiehr 2001) can be found. Since for the present study flow maps are available, the detected fractional granular area can be compared with the fractional upflow area in the velocity maps. As shown in Sect. 4 below, the numbers exhibit a good agreement although after a one to one comparison between granular and upflow areas some differences can be detected. The reason for these differences might be: (i) intrinsic differences between broad band intensities and flow velocities; (ii) different formation heights of the broad band intensities and the line asymmetries used for calculating the flow maps; (iii) a slightly better spatial resolution of the broad band data compared to the flow maps (see Hirzberger et al. 2001); (iv) residual non-convective velocities which have not been removed by the applied subsonic filter.

For the statistical analysis all granules truncated by the image boundaries and structures with $A_{\rm g}\leq 9$ pixel have been removed. After that 5509 granules detected in the broad band images are remaining.