4 Results and discussion

We want to quantize an image into nicely connected areas, so that isolated pixels, or small isolated areas with a gray level different from their background can be eliminated.

As far as dynamics is concerned, we choose a serial mode in which the local field, in each site, is computed immediately before the corresponding site state is updated. We use raster examination, starting at each sweep from the upper left image pixel and finishing with the lower one. When the system converges we display, taking for every site s, the maximal probability from every state q.  
With N sites and q label values (gray levels), MFFA needs O(qN) updates at a fixed temperature while the stochastic Simulated Annealing requires O[(q^N )²] such steps (Acton & Bovik 1996; Bratsolis & Sigelle 1997).  
${\rm H}_{\alpha}$ images are usually so complicated that a simple histogram modification is not sufficient to separate the regions of different activity. In this paper we have presented a method of combinatorial optimization to separate our image in different classes. Previous methods used in photospheric images (e.g. Steinegger et al. 1997), separate the images in three classes - umbra, penumbra and photospheric background - for the measure of sunspot areas. Here we have described how MFFA can be used as a method of segmentation of images previously classified in any number of classes. We have considered a synthetic example in which degradation arose through the simple superposition of uniform label channel noise. After a small number of sweeps (eight in our case) we obtain very good results.

The importance of solar image segmentation is evident because the knowledge of the spatial (on the solar disk) and time variability of sunspots, faculae, network and quiet-Sun is essential to understand the solar cycle (Steinegger et al. 1996). The segmentations of solar images could be considered as a first stage of automated recognition and classification of sunspots, something that we intend to investigate in future work.

Acknowledgements

The authors are grateful to Dr. A. Georgakilas of the Astronomical Institute of National Observatory of Athens for the sunspot image and Dr. T. Roudier for his critical review and suggestions to improve the paper.