1 Introduction

Sunspots and sunspot groups are the most conspicuous features of solar activity. They appear as dark areas in the photosphere of the sun, with sizes and numbers that vary in the 11-year cycle and they are caused by a lower surface temperature.  
The area covered by the sunspot is one of the most relevant parameters used to investigate the solar activity since the sunspot number is only an empirical index. In many occasions a phase delay between the value of the sunspot number and the projected areas of sunspots has been observed (e.g. Pap 1985). There is some recent evidence pointing to a relation between magnetic field strength, continuum intensity and sunspot size (Collados et al. 1994). The ratio of the sunspot and facular areas is linked with the age of the active regions (young or old sunspot groups) (Pap 1985). The energy balance of individual active regions seems to depend mainly on the area ratio of the plage and the corresponding sunspot group (Steinegger et al. 1996). During the solar minimum, when only a few active regions exist on the Sun, the main contribution to the irradiance variations arises from the active network, which is formed by the breakup and dispersion of the active regions (Fröhlich & Pap 1989).
The determination of sunspot area becomes more complicated when one attempts to separate the individual areas of umbra and penumbra. Steinegger et al. (1997) compare two methods of measuring sunspot areas from photospheric observations; one based on histogram modifications and a new method termed inflexion point method (IPM).  
Therefore, it is of great importance to isolate the basic characteristics of the sunspot or sunspot group, in order to compare them with active regions and to study the results of solar activity. In ${\rm H}_{\alpha}$, the chromosphere is particularly bright and the matter is apparently dominated by the chromospheric magnetic field lines.  
The purpose of segmentation is to divide the image into meaningful regions that correspond to structural units in the scene or distinguish objects of interest. In this case it could be useful if one wants to isolate automatically the basic characteristics of the sunspot or sunspot group and study their relation with solar activity using ${\rm H}_{\alpha}$ observations.  
The segmentation is separated here in two stages, the classification in q labels (Sect. 2) and the relaxation labeling process (Sect. 3).