A photometric study of umbral bright features (umbral dots, clusters of umbral dots, bright grains of light bridges) in sunspots is presented. It is based on white-light images taken with a CCD video camera driven by an automatic image selection system. A direct linear relation between the observed brightness of the features and that of the surrounding background areas has been found. To eliminate the influence of the seeing on this result, the radiative fluxes, which are much less sensitive to the image degradation, have been examined and an analogous relation has been found. Finally, a possible physical explanation is suggested.