In this paper, a new criterion for early diagnostics of lymphatic system tumor from images of cell nuclei of lymphatic nodes is considered. A method for image analysis of chromatin structure is developed on the basis of the scale-space approach. A diagnostically important criterion is defined as a total amount of points of spatial intensity extrema in the families of blurred images generated by the given image of a cell nucleus. The procedure for calculating criterion values is presented. Testing of the obtained criterion is carried out.