Nuclear grading of neoplasms has classically been involved in prognosis and must be established by combining different parameters, such as the textural pattern of chromatin, which is subjective and difficult to measure. Mathematical morphology (MM), a branch of mathematics dealing with shapes, and, in particular, the so-called top hat transformation, provides us with a helpful tool for quantitative assessment of chromatin texture. A sequence of MM operations (the top-hat transformation) was applied to Mayer-hematoxylin-stained cytologic smears made immediately after surgical removal to obtain a series of images at different levels of a granulometric chromatin fractionation. These images are related to the size (n = 1, 2, 4, 6 and 8) of a structuring element that performs these operations. A skeletonization of the intergranular area at level 4 was also performed to provide a shape-related image of chromatin grains. Using these granulometric images as a starting point, we defined a series of variables: TH(n) as the granulometric area at top-hat level n; GAD(n) as the grain-associated density at level n; THIOD(n) as the integrated optical density of the granular fraction at level(n); GIOD(n) as the grain-integrated optical density at level n; CP as a chromatin texture variable, chromatin pattern, that estimates the granular versus dispersed aggregation pattern; and CB, a shape descriptor that estimates the roughness of the isolated chromatin grains and is expressed as a coefficient related to the number of branches of the intergranular skeleton. The operation provides a set of variables descriptive of a wide range of chromatin texture properties.(ABSTRACT TRUNCATED AT 250 WORDS)