The reproducible classification of poorly differentiated abnormal epithelium specimens is still a diagnostic problem. The computer-aided method described here improves the differentiation between benign and malignant epithelium specimens. Hematoxylin and eosin-stained sections of normal squamous epithelium, dysplasia, carcinoma in situ, and carcinoma were scanned in a TV microscope system and analyzed by means of image processing methods on a DEC 5000/200 workstation. From the 15-20 microns thick histological sections, 3-5 focus positions in steps of 1-4 microns were scanned. The segmentation of the cell nuclei was performed automatically by color analysis and geometric operations. For each nucleus the best focus level was selected and at this level the center of the cell was calculated. Graph theoretical methods were applied to analyze the morphometry of the epithelium specimens. The minimal spanning tree was computed in the three-dimensional (3D) space of the sections with the selected centers of the nuclei as vertices. The best feature found for discrimination of the specimens is the average length of all edges in a tree. In the two-dimensional (2D) analysis we had to accept an error probability of about 20% in differentiation of dysplasia and carcinoma. In contrast to this we differentiated normal squamous epithelium, dysplasia, and carcinoma with a correct classification rate of 100% in the 3D analysis.