Various methods for serial-section reconstruction from images of tissue sections have been investigated using the Apple Macintosh- based program Triakis. Triakis is a three-dimensional mathematical morphology software package that processes 3-D binary data in the FCC (face centered cubic) tessellation by means of LUT (look-up table) manipulations. Tissue sections have been obtained from a breast tumor and traced using PC3-D $LB@Jandel Scientific, Corte Madera, Calif.$RB were transferred via a software interface to Triakis. Triakis uses the Apple Macintosh polygon filling routine to fill each tracing with binary ones. Next, ranking transforms in the binary FCC tessellation were used in order to demonstrate their capability of smoothly interpolating from one section to the other. The optimum transform is based on the placement of the binarized tissue sections in hexagonal planes and uses three cycles of a rank three transform for the initial interpolation. Irregularities are then removed from the resulting solid by seven cycles of a compound transform. Thereafter, the filled polygons were eroded using Triakis and, from the annular histogram, the spatial interrelationships of malignant cells within the tumor determined.
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