  The size of nuclei in histological preparations from excised breast tumors is
predictive of patient outcome (large nuclei indicate poor outcome).
Pathologists take into account nuclear size when performing breast cancer
grading. In addition, the mean nuclear area (MNA) has been shown to have
independent prognostic value. The straightforward approach to measuring nuclear
size is by performing nuclei segmentation. We hypothesize that given an image
of a tumor region with known nuclei locations, the area of the individual
nuclei and region statistics such as the MNA can be reliably computed directly
from the image data by employing a machine learning model, without the
intermediate step of nuclei segmentation. Towards this goal, we train a deep
convolutional neural network model that is applied locally at each nucleus
location, and can reliably measure the area of the individual nuclei and the
MNA. Furthermore, we show how such an approach can be extended to perform
combined nuclei detection and measurement, which is reminiscent of
granulometry.
