Image Processing and Cancer Detection

Statistical Analysis

A trend of particular interest is the plot of a cell's Run Length Features. Run Length is a term describing the number of contiguous pixels displaying the same optical density value. (Optical density is the -log₁₀ of the Transmission, or amount of light passing through the sample.) Observation of surrounding pixels provides a more detailed account of the goings-on within a cell. Since high grade cancers are associated with increased granularity, the distribution of dark pixel values becomes important.

Another useful diagnostic tool is the Discriminant Function. Discriminant Analysis can be used to establish a "threshold" value beyond which suspect nuclei would be considered cancerous. The threshold is set at zero, with positive numbers indicating abnormally high feature values. Statistical analysis allows for the evaluation of nearly one hundred measurable features and the elimination of those that do not discriminate between cancerous and non-cancerous cells. In the end, twelve to fifteen key features are incorporated into a stepwise discriminant algorithm as follows:

Discriminant Function:

Normal: D=1.1057(fea002) - 0.0027(fea305) + 0.001(fea307) + 348.2396(fea313) - 0.0043(fea319) - 0.1033(fea320) - 21.5103

D < threshold: nucleus from normal tissue
D >= threshhold: nucleus from DCIS

It is important to note that some samples from DCIS cells (light blue) fall below the statistically determined threshold for malignancy. Discriminant Analysis provides guidelines by which to differentiate between different cells, but is not a conclusive indicator of cancer.