Mathematical Definitions
Let be a grayscale image, mapping points from an Euclidean space or discrete grid E (such as R2 or Z2) into the real line. Let be a grayscale structuring element.
Then, the white top-hat transform of f is given by:
- ,
where denotes the opening operation.
The black top-hat transform of f is given by:
- ,
where is the closing operation.
Read more about this topic: Top-hat Transform
Famous quotes containing the words mathematical and/or definitions:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)