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:
“An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.”
—Susan Faludi (20th century)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)