Opera hat described as: Some sources have taken this to describe an early folding top hat, although it is not explicitly stated whether Dollman's design was specifically for male or female headgear. Dollman's patent expired in 1825. Operating from Poissy, Paris, France, around 1840, Antoine Gibus's design for a spring-loaded collapsible top-hat proved so popular that hats made to it became known as "gibus". They were also often called "opera hats" due to the common practice of storing them in their flattened state under one's seat at the opera, though the term can also refer to any tall formal men's hat. The
Top-hat transform grid "E" (such as "R" or "Z") into the real line. Let formula_2 be a grayscale structuring element. Then, the white top-hat transform of "f" is given by: where formula_4 denotes the opening operation. The black top-hat transform of "f" (sometimes called the "bottom-hat" transform ) is given by: where formula_6 is the closing operation. The white top-hat transform returns an image, containing those "objects" or "elements" of an input image that: The black top-hat returns an image, containing the "objects" or "elements" that: The size, or width, of the elements that are extracted by the top-hat transforms can be