Top Hat: binary case

Top Hat is the residue of the primitives identity and opening:

displaymath104

The top hat operator is very used in the segmentation process to extract shapes based on shape and size, both for binary and gray-level images. There are a large classes of top hats as the opening can be the algebraic definition.

Segmenting the teeth of a gear

In this experiment, we will use the simplest top hat which is the difference between the original image and its morphological opening. In this lesson a binary image is used as an example.

The goal is to extract and count the number of teeth of a gear. In the figure below, the original synthetic image of the gear is shown:

original

Below we show the opening by a disk structuring element of diameter 15, and we also show the top hat result.

a)opening; b)top hat
a) b)

To count the number of teeth, we can label the top hat image and find the maximum number of regions. In this case we have 24 teeth.





BRAZILIAN WORKSHOP'96 ON MATHEMATICAL MORPHOLOGY