Thickening is a morphological operation that is used to grow selected regions of foreground pixels in binary images, somewhat like dilation or closing.

It has several applications, including determining the approximate convex hull of a shape, and determining the skeleton by zone of influence.

Thickening is normally only applied to binary images, and it produces another binary image as output.

The thickening operation is related to the hit-and-miss transform.

How It Works

• Like other morphological operators, the behavior of the thickening operation is determined by a structuring element.
• The binary structuring elements used for thickening are of the extended type described under the hit-and-miss transform (i.e. they can contain both ones and zeros).
• The thickening operation is related to the hit-and-miss transform and can be expressed quite simply in terms of it.

• The thickening of an image I by a structuring element J is:

  thicken(I,J) = I ∪ hit and miss(I,J)

• Thus the thickened image consists of the original image plus any additional foreground pixels switched on by the hit-and- miss transform.

• In everyday terms, the thickening operation is calculated by translating the origin of the structuring element to each possible pixel position in the image, and at each such position comparing it with the underlying image pixels.
• If the foreground and background pixels in the structuring element exactly match foreground and background pixels in the image, then the image pixel underneath the origin of the structuring element is set to foreground (one).
• Otherwise it is left unchanged. Note that the structuring element must always have a zero or a blank at its origin if it is to have any effect.
• The choice of structuring element determines under what situations a background pixel will be set to foreground, and hence it determines the application for the thickening operation.
• We have described the effects of a single pass of a thickening operation over the image. In fact, the operator is normally applied repeatedly until it causes no further changes to the image (i.e. until convergence).
• Alternatively, in some applications, the operations may only be applied for a limited number of iterations.
• Thickening is the dual of thinning, i.e. thinning the foreground is equivalent to thickening the background.
• In fact, in most cases thickening is performed by thinning the background.