Morphological Gradient Operator


This morphological operator is a composition of three basic operators: a dilation, an erosion of the input image by the input structuring element and a subtraction of these two results.

In the example bellow, the input image (figure 2) is dilated by the structuring element seen on figure 1, resulting the image shown on figure 3. The same input image is eroded by the same structuring element than before and the result is seen in the image shown on figure 4. The image on figure 5, the final result, is the morphological subtraction of the dilation and the erosion.

One important application of the morphologic gradient in binary images is to find their bounderies.

      0 1 0
      1 1 1  fig 1. Structuring element used
      0 1 0

fig. 2 - Input image

fig. 3 - The Dilation

fig. 4 - The Erosion

fig. 5 - The Subtraction

The same operator applied to graylevel images, but without filtering it does not produce good results because it is very sensible to noise. Figure 6 show a gray scale image and figure 7 its gradient (negated in order to show the details of the image), using the 3x3 square as structural element.

fig. 6 - Input image

fig. 7 - Negation of the gradient.



Back to the initial page