20060925-Dilation, erosion, and the morphological gradient

本文探讨了形态学运算在图像处理中的核心作用,特别是膨胀和腐蚀操作如何结合形成形态学梯度,以及如何利用不同类型的梯度来增强边界识别。详细介绍了基本形态学梯度、内部梯度和外部梯度的概念,并通过MATLAB和Image Processing Toolbox提供了实际的计算方法。

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原文:http://blogs.mathworks.com/steve/2006/09/25/dilation-erosion-and-the-morphological-gradient/

The morphological operator dilation acts like a local maximum operator. Erosion acts like a local minimum operator. You can use them together to compute something called the morphological gradient.

Dilation

The basic form of grayscale image dilation computes, for each image pixel, the maximum value of its neighboring pixels. The neighborhood is defined by the structuring element. For example, this structuring element:

se1 = strel([1 1 1])
defines a neighborhood consisting of the pixel itself, together with its left and right neighbors.

Erosion

Grayscale image erosion computes the minimum of each pixel's neighborhood.

Morphological gradient

Dilation and erosion are often used in combination to produce a desired image processing effect. One simple combination is the morphological gradient. P. Soille, in section 3.8 of the second edition of Morphological Image Analysis: Principles and Applications, talks about three kinds of basic morphological gradients:

  • dilated_image - eroded_image
  • original_image - eroded_image
  • dilated_image - original_image

Soille calls the first one the basic morphological gradient, and you compute it this way using MATLAB and the Image Processing Toolbox:

The second form is called the half-gradient by erosion or internal gradient.

"The internal gradient enhances internal boundaries of objects brighter than their background and external boundaries of objects darker than their background. For binary images, the internal gradient generates a mask of the internal boundaries of the foreground image objects." [Soille, page 86]

The third form is called the half-gradient by dilation or external gradient:

Direction gradients

By using line segments as structuring elements, you can compute directional gradients.

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