Digital Image Processing, 3rd ed

Digital Image Processing, 3rd ed.

www.ImageProcessingPlace.com

Gonzalez & Woods

Chapter 9 Morphological Image Processing

The term morphology refers to the description of the properties of

shape and structure of any objects. Operations of mathematical

morphology were originally defined as operations on sets, but it

soon became clear that they are also useful in the processing tasks

of the set of points in the two-dimensional space. Sets in

mathematical morphology represent objects in the image. It is easy

to see that the set of all background pixels of binary image is one of

the options for a full description.

Mathematical morphology is used to extract some properties of the

image, useful for its presentation and descriptions. For example,

contours, skeletons and convex hulls. Also morphological methods

are used in the preliminary and final image processing. For

example, morphological filtering, thickening or thinning.

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Reflection and translation

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Basic Operations: union, intersection, complement, difference

Input Images

C = A ∪ B C = A ∩ B C = Ac C = A\B

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The input data for the mathematical

morphology are the two images: the

processed image and a structural

element.

Typically, a structural element is much

smaller than the processed. The shape of

the structured element can be arbitrary,

as long as it can be represented as a

binary image of a given size.

Structural Element

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The structural element, S, is applied to all pixels of binary image.

Every time the origin of the structural element is combined with a

single binary pixel, the entire structural element is wrapped and

subsequent alteration of the corresponding pixels of binary image.

The results of logical addition is written into the output binary image,

which was originally initialized to zero.

Gonzalez & Woods

Erosion

For erosion, the structural element passes through all pixels of the

image. The pixel corresponds to the reference of the structure element

is turned on if the entire structure element falls with foreground area

(pixels).

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Erosion examples

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Erosion examples

Image (486486) eroded using

squared structured element of

size 1111, 1515, 4545,

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Dilation example

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Hit-or-Miss Transformation

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Boundary Extraction

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Hole Filling

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Digital Image Processing, 3rd ed

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