Operator Reference
Gray Values
This chapter describes operators of gray value morphology.
Concept of Gray Value Morphology
Gray value morphology provides a set of operators that allow the non-linear manipulation of gray values in an image, depending on their pixel neighborhood. For instance, morphological gray value operators can be used to smooth or emphasize structural features in images. Unlike the binary operations in Morphology / Region, morphological gray value operators deal with input images that contain pixels with a range of more than one bit. Therefore gray value morphology can be seen as a generalization of region morphology. In the following paragraphs, we will take a closer look at the morphological gray value operators.
Dilation and Erosion of a Grayscale Image
To perform a dilation or erosion, each pixel of the image is assigned a gray value depending on its neighborhood. Area and shape of the neighborhood affecting each pixel are defined by the chosen structuring element with the current pixel being the reference point. Implementing a dilation, every pixel of the input image is assigned the maximum gray value of its neighborhood, respectively the minimum gray value for an erosion. Accordingly, bright areas of the input image are enlarged by gray value dilation, whereas gray value erosion emphasizes dark areas.
| ( 1) | ( 2) | ( 3) | ( 4) |
These operators can be used to dilate or erode an image:
| Morphological Operator | Structuring Element | |
|---|---|---|
|
|
arbitrary |
|
|
rectangular |
|
|
rhombus/rectangle/octagon |
Morphological grayscale operations are often part of the preprocessing of
images before information can be extracted properly. The following example
displays a case where a gray value erosion is necessary to read data code
symbols. In order to fit a data model used for decoding, the gaps between
the code elements in the image need to be reduced by enlarging local minima
in a square shape. Therefore a gray value erosion is performed, using an
adequately sized rectangle as the structuring element. The rectangle size
depends on the data model created with create_data_code_2d_model
| ( 1) | ( 2) | ( 3) |
2d_data_codes_minimize_module_gaps.hdev.
Opening and Closing
Gray value opening and gray value closing operators each are a combination
of the operators explained above. Closing is a dilation followed by an
erosion, while for an opening an erosion precedes a dilation operation.
As seen in the example images, gray_closinggray_opening
| ( 1) | ( 2) | ( 3) | ( 4) |
Further Operators
To take a closer look at areas that are affected by gray value opening or
closing, you can perform a gray_tophatgray_bothat
The gray_range_rect
| ( 1) | ( 2) | ( 3) |
By applying the gray_range_rectModePercent
| ( 1) | ( 2) | ( 3) | ( 4) | ( 5) |
ModePercentModePercentModePercentModePercentModePercentGlossary
In the following list, the most important terms that are used in the context of Morphology are described.
- non-linear operator
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Operator which does not necessarily preserve structures of the input image
- structuring element
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Region which is used to scan the input image.
List of Operators
dual_rank- Opening, Median and Closing with circle or rectangle mask.
gen_disc_se- Generate ellipsoidal structuring elements for gray morphology.
gray_bothat- Perform a gray value bottom hat transformation on an image.
gray_closing- Perform a gray value closing on an image.
gray_closing_rect- Perform a gray value closing with a rectangular mask.
gray_closing_shape- Perform a gray value closing with a selected mask.
gray_dilation- Perform a gray value dilation on an image.
gray_dilation_rect- Determine the maximum gray value within a rectangle.
gray_dilation_shape- Determine the maximum gray value within a selected mask.
gray_erosion- Perform a gray value erosion on an image.
gray_erosion_rect- Determine the minimum gray value within a rectangle.
gray_erosion_shape- Determine the minimum gray value within a selected mask.
gray_opening- Perform a gray value opening on an image.
gray_opening_rect- Perform a gray value opening with a rectangular mask.
gray_opening_shape- Perform a gray value opening with a selected mask.
gray_range_rect- Determine the gray value range within a rectangle.
gray_tophat- Perform a gray value top hat transformation on an image.
read_gray_se- Load a structuring element for gray morphology.