This chapter describes operators 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.
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.
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) |
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) |
ModePercentModePercentModePercentModePercentModePercentIn the following list, the most important terms that are used in the context of Morphology are described.
Operator which does not necessarily preserve structures of the input image
Region which is used to scan the input image.
dual_rankgen_disc_segray_bothatgray_closinggray_closing_rectgray_closing_shapegray_dilationgray_dilation_rectgray_dilation_shapegray_erosiongray_erosion_rectgray_erosion_shapegray_openinggray_opening_rectgray_opening_shapegray_range_rectgray_tophatread_gray_se