Gray Values

List of Operators ↓

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)
(1) Original gray value image, (2) structuring element with reference point in the origin, (3) result of eroding the input image, (4) result of dilating the input image.

These operators can be used to dilate or erode an image:

Morphological Operator Structuring Element
gray_dilationgray_dilationGrayDilationGrayDilationGrayDilationgray_dilation gray_erosiongray_erosionGrayErosionGrayErosionGrayErosiongray_erosion arbitrary
gray_dilation_rectgray_dilation_rectGrayDilationRectGrayDilationRectGrayDilationRectgray_dilation_rect gray_erosion_rectgray_erosion_rectGrayErosionRectGrayErosionRectGrayErosionRectgray_erosion_rect rectangular
gray_dilation_shapegray_dilation_shapeGrayDilationShapeGrayDilationShapeGrayDilationShapegray_dilation_shape gray_erosion_shapegray_erosion_shapeGrayErosionShapeGrayErosionShapeGrayErosionShapegray_erosion_shape 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_modelcreate_data_code_2d_modelCreateDataCode2dModelCreateDataCode2dModelCreateDataCode2dModelcreate_data_code_2d_model, where the acceptable module gap size is determined.

(1) (2) (3)
(1) Image of coded object, (2) erosion with square structuring element, (3) applying data model for decoding. These images are from the example program 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_closingGrayClosingGrayClosingGrayClosinggray_closing reduces or even removes parts of the image that are darker than their neighborhood whereas gray_openinggray_openingGrayOpeningGrayOpeningGrayOpeninggray_opening reduces lighter areas. Furthermore, using a suited structuring element you can preserve shapes while removing unwanted image artifacts.

(1) (2) (3) (4)
(1) Original gray value image, (2) structuring element with reference point in the origin, (3) result of closing the input image, (4) result of opening the input image.

Further Operators

To take a closer look at areas that are affected by gray value opening or closing, you can perform a gray_tophatgray_tophatGrayTophatGrayTophatGrayTophatgray_tophat or gray_bothatgray_bothatGrayBothatGrayBothatGrayBothatgray_bothat transformation. The resulting image displays the difference between the original image and the opening respectively closing of an image. You can also use these operators to detect structures that match the shape of the structuring element.

The gray_range_rectgray_range_rectGrayRangeRectGrayRangeRectGrayRangeRectgray_range_rect operator gives you the opportunity to detect fine structures on homogeneous surfaces by visualizing the extent of local variations in pixel values.

(1) (2) (3)
(1) Top hat, (2) bottom hat, (3) gray value range.

By applying the gray_range_rectgray_range_rectGrayRangeRectGrayRangeRectGrayRangeRectgray_range_rect operator you can perform a mitigated form of a gray value opening or closing operation. You can control the transformation by adjusting the parameter ModePercentModePercentModePercentModePercentmodePercentmode_percent.

(1) (2) (3) (4) (5)
Dual rank operations: (1) ModePercentModePercentModePercentModePercentmodePercentmode_percent = 0 (equals opening), (2) ModePercentModePercentModePercentModePercentmodePercentmode_percent = 25, (3) ModePercentModePercentModePercentModePercentmodePercentmode_percent = 50 (equals median), (4) ModePercentModePercentModePercentModePercentmodePercentmode_percent = 75, (5) ModePercentModePercentModePercentModePercentmodePercentmode_percent = 100 (equals closing).


In the following list, the most important terms that are used in the context of Morphology are described.

non-linear operator

Operator which does not necessarily preserve structures of the input image

structuring element

Region which is used to scan the input image.

List of Operators

Opening, Median and Closing with circle or rectangle mask.
Generate ellipsoidal structuring elements for gray morphology.
Perform a gray value bottom hat transformation on an image.
Perform a gray value closing on an image.
Perform a gray value closing with a rectangular mask.
Perform a gray value closing with a selected mask.
Perform a gray value dilation on an image.
Determine the maximum gray value within a rectangle.
Determine the maximum gray value within a selected mask.
Perform a gray value erosion on an image.
Determine the minimum gray value within a rectangle.
Determine the minimum gray value within a selected mask.
Perform a gray value opening on an image.
Perform a gray value opening with a rectangular mask.
Perform a gray value opening with a selected mask.
Determine the gray value range within a rectangle.
Perform a gray value top hat transformation on an image.
Load a structuring element for gray morphology.