Concept – 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)

(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_dilationGrayDilation`	`gray_erosionGrayErosion`	arbitrary
`gray_dilation_rectGrayDilationRect`	`gray_erosion_rectGrayErosionRect`	rectangular
`gray_dilation_shapeGrayDilationShape`	`gray_erosion_shapeGrayErosionShape`	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 2D code symbols. In order to fit a 2d code 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 2D code model created with create_data_code_2d_modelCreateDataCode2dModel, where the acceptable module gap size is determined.



(1)	(2)	(3)

(1) Image of coded object, (2) erosion with square structuring element, (3) applying 2D code 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_closingGrayClosing reduces or even removes parts of the image that are darker than their neighborhood whereas gray_openingGrayOpening 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_tophatGrayTophat or gray_bothatGrayBothat 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_rectGrayRangeRect 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_rectGrayRangeRect operator you can perform a mitigated form of a gray value opening or closing operation. You can control the transformation by adjusting the parameter ModePercentmodePercentmode_percent.



(1)	(2)	(3)	(4)	(5)

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

Glossary🔗

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.