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.

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

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_modelCreateDataCode2dModelCreateDataCode2dModelCreateDataCode2dModel, where the acceptable module gap size is determined.

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_closingGrayClosingGrayClosingGrayClosing reduces or even removes parts of the image that are darker than their neighborhood whereas gray_openinggray_openingGrayOpeningGrayOpeningGrayOpening reduces lighter areas. Furthermore, using a suited structuring element you can preserve shapes while removing unwanted image artifacts.

Further Operators

To take a closer look at areas that are affected by gray value opening or closing, you can perform a gray_tophatgray_tophatGrayTophatGrayTophatGrayTophat or gray_bothatgray_bothatGrayBothatGrayBothatGrayBothat 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_rectGrayRangeRectGrayRangeRectGrayRangeRect operator gives you the opportunity to detect fine structures on homogeneous surfaces by visualizing the extent of local variations in pixel values.

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

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.

List of Operators

dual_rankDualRankDualRankdual_rank

Opening, Median and Closing with circle or rectangle mask.

gen_disc_seGenDiscSeGenDiscSegen_disc_se

Generate ellipsoidal structuring elements for gray morphology.

gray_bothatGrayBothatGrayBothatgray_bothat

Perform a gray value bottom hat transformation on an image.

gray_closingGrayClosingGrayClosinggray_closing

Perform a gray value closing on an image.

gray_closing_rectGrayClosingRectGrayClosingRectgray_closing_rect

Perform a gray value closing with a rectangular mask.

gray_closing_shapeGrayClosingShapeGrayClosingShapegray_closing_shape

Perform a gray value closing with a selected mask.

gray_dilationGrayDilationGrayDilationgray_dilation

Perform a gray value dilation on an image.

gray_dilation_rectGrayDilationRectGrayDilationRectgray_dilation_rect

Determine the maximum gray value within a rectangle.

gray_dilation_shapeGrayDilationShapeGrayDilationShapegray_dilation_shape

Determine the maximum gray value within a selected mask.

gray_erosionGrayErosionGrayErosiongray_erosion

Perform a gray value erosion on an image.

gray_erosion_rectGrayErosionRectGrayErosionRectgray_erosion_rect

Determine the minimum gray value within a rectangle.

gray_erosion_shapeGrayErosionShapeGrayErosionShapegray_erosion_shape

Determine the minimum gray value within a selected mask.

gray_openingGrayOpeningGrayOpeninggray_opening

Perform a gray value opening on an image.

gray_opening_rectGrayOpeningRectGrayOpeningRectgray_opening_rect

Perform a gray value opening with a rectangular mask.

gray_opening_shapeGrayOpeningShapeGrayOpeningShapegray_opening_shape

Perform a gray value opening with a selected mask.

gray_range_rectGrayRangeRectGrayRangeRectgray_range_rect

Determine the gray value range within a rectangle.

gray_tophatGrayTophatGrayTophatgray_tophat

Perform a gray value top hat transformation on an image.

read_gray_seReadGraySeReadGraySeread_gray_se

Load a structuring element for gray morphology.