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imerode

Erode image

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Syntax

J = imerode(I,SE)
J = imerode(I,nhood)
J = imerode(___,packopt,m)
J = imerode(___,shape)

Description

J = imerode(I,SE) erodes the grayscale, binary, or packed binary image I using the structuring element SE.

example

J = imerode(I,nhood) erodes the image I, where nhood is a matrix of 0s and 1s that specifies the structuring element neighborhood.

This syntax is equivalent to imerode(I,strel(nhood)).

J = imerode(___,packopt,m) specifies whether input image I is a packed binary image. m specifies the row dimension of the original unpacked image.

J = imerode(___,shape) specifies the size of the output image.

Examples

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Open Live Script

Read binary image into the workspace.

originalBW = imread('text.png');

Create a flat, line-shaped structuring element.

se = strel('line',11,90);

Erode the image with the structuring element.

erodedBW = imerode(originalBW,se);

View the original image and the eroded image. 

figure
imshow(originalBW)

Figure contains an axes object. The hidden axes object contains an object of type image.

figure
imshow(erodedBW)

Figure contains an axes object. The hidden axes object contains an object of type image.

Open Live Script

Read grayscale image into the workspace.

originalI = imread('cameraman.tif');

Create a nonflat offsetstrel object.

se = offsetstrel('ball',5,5);

Erode the image.

erodedI = imerode(originalI,se);

Display original image and eroded image.

figure
imshow(originalI)

Figure contains an axes object. The hidden axes object contains an object of type image.

figure
imshow(erodedI)

Figure contains an axes object. The hidden axes object contains an object of type image.

Open Live Script

Create a binary volume.

load mristack
BW = mristack < 100;

Create a cubic structuring element.

se = strel('cube',3)
se = 
strel is a cube shaped structuring element with properties:

      Neighborhood: [3x3x3 logical]
    Dimensionality: 3

Erode the volume with a cubic structuring element. 

erodedBW = imerode(BW, se);

Input Arguments

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Input image, specified as a grayscale image, binary image, or packed binary image of any dimension.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical

Structuring element, specified as a scalar strel object or offsetstrel object. SE can also be an array of strel object or offsetstrel objects, in which case imerode performs multiple erosions of the input image, using each structuring element in succession.

imerode performs grayscale erosion for all images except images of data type logical. In this case, the structuring element must be flat and imerode performs binary erosion.

Structuring element neighborhood, specified as a matrix of 0s and 1s.

Example: [0 1 0; 1 1 1; 0 1 0]

Indicator of packed binary image, specified as one of the following.

Value

Description

'notpacked'

I is treated as a normal array.

'ispacked'

I is treated as a packed binary image as produced by bwpack. I must be a 2-D uint32 array and SE must be a flat 2-D structuring element. The value of shape must be 'same'.

Data Types: char | string

Row dimension of the original unpacked image, specified as a positive integer.

Data Types: double

Size of the output image, specified as one of the following.

Value

Description

'same'

The output image is the same size as the input image. If the value of packopt is 'ispacked', then shape must be 'same'.

'full'

Compute the full erosion.

Data Types: char | string

Output Arguments

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Eroded image, returned as a grayscale image, binary image, or packed binary image. If the input image I is packed binary, then J is also packed binary. J has the same data type as I.

More About

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Binary Erosion

The binary erosion of A by B, denoted A ϴ B, is defined as the set operation A ϴ B = {z|(Bz ⊆ A}. In other words, it is the set of pixel locations z, where the structuring element translated to location z overlaps only with foreground pixels in A.

For more information on binary erosion, see [1].

Grayscale Erosion

In the general form of grayscale erosion, the structuring element has a height. The grayscale erosion of A(x, y) by B(x, y) is defined as:

(A ϴ B)(x, y) = min {A(x + x′, y + y′) − B(x′, y′) | (x′, y′) ∊ DB},

DB is the domain of the structuring element B and A(x,y) is assumed to be +∞ outside the domain of the image. To create a structuring element with nonzero height values, use the syntax strel(nhood,height), where height gives the height values and nhood corresponds to the structuring element domain, DB.

Most commonly, grayscale erosion is performed with a flat structuring element (B(x,y) = 0). Grayscale erosion using such a structuring element is equivalent to a local-minimum operator:

(A ϴ B)(x, y) = min {A(x + x′, y + y′) | (x′, y′) ∊ DB}.

All of the strel syntaxes except for strel(nhood,height), strel('arbitrary',nhood,height), and strel('ball', ...) produce flat structuring elements.

Tips

  • If the dimensionality of the image I is greater than the dimensionality of the structuring element, then the imerode function applies the same morphological erosion to all planes along the higher dimensions.

    You can use this behavior to perform morphological erosion on RGB images. Specify a 2-D structuring element for RGB images to operate on each color channel separately.

  • When you specify a structuring element neighborhood, imerode determines the center element of nhood by floor((size(nhood)+1)/2).

  • imerode automatically takes advantage of the decomposition of a structuring element object (if it exists). Also, when performing binary erosion with a structuring element object that has a decomposition, imerode automatically uses binary image packing to speed up the erosion [3].

References

[1] Gonzalez, Rafael C., Richard E. Woods, and Steven L. Eddins. Digital Image Processing Using MATLAB. Third edition. Knoxville: Gatesmark Publishing, 2020.

[2] Haralick, Robert M., and Linda G. Shapiro. Computer and Robot Vision. 1st ed. USA: Addison-Wesley Longman Publishing Co., Inc., 1992, pp. 158-205.

[3] Boomgaard, Rein van den, and Richard van Balen. “Methods for Fast Morphological Image Transforms Using Bitmapped Binary Images.” CVGIP: Graphical Models and Image Processing 54, no. 3 (May 1, 1992): 252–58. https://doi.org/10.1016/1049-9652(92)90055-3.

Extended Capabilities

Version History

Introduced before R2006a

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See Also

Functions

Objects