J = imerode(I,SE) erodes the grayscale, binary, or packed binary image I, returning the eroded image, J. SE is a structuring element object or array of structuring element objects, returned by the strel or offsetstrel functions.

You optionally can perform the erosion using a GPU (requires Parallel Computing Toolbox™).

J = imerode(I,nhood) erodes the image I, where nhood is a matrix of 0s and 1s that specifies the structuring element neighborhood. The imerode function determines the center element of the neighborhood by floor((size(nhood)+1)/2).

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.

This syntax is not supported on a GPU.

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


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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.



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.



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.


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.



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




I is treated as a normal array.


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.




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


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 class 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|(BzA}. 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.


imerode automatically takes advantage of the decomposition of a structuring element object (if a decomposition 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.

Erosion using bit packing is described in [3].


[1] Gonzalez, R. C., R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, Gatesmark Publishing, 2009.

[2] Haralick, Robert M., and Linda G. Shapiro, Computer and Robot Vision, Vol. I, Addison-Wesley, 1992, pp. 158-205.

[3] van den Boomgard, R, and R. van Balen, "Methods for Fast Morphological Image Transforms Using Bitmapped Images," Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, Vol. 54, Number 3, pp. 254-258, May 1992.

Extended Capabilities

See Also



Introduced before R2006a