imerode

Erode image

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.

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

Erode Binary Image with Line Structuring Element

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
imshow(erodedBW)

Erode Grayscale Image with Rolling Ball

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
imshow(erodedI)

Erode MRI Stack Volume Using Cubic Structuring Element

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

I — Input image

grayscale image | binary image | packed binary image

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

SE — Structuring element

strel object | offsetstrel object | array of strel objects | array of offsetstrel objects

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.

nhood — Structuring element neighborhood

matrix of 0s and 1s

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

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

packopt — Indicator of packed binary image

'notpacked' (default) | 'packed'

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

m — Row dimension of original unpacked image

positive integer

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

Data Types: double

shape — Size of output image

'same' (default) | 'full'

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

J — Eroded image

grayscale image | binary image | packed binary image

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

Binary Erosion

The binary erosion of A by B, denoted A ϴ B, is defined as the set operation A ϴ B = {z|(B_z ⊆ 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′) ∊ D_B},

D_B 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, D_B.

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′) ∊ D_B}.

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

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• imerode supports the generation of C code (requires MATLAB^® Coder™). Note that if you choose the generic MATLAB Host Computer target platform, imerode generates code that uses a precompiled, platform-specific shared library. Use of a shared library preserves performance optimizations but limits the target platforms for which code can be generated. For more information, see Types of Code Generation Support in Image Processing Toolbox.

• The input image, I, must be 2-D or 3-D.

• The structuring element argument SE must be a single element——arrays of structuring elements are not supported. To obtain the same result as that obtained using an array of structuring elements, call the function sequentially.

• When the target is MATLAB Host Computer, the packopt and shape arguments must be compile-time constants. When the target is any other platform, the packopt syntax is not supported.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• The input image I must be 2-D or 3-D.

• Packed binary input images (packopt syntax) are not supported.

• For 3-D input images with more than three channels, only C/C++ code is generated.

• The structuring element argument SE must be a compile-time constant. CUDA^® code is generated only for 1-D or 2-D structuring elements. If the structuring element is 3-D, C/C++ code is generated. Code generation is not supported for structuring elements with more than three dimensions.

• For non-flat structuring elements, only C/C++ code is generated.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• gpuArray input must be of type uint8 or logical

• The structuring element SE must be flat and 2-D.

• The packopt argument is not supported on the GPU.

For more information, see Image Processing on a GPU.

Version History

Introduced before R2006a

R2022b: Support for thread-based environments

imerode now supports thread-based environments.