bwmorph

Morphological operations on binary images

Syntax

BW2 = bwmorph(BW,operation)

BW2 = bwmorph(BW,operation,n)

Description

BW2 = bwmorph(BW,operation) applies a specific morphological operation to the binary image BW.

Note

To perform morphological operations on a 3-D volumetric image, use bwmorph3.

BW2 = bwmorph(BW,operation,n) applies the operation n times. n can be Inf, in which case the operation is repeated until the image no longer changes.

Examples

Perform Morphological Operations on Binary Image

Read binary image and display it.

BW = imread('circles.png');
imshow(BW);

Remove interior pixels to leave an outline of the shapes.

BW2 = bwmorph(BW,'remove');
figure
imshow(BW2)

Get the image skeleton.

BW3 = bwmorph(BW,'skel',Inf);
figure
imshow(BW3)

Input Arguments

BW — Binary image

2-D numeric matrix | 2-D logical matrix

Binary image, specified as a 2-D numeric matrix or 2-D logical matrix. For numeric input, any nonzero pixels are considered to be 1 (true).

operation — Morphological operation to perform

character vector | string scalar

Morphological operation to perform, specified as one of the following.

Operation	Description
"bothat"	Perform the morphological bottom hat operation, returning the image minus the morphological closing of the image. The bwmorph function performs morphological closing using the neighborhood ones(3). If you want to perform a morphological bottom hat operation with a different neighborhood, then use the imbothat function.
"branchpoints"	Find branch points of skeleton. For example: 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 becomes 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Note: To find branch points, the image must be skeletonized. To create a skeletonized image, use bwmorph(BW,"skel").
"bridge"	Bridge unconnected pixels, that is, sets 0-valued pixels to 1 if they have two nonzero neighbors that are not connected. For example: 1 0 0 1 1 0 1 0 1 becomes 1 1 1 0 0 1 0 1 1
"clean"	Remove isolated pixels (individual 1s that are surrounded by 0s), such as the center pixel in this pattern. 0 0 0 0 1 0 0 0 0
"close"	Perform morphological closing (dilation followed by erosion). The bwmorph function performs morphological closing using the neighborhood ones(3). If you want to perform a morphological closing operation with a different neighborhood, then use the imclose function.
"diag"	Use diagonal fill to eliminate 8-connectivity of the background. For example: 0 1 0 0 1 0 1 0 0 becomes 1 1 0 0 0 0 0 0 0
"endpoints"	Find end points of skeleton. For example: 1 0 0 0 1 0 0 0 0 1 0 0 becomes 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 Note: To find end points, the image must be skeletonized. To create a skeletonized image, use bwmorph(BW,"skel").
"fill"	Fill isolated interior pixels (individual 0s that are surrounded by 1s), such as the center pixel in this pattern. 1 1 1 1 0 1 1 1 1
"hbreak"	Remove H-connected pixels. For example: 1 1 1 1 1 1 0 1 0 becomes 0 0 0 1 1 1 1 1 1
"majority"	Set a pixel to 1 if five or more pixels in its 3-by-3 neighborhood are 1; otherwise, set the pixel to 0.
"open"	Perform morphological opening (erosion followed by dilation). The bwmorph function performs morphological opening using the neighborhood ones(3). If you want to perform a morphological opening operation with a different neighborhood, then use the imopen function.
"remove"	Remove interior pixels. This option sets a pixel to 0 if all its 4-connected neighbors are 1, thus leaving only the boundary pixels on.
"shrink"	With n = Inf, shrink objects to points by removing pixels from the boundaries of objects. Objects without holes shrink to a point, and objects with holes shrink to a connected ring halfway between each hole and the outer boundary. This option preserves the Euler number (also known as the Euler characteristic).
"skel"	With n = Inf, remove pixels on the boundaries of objects without allowing objects to break apart. The pixels remaining make up the image skeleton. This option preserves the Euler number. When working with 3-D volumes, or when you want to prune a skeleton, use the bwskel function.
"spur"	Remove spur pixels. For example: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 becomes 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0
"thicken"	With n = Inf, thicken objects by adding pixels to the exterior of objects until doing so would result in previously unconnected objects being 8-connected. This option preserves the Euler number.
"thin"	With n = Inf, thin objects to lines by removing pixels from the boundary of objects. An object without holes shrinks to a minimally connected stroke, and an object with holes shrinks to a connected ring halfway between each hole and the outer boundary. This option preserves the Euler number. See Algorithms for more detail.
"tophat"	Perform the morphological top hat operation, returning the image minus the morphological opening of the image. The bwmorph function performs morphological opening using the neighborhood ones(3). If you want to perform a morphological top hat operation with a different neighborhood, then use the imtophat function.

Tip

To perform morphological erosion or dilation, use the imerode or imdilate function, respectively. If you want to replicate the dilation or erosion performed by the bwmorph function, then specify the neighborhood as ones(3).

Data Types: char | string

n — Number of times to perform operation

positive integer | Inf

Number of times to perform the operation, specified as a positive integer or Inf. When you specify n as Inf, the bwmorph function repeats the operation until the image no longer changes.

Example: 100

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

BW2 — Image after morphological operations

2-D logical matrix

Image after morphological operations, returned as a 2-D logical matrix.

Data Types: logical

Algorithms

When used with the "thin" option, bwmorph uses the following algorithm [3]:

1. In the first subiteration, delete pixel p if and only if the conditions G₁, G₂, and G₃ are all satisfied.

2. In the second subiteration, delete pixel p if and only if the conditions G₁, G₂, and $$G_3\prime$$ are all satisfied.

Condition G1:

$$X_H(p)=1$$

where

$$X_H(p)={\displaystyle \sum _{i=1}^4{b}_i}$$

$$b_i=\{\begin{array}{c}1,\text{ if }{x}_{2i-1}=0\text{ and }(x_{2i}=1\text{ or }{x}_{2i+1}=1)\\ 0\text{, otherwise }\end{array}$$

x₁, x₂, ..., x₈ are the values of the eight neighbors of p, starting with the east neighbor and numbered in counter-clockwise order.

Condition G2:

$$2\le \min \left\{n_1(p),n_2(p)\right\}\le 3$$

where

$$n_1(p)={\displaystyle \sum _{k=1}^4{x}_{2k-1}\vee x_{2k}}$$

$$n_2(p)={\displaystyle \sum _{k=1}^4{x}_{2k}\vee x_{2k+1}}$$

Condition G3:

$$(x_2\vee x_3\vee {\overline{x}}_8)\wedge x_1=0$$

Condition G3':

$$(x_6\vee x_7\vee {\overline{x}}_4)\wedge x_5=0$$

The two subiterations together make up one iteration of the thinning algorithm. When the user specifies an infinite number of iterations (n=Inf), the iterations are repeated until the image stops changing. The conditions are all tested using applylut with precomputed lookup tables.

References

[1] Haralick, Robert M., and Linda G. Shapiro, Computer and Robot Vision, Vol. 1, Addison-Wesley, 1992.

[2] Kong, T. Yung and Azriel Rosenfeld, Topological Algorithms for Digital Image Processing, Elsevier Science, Inc., 1996.

[3] Lam, L., Seong-Whan Lee, and Ching Y. Suen, "Thinning Methodologies-A Comprehensive Survey," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 14, No. 9, September 1992, page 879, bottom of first column through top of second column.

[4] Pratt, William K., Digital Image Processing, John Wiley & Sons, Inc., 1991.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• bwmorph supports the generation of C code (requires MATLAB^® Coder™). Note that if you choose the generic MATLAB Host Computer target platform, bwmorph 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.

• When generating code, the character vectors or string scalars specifying the operation must be a compile-time constant and, for best results, the input image must be of class logical.

GPU Code Generation

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

Usage notes and limitations:

• When generating code, the character vectors or string scalars specifying the operation must be a compile-time constant and, for best results, the input image must be of class logical.

GPU Arrays

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

This function fully supports GPU arrays. For more information, see Image Processing on a GPU.

Version History

Introduced before R2006a