# bwmorph

Morphological operations on binary images

## Syntax

``BW2 = bwmorph(BW,operation)``
``BW2 = bwmorph(BW,operation,n)``

## Description

example

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

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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

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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`).

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

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

Operation

Description

`'bothat'`

Performs the morphological “bottom hat” operation, returning the image minus the morphological closing of the image (dilation followed by erosion).

`'branchpoints'`

Find branch points of skeleton. For example:

```0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 becomes 0 0 0 0 0 1 1 1 1 1 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'`

Bridges 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'`

Removes 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'`

Performs morphological closing (dilation followed by erosion).

`'diag'`

Uses 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'`

Finds 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'`

Fills 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'`

Removes 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'`

Sets a pixel to `1` if five or more pixels in its 3-by-3 neighborhood are 1s; otherwise, it sets the pixel to `0`.

`'open'`

Performs morphological opening (erosion followed by dilation).

`'remove'`

Removes 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`, shrinks objects to points. It removes pixels so that 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`, removes pixels on the boundaries of objects but does not allow 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'`

Removes 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`, thickens 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`, thins objects to lines. It removes pixels so that 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'`

Performs morphological "top hat" operation, returning the image minus the morphological opening of the image (erosion followed by dilation).

Example: `BW3 = bwmorph(BW,'skel');`

Data Types: `char` | `string`

Number of times to perform the operation, specified as a numeric value. `n` can be `Inf`, in which case `bwmorph` repeats the operation until the image no longer changes.

Example: `BW3 = bwmorph(BW,'skel',100);`

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

## Output Arguments

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

Data Types: `logical`

## Tips

• To perform erosion or dilation, use the `imerode` or `imdilate` functions. If you want to duplicate the dilation or erosion performed by `bwmorph`, then specify the structuring element `ones(3)` with these functions.

## Algorithms

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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:

`${X}_{H}\left(p\right)=1$`

where

`${X}_{H}\left(p\right)=\sum _{i=1}^{4}{b}_{i}$`

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:

`$2\le \mathrm{min}\left\{{n}_{1}\left(p\right),{n}_{2}\left(p\right)\right\}\le 3$`

where

`${n}_{1}\left(p\right)=\sum _{k=1}^{4}{x}_{2k-1}\vee {x}_{2k}$`
`${n}_{2}\left(p\right)=\sum _{k=1}^{4}{x}_{2k}\vee {x}_{2k+1}$`

### Condition G3:

`$\left({x}_{2}\vee {x}_{3}\vee {\overline{x}}_{8}\right)\wedge {x}_{1}=0$`

### Condition G3':

`$\left({x}_{6}\vee {x}_{7}\vee {\overline{x}}_{4}\right)\wedge {x}_{5}=0$`

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.