# bwlabeln

Label connected components in binary image

## Syntax

``L = bwlabeln(BW)``
``L = bwlabeln(BW,conn)``
``[L,n] = bwlabeln(___)``

## Description

example

````L = bwlabeln(BW)` returns a label matrix, `L`, containing labels for the connected components in `BW`.```
````L = bwlabeln(BW,conn)` returns a label matrix, where `conn` specifies the connectivity.```
````[L,n] = bwlabeln(___)` also returns `n`, the number of connected objects found in `BW`.```

## Examples

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Create simple sample 3-D binary image.

```BW = cat(3, [1 1 0; 0 0 0; 1 0 0],... [0 1 0; 0 0 0; 0 1 0],... [0 1 1; 0 0 0; 0 0 1])```
```BW = BW(:,:,1) = 1 1 0 0 0 0 1 0 0 BW(:,:,2) = 0 1 0 0 0 0 0 1 0 BW(:,:,3) = 0 1 1 0 0 0 0 0 1 ```

Label connected components in the image.

`bwlabeln(BW)`
```ans = ans(:,:,1) = 1 1 0 0 0 0 2 0 0 ans(:,:,2) = 0 1 0 0 0 0 0 2 0 ans(:,:,3) = 0 1 1 0 0 0 0 0 2 ```

## Input Arguments

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Binary image, specified as a numeric or logical array of any dimension. For numeric input, any nonzero pixels are considered to be `on`.

Example: `BW = imread('text.png');`

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

Pixel connectivity, specified as one of the values in this table. The default connectivity is `8` for 2-D images, and `26` for 3-D images.

Value

Meaning

Two-Dimensional Connectivities

4-connected

Pixels are connected if their edges touch. Two adjoining pixels are part of the same object if they are both on and are connected along the horizontal or vertical direction. 8-connected

Pixels are connected if their edges or corners touch. Two adjoining pixels are part of the same object if they are both on and are connected along the horizontal, vertical, or diagonal direction. Three-Dimensional Connectivities

6-connected

Pixels are connected if their faces touch. Two adjoining pixels are part of the same object if they are both on and are connected in:

• One of these directions: in, out, left, right, up, and down 18-connected

Pixels are connected if their faces or edges touch. Two adjoining pixels are part of the same object if they are both on and are connected in

• One of these directions: in, out, left, right, up, and down

• A combination of two directions, such as right-down or in-up 26-connected

Pixels are connected if their faces, edges, or corners touch. Two adjoining pixels are part of the same object if they are both on and are connected in

• One of these directions: in, out, left, right, up, and down

• A combination of two directions, such as right-down or in-up

• A combination of three directions, such as in-right-up or in-left-down For higher dimensions, `bwlabeln` uses the default value `conndef(ndims(BW),'maximal')`.

Connectivity can also be defined in a more general way for any dimension by specifying a 3-by-3-by- ... -by-3 matrix of `0`s and `1`s. The `1`-valued elements define neighborhood locations relative to the center element of `conn`. Note that `conn` must be symmetric about its center element. See Specifying Custom Connectivities for more information.

Data Types: `double` | `logical`

## Output Arguments

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Label matrix, returned as an array of nonnegative integers with the same size as `BW`. The pixels labeled `0` are the background. The pixels labeled `1` make up one object; the pixels labeled `2` make up a second object; and so on.

Data Types: `double`

Label matrix of contiguous regions, returned as a 2-D array of nonnegative integers of class `double`. The kth region includes all elements in `L` that have value k. The number of objects and holes represented by `L` is equal to `max(L(:))`. The zero-valued elements of `L` make up the background.

Data Types: `double`

Number of connected objects in `BW`, returned as a nonnegative integer.

Data Types: `double`

## Tips

• The functions `bwlabel`, `bwlabeln`, and `bwconncomp` all compute connected components for binary images. `bwconncomp` replaces the use of `bwlabel` and `bwlabeln`. It uses significantly less memory and is sometimes faster than the other functions.

FunctionInput DimensionOutput FormMemory UseConnectivity
`bwlabel`2-DLabel matrix with double-precisionHigh4 or 8
`bwlabeln`N-DDouble-precision label matrixHighAny
`bwconncomp`N-D`CC` structLowAny
• To extract features from a binary image using `regionprops` with default connectivity, just pass `BW` directly into `regionprops`, i.e. `regionprops(BW)`.

• To compute a label matrix having a more memory-efficient data type (e.g., `uint8` versus `double`), use the `labelmatrix` function on the output of `bwconncomp`:

```C = bwconncomp(BW); L = labelmatrix(CC); CC = bwconncomp(BW,n); S = regionprops(CC);```

## Algorithms

`bwlabeln` uses the following general procedure:

1. Scan all image pixels, assigning preliminary labels to nonzero pixels and recording label equivalences in a union-find table.

2. Resolve the equivalence classes using the union-find algorithm .

3. Relabel the pixels based on the resolved equivalence classes.

 Sedgewick, Robert, Algorithms in C, 3rd Ed., Addison-Wesley, 1998, pp. 11-20.