bwlabeln

Label connected components in binary image

Syntax

L = bwlabeln(BW)

L = bwlabeln(BW,conn)

[L,n] = bwlabeln(___)

Description

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

Calculate Centroids of 3-D Objects

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

BW — Binary image

numeric array | logical array

Binary image, specified as a numeric or logical array of any dimension. 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

conn — Pixel connectivity

4 | 8 | 6 | 18 | 26 | 3-by-3-by- ... -by-3 matrix of 0s and 1s

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	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.	Current pixel is shown in gray.
8	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.	Current pixel is shown in gray.
Three-Dimensional Connectivities
6	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	Current pixel is center of cube.
18	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	Current pixel is center of cube.
26	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	Current pixel is center of cube.

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 0s and 1s. 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

L — Label matrix

array of nonnegative integers

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

n — Number of connected objects

nonnegative integer

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

Data Types: double

Tips

• This function sorts the connected components from left to right based on the top-left extremum of each component. When multiple components have the same horizontal position, the function then sorts those components from top to bottom, and again along any higher dimensions. This figure illustrates the extrema of two different 2-D regions.

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

  Function	Input Dimension	Output Form	Memory Use	Connectivity
  bwlabel	2-D	Label matrix with double-precision	High	4 or 8
  bwlabeln	N-D	Double-precision label matrix	High	Any
  bwconncomp	N-D	CC struct	Low	Any

• To extract features from a binary image using regionprops with default connectivity, pass BW directly into regionprops using the command regionprops(BW).

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 [1].

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

References

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

Extended Capabilities

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.

Version History

Introduced before R2006a

R2022b: Support for thread-based environments

bwlabeln now supports thread-based environments.