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 on.

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

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-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 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

L — Label matrix

2-D array of nonnegative integers

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

n — Number of connected objects

nonnegative integer

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.

  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, 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 [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.