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A connected component in a binary image is a set of pixels that form a connected group. For example, the binary image below has three connected components.

Connected component labeling is the process of identifying the connected components in an image and assigning each one a unique label, like this:

The matrix above is called a *label matrix*.

`bwconncomp`

computes connected components, as shown in the
example:

cc = bwconncomp(BW) cc = Connectivity: 8 ImageSize: [8 9] NumObjects: 3 PixelIdxList: {[6x1 double] [6x1 double] [5x1 double]}

The `PixelIdxList`

identifies the list of pixels belonging to
each connected component.

For visualizing connected components, it is useful to construct a label matrix.
Use the `labelmatrix`

function. To inspect the results, display the
label matrix as a pseudo-color image using `label2rgb`

.

Construct a label matrix:

labeled = labelmatrix(cc);

Create a pseudo-color image, where the label identifying each object in the label
matrix maps to a different color in the associated `colormap`

matrix. Use `label2rgb`

to choose the colormap, the background
color, and how objects in the label matrix map to colors in the
colormap:

RGB_label = label2rgb(labeled, @copper, 'c', 'shuffle'); imshow(RGB_label,'InitialMagnification','fit')

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 older
functions.

Function | Input Dimension | Output Form | Memory Use | Connectivity |
---|---|---|---|---|

`bwlabel` | 2-D | Double-precision label matrix | High | 4 or 8 |

`bwlabeln` | N-D | Double-precision label matrix | High | Any |

`bwconncomp` | N-D | `CC` struct | Low | Any |

You can use the `bwselect`

function to select individual objects
in a binary image. You specify pixels in the input image, and
`bwselect`

returns a binary image that includes only those
objects from the input image that contain one of the specified pixels.

You can specify the pixels either noninteractively or with a mouse. For example, suppose you want to select objects in the image displayed in the current axes. You type

BW2 = bwselect;

The cursor changes to cross-hairs when it is over the image. Click the objects you
want to select; `bwselect`

displays a small star over each pixel
you click. When you are done, press **Return**.
`bwselect`

returns a binary image consisting of the objects you
selected, and removes the stars.

See the reference page for `bwselect`

for more
information.

The `bwarea`

function returns the area of a binary image. The
area is a measure of the size of the foreground of the image. Roughly speaking, the
area is the number of `on`

pixels in the image.

`bwarea`

does not simply count the number of pixels set to
`on`

, however. Rather, `bwarea`

weights
different pixel patterns unequally when computing the area. This weighting
compensates for the distortion that is inherent in representing a continuous image
with discrete pixels. For example, a diagonal line of 50 pixels is longer than a
horizontal line of 50 pixels. As a result of the weighting `bwarea`

uses, the horizontal line has area of 50, but the diagonal line has area of
62.5.

This example uses `bwarea`

to determine the percentage area
increase in `circbw.tif`

that results from a dilation
operation.

BW = imread('circbw.tif'); SE = ones(5); BW2 = imdilate(BW,SE); increase = (bwarea(BW2) - bwarea(BW))/bwarea(BW) increase = 0.3456

See the reference page for `bwarea`

for more information about
the weighting pattern.

The `bweuler`

function returns the Euler number for a binary
image. The Euler number is a measure of the topology of an image. It is defined as
the total number of objects in the image minus the number of holes in those objects.
You can use either 4- or 8-connected neighborhoods.

This example computes the Euler number for the circuit image, using 8-connected neighborhoods.

BW1 = imread('circbw.tif'); eul = bweuler(BW1,8) eul = -85

In this example, the Euler number is negative, indicating that the number of holes is greater than the number of objects.