After completing this lesson, learners should be able to:
Understand how objects in images are represented as a label mask image.
Apply connected component labeling to a binary image to create a label mask image.
Motivation
A main task of bioimage analysis is to detect objects in images. To do so one needs to be able to label pixels that are part of the same object in a way that this can be efficiently stored and processed by the computer. A prevalent way of doing this is connected component labeling, which is discussed in this module.
Concept map
graph TD
BI("Binary image") -->|input|CC("Connected component analysis")
C("Connectivity") -->|parameter|CC
OD("Output data type") -->|parameter|CC
CC -->|output|LI("Label image")
LI -->|display with|MCL("Multi color LUT")
LI -->|content|PV("Integer pixel values")
PV --> BG("0: Background")
PV --> R1("1: Region 1")
PV --> R2("2: Region 2")
PV --> R3("...")
Figure
Connected components
A typical workflow is to first categorise an image into background and foreground regions, which can be represented as a binary image. If there are more than one object of interest, cluster of pixels which are spatially connected to each other can be assigned a same pixel value. Such clusters in the segmented image can be called as connected components. The relation between two or more pixels is described by its connectivity. The next step is a connected components labeling, where spatially connected regions of foreground pixels are assigned (labeled) as being part of one region (object).
Connectivity
In an image, pixels are ordered in a squared configuration.
For performing a connected component analysis, it is important to define which pixels are considered direct neighbors of a pixel. This is called connectivity and defines which pixels are considered connected to each other.
Essentially the choice is whether or not to include diagonal connections.
Or, in other words, how many orthogonal jumps to you need to make to reach a neighboring pixel; this is 1 or an orthogonal neighbor and 2 for a diagonal neighbor.
This leads to the following equivalent nomenclatures:
# Import modules
importnaparifromskimage.ioimportimread# Instantiate the napari viewer
viewer=napari.Viewer()# Read a binary 2D image
binary_2D_image=imread('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit_binary__nuclei.tif')viewer.add_image(binary_2D_image)# Connected components with connectivity 1 (aka 2D 4 connectivity)
fromskimageimportmeasurelabels_2D_conn1_image=measure.label(binary_2D_image,connectivity=1)viewer.add_labels(labels_2D_conn1_image)# Connected components with connectivity 2 (aka 2D 8 connectivity)
labels_2D_conn2_image=measure.label(binary_2D_image,connectivity=2)viewer.add_labels(labels_2D_conn2_image)# Read a binary 3D image
binary_3D_image=imread('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xyz_8bit_binary__spots.tif')# Connected components with connectivity 2 (aka 3D 26 connectivity)
labels_3D_conn2_image=measure.label(binary_3D_image,connectivity=2)viewer.add_labels(labels_3D_conn2_image)# Interrogate the values in the 3D label image
print(np.unique(labels_3D_conn2_image))# the object indices
print(len(np.unique(labels_3D_conn2_image))-1)# the number of objects (minus background)
print(np.max(labels_3D_conn2_image))# the number of objects (minus background) (if the labels are consecutive!)
np.sum(labels_3D_conn2_image==2)# the number of pixels (~volume) in object number 2