Connected Components

Since the characteristics selected as important are geometric in nature, the Connected Components Data (CC) [1] of the image will be used as the basic data element instead of the image pixels. The rationale is that the same degree of information can be obtained from the CC information as from the image data itself, but with a great gain in simplicity and performance.

The basic concepts behind the construction of the CC data are the following:

• An 8-connected component is a set of neighboring pixels of the same color such that any pixel in the set can be reached from any other pixel in the set by only passing through pixels contained in the set. The eight possible directions (N, S, W, E, NE, SE, SW, NW) can be used to travel within the set. Figure 3.7 shows the difference between 8-connected and 4-connected components.
  

  

  Figure 3.7: Connected Components

• A connected component box, also known as the minimum bounding rectangle, is the smallest rectangle that completely encloses an 8-connected component. Figure 3.7 exemplifies this concept.
  

  

  

  

  Figure 3.7: Width-Height Map (histogram and closed-contours views)

• A connected components file is the collection of the starting position (x,y coordinates) and the size (width and height) information for each and all of the connected components in an image or part of an image.

• A Width-Height Map (WH-Map) is a 3D frequency distribution of the contents of a connected components file with the CC box width and height as the axis. Figure 3.8 shows the 3D histogram and Figure 3.9 shows a closed contour representation of the WH-Map for a typical image.