Neighborhood, adjacency, pathway, connectivity, connected set, area concept distinction

Some concepts are like this, at first very clear, and then long time not to look more and more blurred, are blended a group, here to re-summarize.

1. Neighborhood: In Digital image, the neighborhood is divided into 4 neighborhood and 8 neighborhood, 4 neighborhood is one (x, y) point up and down four points, 8 neighborhood plus upper left upper right upper left lower right bottom four points. If P is within the 8 points around Q, it is p in the 8 neighborhood of Q.

2. Adjacency: Adjacency is a neighborhood, if P and Q are contiguous, then p and Q must be in the neighborhood, and both of the pixels are within the same set V1. (What is called in the set V1: If the set V1 contains {012345}, the five numbers represent the pixel values, and the P-value is the 2,Q value 6, then they are not in the same set V1, of course, if there is a set V2, they may also be in another set V2) the number of adjacency in the digital image is three, 4 adjacency, 8 adjacency, and M adjacency. If P is within the 4 neighborhood of Q, and the values of Q and P are in V, then P and Q are 4 contiguous and 8 adjacency concepts. M adjacency is not the same, if Q and P in the 8 neighborhood, p and Q are within the V, and Q of the 4 neighborhood and P of the 4 neighborhood of the common coverage point is not within V, then P and q is M adjacency. M adjacency is introduced in order to eliminate the two semantics of 8 adjacency. For example, there is a 3*3 matrix {0,1,1;0,1,0;0,0,1}, assuming that for the collection of V={1}, if two points can form an adjacency, even if there is a way to pass, then the upper right corner of 1 to the lower right corner of 1, if the 8 adjacency has two roads, and according to M adjacency, there is only one road, This is the meaning that M adjacency proposes.

3. Access: If from (x0,y0) point to (Xn,yn) point, where each point and before and after the K adjacency (K for 4, 8, m), then said that there is a K-channel between the two points, note must be emphasized to understand K, and N is the length of this pathway, if (x0,y0) and (Xn, Yn) is coincident, then it is a closed pathway.

4. Connectivity: For a subset of pixels in the image u and two of the points P and Q, if there is a path between P and Q with all the elements of U, it is said that P and Q are connected.

5. Connected sets: Connected, for elements in U p,u can be connected to the elements of P is a connected component of U, if you have only one connected component, then U is a connected set.

6. Area: T is a subset of the image, and if T is a connected set, then T is an area.

When understanding these concepts, it is not possible to look at them in isolation, and to combine the process of image segmentation, such as the foreground and background of images, which are related to the region. Assuming that there are m non-connected areas in an image, and that they do not touch the boundary of the image, so that R1 represents the R2 of the M-region, so that the R1 represents its complement, then all the points in the R2 are the foreground in the image, and all the points in the image are the backgrounds of the images.