Moving Object Segmentation--Regional growth

I. Principles and procedures for regional growth

The basic idea of regional growth is to assemble pixels with similar properties to form a region. In particular, a seed pixel is used as the starting point for each area that needs to be segmented, and then the pixels surrounding the seed pixels with the same or similar properties as the seed pixels (judged by some predetermined growth or similarity criteria) are merged into the region where the seed pixels are located. Use these new pixels as new seed pixels to continue with the above process until there are no more pixels that meet the criteria to be included. Such an area would have grown.

Figure 2-12 shows an example of region growth for a known seed point. Figure 2-12 (a) gives an image that needs to be segmented and has two seed pixels (marked as shades of gray squares) that are now being grown in the region. The criterion used here is that if the absolute value of the difference between the pixel and the seed pixel is considered to be less than a threshold T, the pixel is included in the region of the seed pixel. Figure 2-12 (b) gives the regional growth results of t=3, and the whole picture is well divided into 2 regions. Figure 2-12 (c) gives the region growth result of T =1, some pixels cannot be determined; Figure 2-12 (d) gives the region growth result of T = 6 o'clock, and the whole picture is divided into one area. This shows that the selection of thresholds is very important.

From the example, there are 3 problems that need to be solved in the actual application of the region growth method: ① How to select a set of seed pixels that correctly represent the desired region, and ② how to determine the criteria by which neighboring pixels can be included in the growth process, and ③ how to determine the condition or rule of the growth termination.

The first problem can usually be based on the characteristics of the specific image to select the seed pixels. For example, in the infrared image detection technology, usually the target radiation is relatively large, so you can select the brightest pixel in the image as the seed pixel. If there is no prior knowledge of the image, then the growth criterion can be used to calculate the pixel accordingly. If the results of the calculation can be seen in the cluster, then the cluster center can be selected as the seed pixel.
The solution to the second problem depends not only on the characteristics of the specific problem, but also on the data type of the image. If the image is an RGB color image, then using the monochrome criterion will affect the split result. In addition, there is a need to consider the connectivity between pixels, otherwise there will sometimes be meaningless segmentation results.

The general growth process stops when the pixel that does not meet the growth quasi is reached. However, the commonly used criteria based on gray, texture and color are mostly based on the local properties in the image, and the "history" of growth is not taken into account. The ability to increase regional growth takes into account some of the criteria related to the global nature of images and targets, such as size and shape. In this case, it is often necessary to establish a certain model for the segmentation result or to be supplemented by some prior knowledge.

II. Growth guidelines and processes

A key to regional growth is the selection of suitable growth or similarity criteria, with most regional growth criteria using the local nature of the image. Growth criteria can be formulated according to different principles, while the use of different growth criteria can affect the process of regional growth. 3 basic growth criteria and methods are described below.

(1), gray scale difference criterion

The region growth method operates on the pixel of the image as the basic unit, and the fundamental area gray difference method mainly has the following steps:
① a gradual scan of the image to find the pixels that have not yet been attributed;
② examines its neighborhood pixels at the center of the pixel, comparing the pixels in the neighborhood to it one by one, and merging them if the grayscale difference is less than the predetermined value;
③ is centered on the newly merged pixel and returns to step ②, checking the neighborhood of the new pixel until the region expands further;
④ returns to step ① and continues the scan until the pixel without attribution is not found, ending the entire growth process.
The results obtained by using the above method have a great dependence on the selection of regional growth starting point. To overcome this problem, you can use the following improvement methods:
The threshold value of ① setting gray difference is zero, and the above method is used to expand the region, so that the same gray pixels are merged.
② The average gray difference between all adjacent regions, and merges adjacent regions with the lowest gray difference;
③ set the termination criteria, and then merge the areas sequentially until the termination criteria are met by repeating the steps in the ② above.
In addition, when there is a slow-changing area in the image, the above method will be able to gradually merge different regions and produce errors. In order to overcome this problem, we can compare the gray value of the neighborhood pixel with the grey value of the new pixel, and use the average gray value of the area of the new pixel in comparison with the gray value of each neighborhood pixel.

For an image region with N pixels, the mean value is:

Comparison tests for whether a pixel is merged are represented as:

Where T is the given threshold value.

In the process of regional growth, the gray values in the same area of the image are required to change as small as possible, while the gray difference between different regions is as large as possible. The following are discussed in two ways:

1) The set area is uniform, the gray value of each pixel is m and a 0 mean Gaussian noise superposition. When testing whether a pixel is merged, the probability that the condition is not established is:

This is the error probability function, when T takes 3 times times the variance, the probability of miscalculation is 1-99.7%. This shows that when the gray-scale mean is considered, the gray changes in the area should be as small as possible.
2) The region is non-uniform, and the two parts of the image pixels of different targets. These two parts of the pixel in R accounted for Q1 and Q2, respectively, gray values of M1 and M2, the region mean is q1m1+q2m2. For pixels with a grayscale value of M, the difference between it and the region mean is:

The correct probability of judgment is:

This shows that when considering the gray-scale mean, the gray gap between different parts of pixels should be as large as possible.

(2), gray distribution statistical criteria

It is considered that the gray-scale distribution similarity is used as the growth criterion to determine the merging of regions, the following steps are:
① the image into a small area of non-overlapping;
② the cumulative gray-scale histogram of the adjacent region is based on the similarity of gray distribution.
③ sets the termination criteria by merging the regions sequentially until the termination criterion is met by repeating the actions in step ②.
There are two methods to detect the similarity of gray-scale distributions (set H1 (Z) and H2 (Z) as the cumulative grayscale histogram for two adjacent regions):

Kolmogorov-smirnov Detection:

Smoothed-difference Detection:

If the detection result is less than the given threshold, the two regions are merged.

The effect of generating region by using gray-scale distribution similarity merging method is closely related to the selection of the size and threshold of the micro-region, in general, the micro-region is too large, which will result in the division of the region due to the transition merger: Conversely, the area is severed due to insufficient merger. Moreover, the complexity of the image, the original image generated by different conditions, the choice of the above parameters have a great impact. Typically, the micro-region size Q and threshold T are determined by the region-generated effect under specific conditions.

(2), regional shape guidelines

You can also take advantage of the results of the target shape when deciding on the merging of regions, and there are two common methods:
① the image into a fixed gray area, the perimeter of the two adjacent area is P1 and P2, respectively, the two regions common boundary line gray difference is less than the given value of that part length set to L, if (T1, for the predetermined threshold), then merge two regions;

② the image is divided into gray fixed area, set two adjacent region of the common boundary length of B, the two regions common boundary between the gray difference is less than the given value of the length of the portion is set to L, if (T2 is predetermined threshold) merge two regions.

The difference between the above two methods is: The first method is to merge the two adjacent areas of the common boundary in the lower part of the region to occupy a larger portion of the area, while the second method is to merge the two adjacent regions of the common boundary of the lower contrast of the region more.

Iii. Splitting and merging

The area growth method described above is to start with a single seed pixel and finally get the entire region by continuously admitting new pixels. Another way to split the idea is to start by splitting the entire image and getting all the regions. In practice, the image is often divided into overlapping areas of arbitrary size, and then merging or splitting these areas to meet the requirements of segmentation.

In this kind of method, the most common method is Quadtree decomposition method. Set R to represent the entire square image as shown in the area graph, P represents a logical predicate. Starting at the top, the R is continuously split into smaller 1/4 Square sub-region Ri, and always makes P (Ri) = TRUE. In other words, if P (Ri) = FALSE then divide the image into 4 equal portions. So and so on, until Ri is a single pixel.

If only the use of splitting is allowed, it is possible that the adjacent two regions have the same properties but are not synthesized in one case. In order to solve this problem, it is permissible to continue splitting or merging after each division. The merge here merges only those areas of the adjacent and merged new regions that satisfy the logical predicate P. The following steps are summarized in the basic split merge algorithm described earlier:
① to either region, if P (Ri) = FALSE divides it into 4 equal parts that do not overlap;

② to the adjacent two regions Ri and Rj Gate can also be different in size, that is, not on the same layer, if the condition P (Ri u Rj) = TRUE satisfied, they are merged together;

③ if further splits or mergers are impossible, then the end.

Moving Object Segmentation--Regional growth