Gray information of image registration

Cross-correlation method is the most basic image registration method based on gray statistics, which is usually used for template matching and pattern recognition. It is a matching measure, and the matching degree is determined by calculating the cross-correlation value between the template image and the search window. The position of the search window with the largest cross-correlation value determines the position of the template image in the image to be registered.

Let image A be a reference image or a reference image, which means that B is an image to be registered with A after correction, which means that several small areas with rich feature information are selected as templates in image A, and an overlapping area in the overlapping part of the image is selected as the search area of the template, as shown in figure 14-3. Then each template is placed in its corresponding search area. Through the relative movement of the two templates, the similarity between the search area parts covered by the templates is calculated line by line at each position, and the position of the function value indicating the maximum similarity between the two templates is generated. Set the similarity region searched by the image B to be registered as, and then use it as a template, and use the same method to search the region with the largest similarity function value in the reference image, and set the threshold Z. If so, it is considered to be coincident, and the position in the image B is the position where the image B matches the image A; On the other hand, it is considered that the matching of feature regions is incorrect, that is, wrong matching. There are three main methods to evaluate the similarity between two images:

14-3 Template Matching Diagram

Figure 14-3 template matching sample image

A. mean square

( 14-7)

B. Langmuir distance

( 14-8)

C. standardized standard correlation coefficient

( 14-9)

Wherein, in the definition,

Representing gray values of pixels in rows and columns in the template sub-image;

Is the gray value of pixels in rows and columns on the reference sub-image at the reference point in the matching image;

And the average values representing the gray levels of pixels in the two sub-images respectively;

The left side of the definition represents the similarity measure of the template sub-image and the sub-image at the reference point in another image.

Among these three formulas, the minimum value of the first two formulas represents the possible matching position, and the maximum value of the latter formula represents the possible matching position. Other evaluation criteria are derived from these basic evaluation criteria. For example, correlation coefficient and standard correlation coefficient are simplified forms of normalized standard correlation coefficient, which are essentially the same.

Sequential similarity detection matching method (SSDA)

Sequential similarity detection algorithm (SSDA) was proposed by Barnea et al. The main feature of SSDA method is its high processing speed. In this method, a simple fixed threshold t is selected. If the residual sum of the two images is greater than the fixed threshold t at a certain point, the current point is not considered as a matching point, so the calculation of the current residual sum is terminated and the residual sum is calculated at another point. Finally, the point where the residual sum grows slowest is considered as the matching point. The basic idea of this method is based on the analysis of error accumulation. So for most non-matching points, only the first few pixels in the template need to be calculated, and only the points near the matching points need to calculate the whole template. In this way, on average, the number of operations of each point will be far less than the number of points in the measured image, thus achieving the purpose of reducing the calculation amount of the whole matching process.

In the SSDA algorithm, the similarity evaluation standard between the reference image and the image to be registered is measured by a function, and the formula is as follows:

( 14- 10)

The sum and coordinates of residuals are non-repetitive point coordinate sequences randomly extracted from the images to be registered. The bigger it is, the slower the error increases, that is, the more similar the two images are. The key of this method is the selection of threshold T, which not only affects the operation speed of the algorithm, but also affects the matching accuracy of the algorithm. Viola et al. introduced the interactive information method into the field of image registration for the first time in 1995. It is a similarity criterion of interactive information based on information theory. The original intention is to solve the registration problem of multimodal medical images.

Interactive information is used to compare the statistical correlation between two images. Firstly, the gray level of the image is regarded as a spatially uniform random process with independent samples, and the related random field can be established by Gaussian-Markov random field model, and the statistical characteristics and probability density function are used to describe the statistical properties of the image. Mutual information is a measure of the statistical correlation between two random variables A and B, or a measure of the amount of information that one variable contains the other.

The mutual information is represented by the sum of individual entropy and joint entropy of A and B:

( 14- 1 1)

These include:

Here are the marginal probability densities of random variables A and B respectively; Is the joint probability density distribution of two random variables. The key idea of mutual information used in image registration is that if two images match, their mutual information reaches the maximum. In the application of image registration, the joint probability density and marginal probability density can usually be estimated by the joint probability histogram and marginal probability histogram of the overlapping area of two images, or the mutual information can be calculated by the Parzen window probability density estimation method.

Once the mutual information image registration method was put forward, there were many researches based on this method, especially in medical image registration. For example, the algorithm of combining interactive information with gradient to improve its extreme performance, multi-resolution image pyramid method and so on. However, interactive information is based on probability density estimation, and sometimes it is necessary to establish a parameterized probability density model, which requires a lot of calculation and a large overlapping area between images, so the function may be ill-conditioned and have a large number of local extrema.