The aim of the research is finding an image obtaining method which is invariant to shooting conditions for further application of correlationextremal matching method in technical vision systems. The method based on entropy analysis is offered. Some testings of the method were carried out; images obtained in different conditions were used. The tests showed that preprocessed images have more stable correlation coefficient than original images.
2. Image correlation analysis. Formulation of the problem
One of the typical objectives in technical vision is element-wise matching of two images of one object which were captured by different sensors or images captured by the same sensor but under different conditions or at different time. To make such a comparison we should do mutual binding of the images and compensate shifts, rotations, geometric and brightness distortions etc.
The classic way of finding superimposition of the pair of functions (to match pair of functions) is to find meaning of value measured correlation between these functions, and find position of the maximum of the correlation function.
For example, we need to match aerial photograph and topographic map of the same area (figure 1). Figure 2 shows the normalized cross-correlation function of the images.
The figure shows that the function has several peaks (two equal-amplitude maxima). The positions of both peaks are different from zero; although in this example images have zero shift. This example shows that the correlation-extreme method has serious limitations on the types of the compared images. -10 0 10 20
As usual, methods of structural analysis are used for image matching. For example, specific points are detected and compared. But even for shifted images of the same type specific points can be different. Consequently, some special points may not have a pair, or the specific points in the pair will have a slightly different spatial position. In the case of dissimilar images special points will be unique for each image.
There is one thing that we should take into consideration: correlation-extremal method gives more precise solution than structural methods. Besides, there are effective algorithms and hardware for image correlation analysis which are already used.
That’s why it is of great interest to adapt correlation-extremal method for matching dissimilar images. It’s offered to use preprocessing method based on entropy analysis. To be more correct it is offered to substitute image with its’ local entropy map, because local entropy map is more resistant to the effects of the factors we studied (as will be shown below). 3. Image preprocessing method based on entropy analysis
The solution of the problem is achieved by using the method of image preprocessing based on by taking into account existing internal statistical relationships between image elements. This decision is based on the assumption that statistically interconnected elements in a changing conditions of image capturing are statistically related.
Information-theoretic methods are used for identification of internal statistical relations in any type of data. To adapt correlation-extremal method for matching dissimilar images it is proposed to do entropy analysis of the images, namely to calculate local entropy maps of the images.
The image is considered as a realization of random process. Local entropy (Hi) characterizes the degree of surprise happening of i-th event (occurrence). The less its’ a-priori probability is, the greater its’ local entropy.
Let’s define what is implied under “event”. An event (e) is a specific brightness of the pixel. To calculate the probability of event e (p(e)) we should count the number of occurrences of the combination over the defined area M×N (or entire image) and divide by the total number of considered pixels.
The output image is formed by replacing each pixel with value, calculated according to the formula of local entropy (i.e. local entropy map is calculated): Y (i, j) (M 1)/2 ( N 1)/2
m(M 1)/2 n( N 1)/2
p(eim, jn ) log( p(eim, jn )) .
(
Similar results were obtained using other test images: maps and aerospace photographs, photographs in winter and in summer, optical and infrared photographs. Test images after preprocessing demonstrate greater correlation coefficient and smoother correlation function than original images.
Thus, the entropy preprocessing method can be recommended for application in the correlation-extreme image matching for two reasons: ─ it increases the correlation between dissimilar images; ─ correlation function of entropy maps is smoother than the correlation function of the original images, whereby it is possible to significantly reduce the amount of computation to find the extremum. 4. Conclusion
The advantages of the correlation analysis are: this technology has been worked out many times before; there are fast algorithms to calculate correlation and hardware-based solutions. Currently it is of great interest to develop simple and cheap correlation vision systems implemented as special processors.
The aim of this paper was to use correlation method for image matching but in difficult conditions. Information-theoretic preprocessing technology allows comparing images more effective and correct. Researches of the method based on local entropy have shown that dissimilar images of the same scene have greater correlation coefficient after preprocessing. Developed method allows matching the following types of images automatically: ─ aerial photographs captured at different times; ─ aerial photographs and topographic map; ─ optical and infrared images.
Thus, the application of developed method will significantly expand the application area of the correlation-extreme image matching method in computer vision systems.