AN IMPROVED APPROACH FOR IMAGE MATCHING USING PRINCIPLE COMPONENT ANALYSIS

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1 Abstract AN IPROVED APPROACH FOR IAGE ATCHING USING PRINCIPLE COPONENT ANALYSIS Xiaohong Liu, Jiali Zhang The traditional NCC algorithm has considerable computational burden, but is with high rate of matching accuracy when people use it in image matching. The PCA algorithm has high matching speed and can be anti-interference when it is used in image matching. Based on experiment, we propose one improved algorithm which can greatly reduce the matching time as well as get high rate of matching accuracy. Introduction Image matching has substantial applications in real life. In this field, several algorithms have been proposed but the applications have been limited due to its considerable computation burden and sensitivity. This research presents an improved approach, improved fusion matching algorithm using Principle Components Analysis (PCA), which reduce the computation burden substantially and improve the capability of antiinterference greatly. Based on Principle Component Analysis (PCA), this study identifies improved fusion matching algorithm. This algorithm has been compared against existing leading methods, such as NCC algorithm, on a variety of scenarios and real images. In addition to producing the same results as other tested methods, the study finds that, using single gray level normalized cross-correlation matching method, improved fusion matching algorithm scales extremely well with the dataset size, considerably reduce the computing time to 60% or less, dramatically improve its capability of anti-interference. ethod 1.1 Principle Component Analysis The concept of Principle Component is first proposed by Karlpasrno in This concept is only applied to non-random variable on that time. Hotelling began to applied this concept to random variable in Principle Component Analysis is one of the most popular method to extract main feature now. This method can simplify the process of solving the problem, increase signal-noise ratio and improve capacity of antijamming by processing the raw data.

2 Principle Component Analysis is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables ( P variables) into a set of values of linearly uncorrelated variables ( K variables) called principal components. The number of principal components is less than or equal to the number of original variables(k P). When we apply this method to image matching, we treat the matching image and the template image as matrices. We can get eigenvalues of template image by linear transformation and get uncorrelated eigenvectors corresponding to these eigenvalues. After we get the eigenvalues, we can sort them with the descending order and obtain the first K eigenvalues based on accumulative proportion. The eigenvectors corresponding to the first K eigenvalues are principle components we want to obtain. Suppose that the formwor drawing is g and the matching image is S. The size of g is w*h and the size of S is *N. We can obtain the variance-covariance matrix according to the definition of Principle Component Analysis: 1 1 S E X X E X X Y Y AA ' ' ' t ( )( ) ( ( )( ) ) K 1 K1 T 1 1 Where X, Y X, A [ Y1, Y2... Ym ]. i1 The eigenvalues of g are, and corresponding eigenvectors are (=1,2 n). i According to formula 1 p i1 i, we can choose first P eigenvalues which mae the i accumulative proportion greater than 85%. The corresponding eigenvectors are the principle components. These eigenvectors become the orthogonal basis in the new space Q after be orthogalized. The projection of each image in new space Q are correspond to one vector with size P and the new low-dimension vectors contain information we use to do matching. We choose several sub-image from the matching image. The size of each sub-image is the same as that of template image(w*h). We express each sub-image as vector R (I, j). The dot on sub-image (m, n) is expressed as R ( i 0,1,... N h 1, j 0,1,... w 1). We mae the projection of each sub-image ( i, j, m, n) to the new space which is based on principle components of template image, and we can determine the matching location after evaluating the similarity of two images. We can use the formula

3 p1 r i, j i, j 1 D S ( K) (r=1,2,3.l) to solve the point (i, j) which has the smallest distance with origin in new space, then we can determine the approximate matching location. 1.2 NCC atching Algorithm NCC algorithm is the image grayscale matching algorithm based on similarity measures. If two vectors are similar, their direction is the same and the angle between the two vectors are zero according to formula a*b= a * b *cos. Therefore, we can determine the similarity between two vectors based value of cos. We implement this method to two-dimension space and we can obtain the formula R n1 n2 ( x y iu, jv ij) i1 j1 ( uv, ) n1 n2 n1 n2 2 1/2 2 1/2 ( ( x iu, jv)) ( yij ) i1 j1 i1 j1 In this fomurla, R(u,v) represents normalized cross correlation coefficient of point(u,v). X( i u, j v) and represent the grayscale of (i+u,j+u), (i,j) in two images Y( i, j ) needed to be matched. The bigger the value of R(u,v) is, the better the matching can be done. Therefore, we can get the accurate matching location by the maximum value of cross correlation coefficient. For determining matching area based on NCC algorithm, we can set the matching location (i,j) as center and do normalized cross correlation matching between (ih/2,i+3h/2) and (j-w/2,j+3h/2). We determine the interval between (i-h/2, i+3h/2) and (j-w/2,j+3w/2) by matching accuracy of PCA and experimental data based on distribution of image feature. We can also use this experimental data to determine how much we can improve the speed of NCC algorithm. Experiments and results 2.1 Experiments

4 Using original image and matching image with greyscales are all (0:255), and setting the original point (0,0) as the left top corner of the original point, we design two experiments to chec this algorithm and mae comparison with classical NCC algorithm. Experiment 1: Figure 1(Left): original image Figure 2(Below): matching image Experiment 2: Figure 3: original image Figure 4: matching image Figure 5: matching image 2 (rotated by 5 degree) 2.2 Experiment results

5 PCA+NCC algorithm computation time VS. NCC algorithm computation time Time Image size atching image size NCC algorithm 1 525*525 64* *525 64* *496 64* *496 64* *496 64* PCA+NCC algorithm Comparison of anti-interference between NCC algorithm and PCA_NCC algorithm Time Image size atching image size NCC algorithm PCA+NCC algorithm 1 525*525 64*64 Fail Success 2 525*525 64*64 Fail Success 3 505*496 64*48 Fail Success 4 505*496 64*48 Fail Success 5 505*496 64*48 Fail Success

6 Left: PCA_NCC algorithm image matching results.right: NCC algorithm image matching results. Conclusion and Suggestion We get three main conclusions based on our experiment. First, the computational time is reduced greatly by our improved algorithm. From chart 1 and chart 2, we can see that the computational time is reduced by 40%. This is a big improvement for traditional NCC program. Second, the new algorithm is with high anti-interference feature which is a considerable improvement for PCA algorithm. When we rotate the sub-image for a certain angle and use the improved algorithm on it, we can still get accurate result. Third, although our new improved algorithm can combine good characteristics of traditional NCC algorithm and PCA program, it is still with some limitations. First, the subimage should be small for ideal matching result. If we extract the large sub-image, we get more wrong matching. Second, the more distinct feature the sub-image has, the higher rate of matching accuracy we can get. When the extracted sub-image is gray and does not have some specific feature, it is more difficult to get accurate matching. Every algorithm for image matching has its limitation when it is applied in practice. It wors better for image with certain characteristics, which limits suitability of this algorithm. ore future wor need to do for solving this problem. Combining two algorithms provide an idea to improve image matching algorithm. The new combined algorithm can obtain good characteristics of both algorithms and get high suitability. Reference 基于主成分分析的快速图像匹配研究 ( Computer Technology and Its Applications, 2010,vol 4)By Peng Zhao, Zhenxing Bai, & Wentong Fan.

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