A New Method for Correcting Vehicle License Plate Tilt

Transcription

1 International Journal of Automation and Computing 6(2), May 2009, DOI: /s A New Method for Correcting Vehicle License Plate Tilt Mei-Sen Pan 1, Qi Xiong 1,2 Jun-Biao Yan 2 1 Department of Computer Science and Technology, Hunan University of Arts and Science, Changde , PRC 2 Office of Academic Affairs, Hunan University of Arts and Science, Changde , PRC Abstract: In the course of vehicle license plate (VLP) automatic recognition, tilt correction is a very crucial process. According to Karhunen-Loeve (K-L) transformation, the coordinates of characters in the image are arranged into a two-dimensional covariance matrix, on the basis of which the centered process is carried out. Then, the eigenvector and the rotation angle α are computed in turn. The whole image is rotated by α. Thus, image horizontal tilt correction is performed. In the vertical tilt correction process, three correction methods, which are K-L transformation method, the line fitting method based on K -means clustering (LFMBKC), and the line fitting based on least squares (LFMBLS), are put forward to compute the vertical tilt angle θ. After shear transformation (ST) is imposed on the rotated image, the final correction image is obtained. The experimental results verify that this proposed method can be easily implemented, and can quickly and accurately get the tilt angle. It provides a new effective way for the VLP image tilt correction as well. Keywords: Tilt correction, K-L transformation, projection profile, Hough transformation. 1 Introduction In the process of taking the vehicle license plate (VLP) images, because of the weather, illumination, road condition and so on, the VLP in the image frequently has some obvious and serious tilt so that touching and broken characters are created, which has costly negative effect on the character segmentation and recognition [1 7]. In order to resolve the above problem, experts have undertaken colossal and in-depth researches over the past years and have achieved many ingenious and practical solutions. In [1], a sensing system with a wide dynamic range was developed to acquire fine images of vehicles under varied illumination conditions. The developed sensing system can expand the dynamic range of the image by combining a pair of images taken under different exposure conditions. In [2], on the basis of a novel adaptive image segmentation technique (sliding concentric windows) and connected component analysis in conjunction with a character recognition neural network, a new algorithm for vehicle license plate identification was proposed when limitations in distance, angle of view, and illumination conditions were set, and background complexity was low. In [4, 7], some feature points of the character were extracted, and template matching operators were used to get a robust solution under multiple acquisition conditions. In [5], the approach focused on dealing with images taken under weak lighting condition. In [8-10], Hough transformation method (HTM) was used to estimate the license plate position and the normalization angle, especially for the tilt angle. In [11], by using a holographic nearest-neighbor algorithm, a method for object tilt correction and recognition was proposed. In [12], the orientation was detected by using the histogram of nearest neighbor directions. In [13], a method for structural page layout analysis based on Manuscript received May 20, 2008; revised November 25, 2008 This work was supported by Scientific Research Fund of Hunan Province, PRC (No. 07JJ6141) and Scientific Research Fund of Hunan Provincial Education Department, PRC (No. 06C582). *Corresponding author. address: pmsjjj@126.com bottom-up and nearest-neighbor clustering of page components was proposed to get the tilt angle of the document page. In summary, three kinds of methods are concluded, i.e., HTM, projection profile method (PPM), and component nearest neighbor clustering method (CNNCM). Among them, HTM, as the most widely-employed and prevalent one, uses Hough transformation to calculate the possible track in parameter space according to target pixel coordinates in the image space. It is very well adapted to linear graphic, but with a lot of computations and lack of robustness for a tilt VLP image. PPM, which is built on the analysis for the projection shape, has an extremely heavy computational load because it needs to calculate the projection shape of each angle. CNNCM, by discovering K nearest neighbors of the central point of all connected components, computes the vector direction of each couple nearest neighbor and gets the statistical histogram where the peak value denotes the entire image tilt angle. Since there exist some connected components in the image, its processing time is also a quite prodigious load. As has been said, the above correcting tilt methods have the same drawbacks that the computational load is considerably heavy and the processing time is rather long. In addition, the correction accuracy is very poor in the VLP tilt image. In order to address the issues, on the basis of a comprehensive and thorough investigation into Karhunen-Loeve (K-L) transformation, we propose a new method for correcting a VLP tilt. In the horizontal tilt correction process, the method settles the coordinates of characters in the image into two-dimensional nonzero mean covariance matrix, on which the centered process is operated. Then, the eigenvector and the rotation angle α are computed. The whole image is rotated by α, i.e., image horizontal tilt correction is implemented. In the vertical tilt correction process, three correction methods are worked out to compute the vertical tilt angle. Shear transformation (ST) is inflicted on the rotated image and the final correction image is obtained.

2 M. S. Pan et al. / A New Method for Correcting Vehicle License Plate Tilt 211 The rest of this paper is organized as follows. Section 2 describes the proposed method. Section 3 gives experimental results and comparisons. Conclusions are drawn in Section 4. M x 1 N x i. (2) N 2 A new method for correcting vehicle license plate tilt According to the tilt direction of the VLP region, the VLP has three possible tilts: horizontal tilt (see Fig. 1), vertical tilt (see Fig. 2), and hybrid tilt (see Fig. 3). In Fig. 1, the characters have no ST, but there is a tilt angle α between the tilt region principal axis X and the horizontal axis X. Once α is obtained, the entire image can be rotated by α. In Fig. 2, in fact the characters have ST along the horizontal axis X, and all the pixels in the same row have heterogeneous offset. Therefore, we only do inverse ST to finish the vertical tilt correction in the case of knowing the vertical tilt angle θ. Fig. 3 includes horizontal tilt and vertical tilt. In fact, we first perform horizontal tilt correction and then vertical tilt correction [7]. (a) α > 0 (b) α < 0 Fig. 1 Horizontal tilt (a) θ > 0 (b) θ < 0 Fig. 2 Vertical tilt (a) α > 0 (b) α < 0 Fig. 3 Hybrid tilt 2.1 Calculating the rotation angle using K-L transformation K-L transformation is an orthogonal one based on the image statistic characteristics. In this paper, suppose that X R K N, x i = [x il x ik] T (i = 1, 2,, N) is an element of the vector set X. Then, K-L transformation is described as follows: Step 1. Calculate the mathematical expectation (mean) M x : M x = E{X} (1) where E is the mathematical expectation operator. The mean vector M x of all N vectors is defined as follows: Step 2. Compute the covariance matrix Cov X of set X : Cov X = 1 N (x i M x )(x i M x ) T = N [ N ] 1 x ix T i M x M T x. (3) N Step 3. Respectively count the eigenvalue and eigenvector λ and e of Cov X : λi Cov X = 0 (4) where λ = (λ 1,, λ K), λ 1 > > λ j > > λ K. The eigenvector of λ j is e j = [e il e ik] T. Step 4. Calculate the transformation kernel matrix A: A = e T 1 e T K = e 11 e 1K e K1 e KK (5) Step 5. Compute K-L transformation and get a new vector set Y: Y = A(X M x ). (6) From (6), we know that Y is a vector set with its mathematical expectation being 0, namely M Y = 0, whose origin of coordinates has moved to the central position. We can further get the covariance matrix Cov Y = λ λ K. The diagonal elements of Cov Y are the variance of the vector set Y and its values are the eigenvalues of Cov X, in which the upper-left element λ 1 and lower-right element λ K are the maximum and the minimum, respectively. The non-diagonal elements with zeroes in Cov Y are the covariance of set Y, which are zeroes. This shows that the correlation is the smallest among vectors in set Y. But the non-diagonal elements in Cov X are not zeroes, which shows that the correlation is very strong. Therefore, K-L transformation is essentially a coordinate one, which turns the original coordinates into the variance maximum direction to achieve the maximum variance of each pixel coordinate projection along the above direction. Suppose X R 2 N, namely X is a two-dimensional coordinate plane point set. As stated before, after getting transformation kernel matrix A, we use the rotation transformation matrix formula in [ computer graphics ] to get the e 11 e 12 absolute value of e 11 in A = to compute the e 21 e 22 arccosine value (or get the absolute value of e 12 to compute the arcsine value) and finally obtain the tilt angle.

3 212 International Journal of Automation and Computing 6(2), May Horizontal tilt correction Suppose the original image is a binarization image with the upper-left pixel being (1, 1), in which the background is black (gray value is 0) and the characters are white (gray value is 255). P is the set of coordinates (x, y) representing all the white pixels in the image, N is the number of elements, namely P R 2 N. P is regarded as the vector set X in K-L transformation. A method for VLP horizontal tilt correction based on K-L transformation is described as follows: Step 1. Regard P as the vector set X in K-L transformation. Step 2. Compute the transformation kernel matrix A of set P using K-L transformation. Step 3. Calculate the tilt angle α according to e 11 or e 12 in matrix A: or α = arccos( e 11 ) 180 π α = arcsin( e 12 ) 180 π. (7) Step 4. Rotate the entire image by α and finish horizontal tilt correction. 2.3 Vertical tilt correction In general, there are horizontal tilt and vertical tilt in a VLP image. In this paper, we propose three methods, namely K-L transformation, line fitting method based on K-means clustering (LFMBKC) and line fitting based on least square (LFMBLS), to operate on vertical tilt correction, by which the tilt angle is obtained in dint of the boundary pixels of the VLP region. After horizontal tilt correction, the image basically keeps in the horizontal direction. Therefore, we can detect the top horizontal line Top Line and the left vertical line Left Line. They are expressed as: T op Line = {x f(x, y) = 255 and x is the minimum row} Left Line = {y f(x, y) = 255 and y is the minimum column} where f(x, y) is the gray value of pixel (x, y), Top Line is the x coordinate of the first pixel whose gray value is 255 (white) from the image s top row to bottom, Left Line is the y coordinate of the first pixel whose gray value is 255 (white) from the image s left column to right (see Fig. 4). From the VLP region, we detect the coordinates of the first pixel whose gray value is 255 in each row, then compute the relative coordinates according to Top Line and Left Line, and finally get two sets Set X and Set Y as Set X = {x T op Line f(x, y) = 255 and y is the minimum column} Set Y = {y Left Line f(x, y) = 255 and y is the minimum column}. (8) (9) Fig. 4 Horizontal and vertical lines Suppose there are n elements in set Set Y and compute the mathematical expectation ymean and the standard deviation ystd: ymean = 1 Set Y (i) n (10) ystd = 1 (Set Y (i) ymean) 2. n Because of significant difference among the elements in Set Y, they cannot exactly reflect the vertical tilt angle θ. Therefore, we filter the elements in Set Y. Set Y (i) is the i-th element in Set Y. The filtering rule is described as follows: 1) If Set Y (i) ymean < ystd, then Set Y (i) and Set X (i) are retained; 2) Otherwise, Set Y (i) and Set X (i) are removed. In the vertical tilt correction process, the filtered sets Set X and Set Y are combined into a new vector set Set XY, namely Set XY = [Set X Set Y ]. (11) K-L transformation According to the description in Section 2.1, we regard Set XY as the vector set X of K-L transformation. The method for VLP vertical tilt correction based on K-L transformation is described as follows: Step 1. Regard Set XY as the vector set X. Step 2. Compute the transformation kernel matrix, A of set X using K-L transformation; Step 3. Calculate k according to e 11 in matrix A: k = e 11. (12) Step 4. Obtain tan θ = k according to k and perform the image vertical tilt correction. Since vertical tilt is regarded as ST along the direction of axis X, in turn, vertical tilt correction as inverse ST along the same direction. The vertical tilt correction matrix formula is shown as follows: [ X 1 Y 1 1 ] = [X 1 Y 1 1 ] tan θ (13) where X 1 and Y 1 represent the x and y coordinate matrixes in the horizontally corrected image, respectively. By comparison, X 1 and Y 1 represent the x and y coordinate matrixes in the final correction image, respectively LFMBKC K-means clustering algorithm, as a widely-used clustering method in pattern recognition, by circulation splittingiteration, successively gets N classes from a given input vector set. Suppose Y is the Voronoi partition πa about the

4 M. S. Pan et al. / A New Method for Correcting Vehicle License Plate Tilt 213 set A (A R k ) and X is a stationary stochastic process and an ergodicity, K-means clustering algorithm is given as follows [14 16] : Step 1. Initialization: given class set size N and ξ > 0, Y 0 = {y 0 i ; i = 0, 1,, N 1}, x j, j = 0, 1,, I 1, m = 0, D 1 =. [ I 1 ] Step 2. Compute D m(q m ) = j=0 d(x j, Q m (x j)) /I by Y m and Y m = {y m i ; i = 0, 1,, N 1}. Step 3. If [D m 1(Q m 1 ) D m(q m )]/D m(q m ) ξ, then classifying stops. Step 4. Search x (πy m) = { x (R i); i = 0, 1,, N 1}, let Y m+1 = x (πy m), and go to Step 1. In above steps, I denotes the number of input vectors, m is the number of circulation iterations, d(x j, Q m (x j)) indicates the distortion error between the input vector x j and the corresponding class with x j in the class set Y m of the m-th iteration. If the distortion error is defined by the square of Euclidean distance, then d(x j, Q m (x j)) is defined as follows: d(x j, Q m (x j)) = x j Q m (x j) 2. (14) πy m in Step 4 denotes that class set Y m is optimally repartitioned; x (πy m) = { x (R i); i = 0, 1,, N 1} denotes that R i(i = 0, 1,, N 1) is the class repartitioned optimally and x(r i) is the class center. The constraint condition, D m(q m ) < D m 1(Q m 1 ), can guarantee the convergence of clustering. According to the above analysis, the purpose of clustering is that the I input vectors are optimally divided into N classes. The basic thought of K-means clustering algorithm is that given an initial class set, circulation iteration processing achieves the minimum distortion error between input vectors and classes. We regard Set XY as the input vectors X of K-means clustering algorithm, and let N = 2. Finally, we get two classes, which are fitted in a line to compute the slope. In summary, LFMBKC is described as follows: Step 1. Regard filtered Set XY as the input vector X of K-means clustering algorithm. Step 2. Get two classes (clustering centers) using K- means clustering algorithm. Step 3. Fit two classes to a line and compute the line slope k. Step 4. Obtain tan θ = k according to k and perform the image vertical tilt correction. The matrix formula is as same as (13) LFMBLS In the course of engineering design and experimental statistics, upon analysis and processing of a lot of data, they are often fitted to a curve. The least squares is a commonly employed fitting method. Given a batch of ordinal data processed, we use a smooth curve y=f(x) to fit them. In principle, the deviation between the data and the fitting curve should be minimized. The deviation ε = f(x i) y i is usually called residue. The purpose of the least square is to enable objective function Q = n ε2 to achieve the minimum. We use a linear equation y=a 0x+a 1 to fit the data, then the objective function Q is Q = ε 2 = (a 0x i + a 1 y i) 2. (15) From (15), partial derivatives of a 0 and a 1 are obtained: Q a 0 = Q a 1 = (a 0x i + a 1 y i)x i = 0 (a 0x i + a 1 y i) = 0. (16) Solving the above equations, a 0 is obtained as n n y ix i n x i y i a 0 = ( n n n ) x 2 i 2 (17) x i where n is the number of the elements in the filtered Set X and Set Y. We put Set X and Set Y into (17), get the fitting line slope a 0. Let tan θ = a 0, and perform the image vertical tilt correction, its matrix formula is as same as (13). 3 Experimental results and comparisons In this section, we take the VLP images (see Fig. 5) as the experimental examples, which have been binarized to black background and white characters. The experiments are performed in MATLAB 7.01 on a PC with a Celeron 2.4 GHz processor and 512 MB RAM, running Windows XP. Fig. 5 Experimental images 3.1 Horizontal tilt correction experiments and results In horizontal tilt correction experiments, we compare the results of this proposed method with those of Hough transformation, Radon transformation and CNNCM (K-means clustering). The results are shown in Figs. 6 9, and correlation performance indexes are shown in Table 1. In Hough transformation, the angle varying range is [ 90, 90 ] and the varying size is 1. In Radon transformation, the angle varying range is [0, 180 ] and the varying size is also 1. In Fig. 6, this proposed method has already performed more precise horizontal correction, and the top line is basically horizontal. However, both Hough and Radon transformations have some horizontal tilt and the rotation angles are not enough. In CNNCM, we use K-means clustering to divide the image character coordinates into two classes to fit a straight line, and then compute the rotation angle α. Compared with Fig. 6, Fig. 9, which results from CNNCM (K-means clustering), has also some horizontal tilt, and the

5 214 International Journal of Automation and Computing 6(2), May 2009 rotation angle is not enough but better than Figs. 7 and 8. The correlation indexes in Table 1 are in accordance with the results in Figs Fig. 10 is the Radon transformation coefficient figure, in which the brighter the color, the higher the coefficient. In Fig. 10 (a), the biggest Radon coefficient is about 87, so α = (90 87) = 3. In Fig. 10 (b), the highest Radon coefficient is about 83, so α = (90 83) = 7. Fig. 11 is the Hough transformation coefficient figure, in which the brighter the color, the higher the coefficient. In Fig. 11 (a), the highest Hough coefficient is about 3, so α = 3. In Fig. 11 (b), the biggest Hough coefficient is about α = 7, so α = 7. In Table 1, the processing time of this proposed method is 4.02 times faster than that of Hough transformation and 4.06 times faster than that of Radon transformation. The lower processing time in real-time tilt correction of intelligent transportation system is very important and competitive. In Fig. 8, the correction effect of Radon transformation is the same as that of Hough transformation, but the processing time is not the same. In Fig. 12, CNNCM (K-means clustering) fits tilt lines that reflect the horizontal tilt trends of the experimental images, but the accuracy of the slope needs to be further improved. Table 1 Correction method The proposed method Hough transformation Radon transformation Horizontal tilt performance index comparisons Index Experimental images No. 1 No. 2 Time (s) Angle ( ) Time (s) Angle ( ) Time (s) Angle ( ) CNNCM(K -means Time (s) clustering) Angle ( ) Fig. 9 Horizontal tilt correction of CNNCM (K -means clustering) Fig. 10 Radon transformation Fig. 11 Hough transformation (a) Original image 1 Fig. 6 Horizontal tilt correction of the proposed method Fig. 12 (b) Original image 2 CNNCM (K -Means Clustering) Fig. 7 Horizontal tilt correction of Hough transformation Fig. 8 Horizontal tilt correction of Radon transformation 3.2 Vertical tilt correction experiments and results In vertical tilt correction experiments, we compare the results of K-L transformation with those of LFMBKC and LFMBLS. The results are shown in Figs , and correlation performance indexes are shown in Table 2. In these figures, the differences of the correction effects among the three methods are not obvious and two experimental images can be good correction. However, the correction effect of LFMBKC in Fig. 14 is the worse than those in Figs. 13 and 15, and the tilt angle is slightly bigger, which may be verified by the correlation data from Table 2. By carrying on the many comparative experiments, we find that

6 M. S. Pan et al. / A New Method for Correcting Vehicle License Plate Tilt 215 all the characters in Figs can be precisely segmented and recognized. Thus, these correction results can be accepted. In Table 2, the differences of the processing time among the three methods are obvious. The processing time of K-L transformation is times faster than that of LFMBKC and times faster than that of LFM- BLS. Considering the higher condition in time factor, K-L transformation is a better correction method. In Fig. 16, LFMBKC fits the tilt line, and in Fig. 17 LFMBLS fits the tilt line. They all reflect the vertical tilt trends of experimental images well. Table 2 Vertical tilt performance index (a) Original image 1 Correction method K-L transformation LFMBKC LFMBLS Index Experimental images No. 1 No. 2 Time (s) Angle ( ) Time (s) Angle ( ) Time (s) Angle ( ) Fig. 17 (b) Original image 2 LFMBLS fitting line Fig. 13 Vertical tilt correction of K-L transformation Fig. 14 Vertical tilt correction of LFMBKC Fig. 15 Vertical tilt correction of LFMBLS 4 Conclusions After thoroughly and deliberately analyzing K-L transformation feature, we proposed this method. In the horizontal tilt correction, we used K-L transformation to carry on tilt correction. In the vertical tilt correction, we proposed three correction methods to get the vertical tilt angle. The experimental results show that 1) this proposed method is more effective; 2) K-L transformation, LFMBKC, and LFMBLS are good vertical tilt correction methods, among which the correction effect difference is not obvious. In view of time factor, K-L transformation is superior to LFMBKC and LFMBKC. However, we have to mention that in the final corrected image the characters appear to have some burrs and the smoothing operation needs to be carried out, but this paper does not cover the topic. The study of this problem will be the focus of a future research activity. References [1] T. Naito, T. Tsukada, K. Yamada, K. Kozuka, S. Yamamoto. Robust License-plate Recognition Method for Passing Vehicles under Outside Environment. IEEE Transactions on Vehicular Technology, vol. 49, no. 6, pp , (a) Original image 1 [2] C. N. E. Anagnostopoulos, I. E. Anagnostopoulos, V. Loumos, E. Kayafas. A License Plate-recognition Algorithm for Intelligent Transportation System Applications. IEEE Transactions on Intelligent Transportation Systems, vol. 7 no. 3, pp , [3] R. Zunino, S. Rovetta. Vector Quantization for License Plate Location and Image Coding. IEEE Transactions on Industrial Electronics, vol. 47, no. 1, pp , Fig. 16 (b) Original image 2 LFMBKC fitting line [4] P. Comelli, P. Ferragina, M. N. Granieri. Optical Recognition of Motor Vehicle License Plates. IEEE Transactions on Vehicular Technology, vol. 44, no. 4, pp , [5] S. Kim, D. Kim, Y. Ryu, G. Kim. A Robust License-plate Extraction Method under Complex Image Conditions. In

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