Parameter estimation and restoration of motion blurred image

Abstract: according to the real motion blur image restoration problems, analyze the difference between the image features and Simulation of real blurred images, this paper proposes a method that applied to real image degradation parameter estimation. First calculate the degraded image using cepstrum, taking the cepstrum to binary image using absolute value of minimum gray as the threshold, and then remove the center cross bright line; and then use formula of point to line to calculate the distance of bright fringe direction of binary image, that is direction of motion blur; the direction of motion blur is rotated to the horizontal direction by the degraded image center of rotation axis, divided the autocorrelation method to calculate fuzzy scale. To estimate the point spread function is take into the Wiener filtering algorithm to recover images, image restoration effect prove that parameter estimation results are correct.

Keywords: parameter estimation; image restoration; motion blur ; point spread function;

0 Introductions

In the process of taking a picture, photographed the relative motion between the scene and imaging equipment, resulting in blurred images is a very common degradation phenomena. Study on the restoration of motion blurred image is one of the important research topics in the field of image restoration, with the development of research, there are some effective algorithms and methods. But in different situations, these methods have different restoration effect. Because these methods are process with a certain precondition to propose and the assumption of image degradation, and the actual take a motion blurred image which not necessarily have the premise of these methods, or have only part of its premise. The key of image degradation lies in the accurate identification of the point spread function; motion blur degradation of PSF is determined by the blur direction and blurs scale two parameters. Most of the motion blur degradation research assumes that the degradation process for uniform linear motion ideal, Cannon[1]fuzzy image in the frequency domain using the motion space zero characteristic proposed frequency domain method to estimate the PSF parameters. Then, according to the frequency domain method had many improved algorithm. The literature [2] takes the Radon transform to detect the spectrum in the dark ,bright fringe estimation of motion blur direction; the literature[3] increase in the frequency spectrum of the two values processing, improve the precision of the estimation of the blur direction based on the literature [2];

The above algorithm even cannot correctly estimate PSF parameters of real motion blurred images, in order to solve this problem; this paper presents a method applicable to the real motion blur image parameter estimation and restoration. On the estimation and restoration of a degraded image parameters of camera shot, prove that the method is effective.

1 Analysis of the ideal of motion blurred image

Linear shift invariant system, describe the degradation process of image as the:

The analysis of uniform linear motion blurred image of the Fourier transform and cepstrum can obtain : spectrum of blurred image have regular light , dark fringes in uniform linear motion, image is as broad as it is long, dark fringes and the vertical to the movement direction, and the adjacent two dark fringe spacing and fuzzy scales inversely in the cepstral along; the direction of movement is a bright band, light with two negative peak distance exactly two times fuzzy scale. A lot of literature [1-5] is the feature design and the improved algorithm based on the above spectrum and cepstrum.

Figure 1 (b) is shown in Figure 1 (a) for fuzzy scale is 20 pixels, fuzzy angle is 45 the simulation of fuzzy image, Fig. 1 (c) -1 (E) is the corresponding spectrum, cepstrum. In order to highlight the cepstral features, Fig. 1 (d), 1 (E) of cepstrum is long, wide cut, and artificially lower center gray value after effects

Figure 1 (a) - graph (d) show that the ideal of uniform linear motion blurred image spectral and cepstral features very clear. Therefore, estimation of parameters for the simulation of motion blurred image, most algorithms can achieve good results.

2 Analysis of real motion blur image

Take pictures with the camera when the hand shake or subject to like movement, as well as in fast moving vehicles such as shooting, that will obtain the motion blurred image. Fuzzy images of these ways are not ideal uniform linear motion blur the spectrum of the bright, dark streaks along the direction of motion and the cepstrum of the bright band interference by other information or cover up. But, reality because of camera imaging space is fixed, the fuzzy image fuzzy image around the ideal must exist certain edge cut. In fact, it is because of the steep edge of truncated destroyed near the edge of the convolution relation, the degradation process is not a complete convolution, eventually lead to real blur image in the spectrum and cepstrum also appeared in the bright line (2). Figure 2 shows the camera shooting motion blurred image and its spectrum, the cepstrum, information is very weak, Fig. 2 (d) is cut and the lower center gray value after the display effect.

We compare Figure 2 (c), 2 (d) and 1 (c), 1 (d) to obtain: the real motion blur image spectrum and cepstrum does not have the characteristics of simulated images. Spectral images in the dark fringe basic cannot be identified, and have emergence of strong cross light; bright band is very weak along the direction of motion of cepstrum, was almost completely cover up cross bright line.

3 Parameter estimation of real motion blur image

Compare real motion blur image and simulated image, there are significant differences between the spectrum and cepstrum. Therefore, many of the spectrum or cepstrum based motion blur direction estimation algorithms applied to real image is very poor, most of the estimated angle is 0 degree or 90 degree. The literature [1-3] presented in the airspace of the blurred image after different angle differential summation, corresponding to the minimum angle for the fuzzy direction. Applicable scope is not limited to the airspace law uniform speed linear motion blur, but the estimation error, especially when the fuzzy image texture is less and there is a large area of smooth regions, there will be wrong. The experiment data in the literature (4) fuzzy image on the simulation showed that the average absolute error of 3 degrees in. The bright band is very weak along the direction of motion images cepstrum, but cross bright line, other regional uniform cepstrum is black (low gray value). After cepstrum processing, motion blur direction is determined by the cepstral features. The specific steps are as follows:

(1). Calculate the degraded image spectrum , Then in logarithmic form ;

(2). to (1) results for inverse Fourier transform to image degradation of cepstrum, denoted as

(3). The cepstrum transform translate into binary image. Switching threshold set the absolute value of cepstrum minimum (negative), i.e.:

Fig. 3(a) is binary image of fig.2

(4). Remove the binary image of the cross line of light. Analysis of experimental data of different size images showed that, the M*N size of image, M, N is odd, cepstrum of the cross line of light appear in (M+1) /2) and (N/2+ 1); M, N is even, the bright lines appear in the (M/2) line and the (N/2+ 1) column. The actual operation is directly arranged bright line where the whole line and numerical columns is zero, Fig. 3 (b) is the treatment effect, for the rest of bright fringe direction is the direction of motion blur

(5) We draw Different slope by the center point of binary image,Calculate all point to the straight line distance and summation, the minimum inclination angle for corresponding linear fuzzy direction.

Point , The tilt angle α of linear equation:

Fig. 3(C) is Tilt angle and distance summation curve of Fig. 3(b) in, to identification of fuzzy angle is 13 degrees. If the identification accuracy of decimal digits, you can set the inclination angle step is 0.1, reducing the step size after the identification to figure 2 (a) fuzzy images of 12 degrees.

4 Conclusions

In the motion blurred image restoration, the correct estimation of blur direction and blur scale is the key to guarantee the quality of image restoration. Through the comparative analysis of spectral and cepstral features real motion blurred image and Simulation of fuzzy image, although the simulation image can be achieved very good results for the algorithms in the literature, but not suitable for parameters on real blurred image estimation. According to the cepstral features and spatial features real blurred images, the cepstral values of two and then remove the cross center line of light, the fuzzy direction estimation; the image center axis of rotation, the motion blurred direction is rotated to the horizontal direction with differential auto correlation method to determine the fuzzy scale. On dozens of real fuzzy image parameter estimation and the estimation results into the Wiener filter restoration image restoration results show, this method can correctly identify real fuzzy direction of motion blurred image and blur scale, better practicality. In practical application, crop the image texture more (fuzzy characteristics) area used for parameter estimation, can guarantee the correct identification results, and while reducing the computational time. Fuzzy scale is larger, Wiener filtering restoration effect appears strong ringing effect, the research on image restoration and super-resolution reconstruction will proceed to the next step.

Reference

[1]He Weiguo,Li Shaofa.Estimating the blurring length of uniform linear motion blurred images [J].journal of computer Applications, 2005,25(6):1316-1317.(in Chinese)

[2]Li Yucheng,Jia Baohua,Yang Guangming. Blur parameter identification and restoration of motion blurred image[J].Computer Engineering and Design,2010,30(19):4247-4249.(in chinese)

[3]Guo Yongcai,Guo Ruirui,Gao Chao. Identification of blur parameters from motion blurred image[J].Chinese Journal of Scientific Instruments ,2010,31(5):1052-1057.

[4] Xie Wei,Qin Qiangqing. Estimating blur parameters of point spread function of motion-blurred image based on cepstrum[J]. Geometrics and Information Science of Wuhan University,2008,33(2):128-131.

[5] Le Xiang,Cheng Jian,Li Min. Improved approach to motion blur identification based on random transform[J] infrared and laser engineering,2011,40(5):963-969