An Efficient Method for Traffic Image Denoising - Science Direct

Available online at www.sciencedirect.com

ScienceDirect Procedia - Social and Behavioral Sciences 138 (2014) 439 – 445

The 9th International Conference on Traffic & Transportation Studies (ICTTS’2014)

An Efficient Method for Traffic Image Denoising Zhaojun Yuan, Xudong Xie, Jianming Hu*, Danya Yao Department of Automation, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Haidian District, Beijing 100084, P.R. China

Abstract In this paper, a novel method for traffic image denoising based on the low-rank decomposition is proposed. Firstly, the low-rank decomposition is carried out. Under the sparse and low-rank constraints of low-rank decomposition, the foreground images with complanate background and moving vehicles and the background images with similar road scene are obtained. Then the foreground image is segmented into blocks of a certain size. The variance of each block is calculated, among that the minimum is considered the estimate of the noise power. KSVD algorithm is performed for the foreground image denoising. Furthermore, the noisy pixel discrimination algorithm is performed to distinguish the noisy pixels from the noiseless pixels and the eightneighborhood weight interpolation algorithm is performed to reconstruct the noisy pixels, where the weighted coefficients are inversely proportional to the Euclidean distances between the pixels. And PCA recovery combined with noisy pixel discrimination and eight-neighborhood weight interpolation is adopted for the background image denoising. Finally, our proposed method is conducted based on the traffic videos obtained under the same view and angle. Moreover, our proposed method is compared with several state-of-the-art denoising methods including BM3D, KSVD and PCA recovery. The experiment results illustrate that our proposed method can more effectively remove the noise, preserve the useful information and achieve a better performance in terms of both PSNR index and visual qualities. © by Elsevier Ltd.byThis is an open © 2014 2014 Published The Authors. Published Elsevier Ltd. access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of Beijing Jiaotong University (BJU), Systems Engineering Society of China (SESC). Peer-review under responsibility of Beijing Jiaotong University(BJU), Systems Engineering Society of China (SESC). Keywords: Traffic image denoising; Low-rank decomposition; PCA; Noisy pixel discrimination; Neighborhood weight interpolation

1. Introduction With the fast development of computer vision and image processing techniques, the intelligent transportation system(ITS) has been widely applied. The traffic images contain abundant information and great intuition and are

*

Corresponding author. Tel: +86-(0)10-6279-0756; fax: +86-(0)10-6278-6911. E-mail address: [email protected].

1877-0428 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Peer-review under responsibility of Beijing Jiaotong University(BJU), Systems Engineering Society of China (SESC). doi:10.1016/j.sbspro.2014.07.222

440

Zhaojun Yuan et al. / Procedia - Social and Behavioral Sciences 138 (2014) 439 – 445

important sources of the traffic conditions. However, the traffic images are vulnerable to the noise of the equipments and external environment, which results in blurring. And traffic images with high qualities are of notable significance for the subsequent applications such as license plate recognition, traffic monitoring and Vehicle tracking. Therefore, seeking an effective denoising method that preserves the traffic scene while remove the noise is of great importance and value. In the last twenty years, image denoising techniques have made great progress within the field of image processing and computer vision. Dabov et al. (2006) presented the BM3D method, which decomposes an image into blocks of a certain size. These 2D blocks then are assembled based on the structural similarity measurement to construct a 3D array, which is processed by the joint filter and inverse 3D transformation to obtain the denoised image. Wang et al. (2012) used the Gabor-feature-based nonlocal means (GFNLM) filter for texture image denoising. Noise-corrupted images are recovered by replacing each pixel value with a weighted sum of pixel values within its search window, where the weighting coefficients are calculated based on the Gabor texture correlativity. Thierry and Florian (2007) proposed a denoising algorithm which reformulates the denoising issue as a search for the denoising process. It can be expressed as a linear combination of the elementary denoising methods, which are based on the image-domain minimization of the mean squared errors. Different from general images, the traffic images obtained by the ITS is under the same angle and view. Therefore, they are with the similar scenes (Lipton, 1998). Inspired by this point, in this paper, a denoising method for traffic images is proposed. Firstly, the RPCA (Wright, 2009) is performed for sparse and low-rank decomposition. Then corresponding denoising algorithms are adopted for the foreground and background images, respectively. The experimental results show that the proposed method can perfectly eliminate the noise, preserve the traffic scene and is effective to different kinds of noise. 2. Low-rank and Sparse Decomposition RPCA is a subspace decomposition method, which divides the original matrix into a low-rank matrix and a sparse error matrix˖

min rank ( Lk ) O || Ek ||0 Lk , Ek

I

Lk Ek

(1)

where I is the original matrix, Lk is the low-rank matrix, Ek is the sparse matrix, || x ||0 is the zero norm and λ is the regularization parameter to balance the rank of Lk and the sparsity of Ek , which is propositionally set at 1/ m u n (Jiang 2011) and m×n is the resolution of the query image. The above-mentioned problem has been proved NP-hard (Candes, 2010) and been equivalent to the following convex substitution˖

min || Lk ||* O || Ek ||1 Lk , Ek

I

Lk Ek

(2)

where || x ||* is the nuclear norm and || x ||1 is the one norm. Traffic images obtained by the same camera are with similar background while the position of the moving vehicles is stochastic, which exactly coincides with the low-rank and sparse constraints of RPCA. The low-rank background images and foreground images with vehicles obtained by RPCA are shown in Fig. 1.


441

Fig. 1. Images obtained by low-rank decomposition. The first row are the original traffic images, the second row are the low-rank background images and the third row are the foreground images with moving vehicles.

3. Background Image Denoising The background images obtained by RPCA are with similar road scenes, which is of great correlativity. PCA recovery is first performed for that its subspace is orthotropic and it is the optimal decorrelation transform with the minimum reconstruction error (Kirby, 1990). However, PCA recovery removes the noise, as well as the highfrequency information, which results in image blurring. Therefore, a supplementary algorithm for distinguishing a noisy pixel from a noiseless pixel is requisite. It is reasonable to assume that the inter-pixel difference can be measured by their Euclidean distance (Tan, 2009). To describe the distribution of pixel (i,j), we propose the pixel Euclidean distance variance, (denoted as PEDVi,j), which is defined as follows:

PEDVi,j

1 N

N

¦ || L(u

n ,i , j

, ui , j ) L(un,i , j , ui , j ) ||2 2

n 1

L(u1 , u2 ) || u1 u2 ||2 1 N

L(un ,i , j , ui , j )

u

N

¦ L(u

n ,i , j

(3)

, ui , j )

n 1

L(u , u )

1 2 where N is the number of images in the training database, i , j is the average gray intensity at pixel(i,j), the Euclidean distance between two pixels. The Chebyshev Inequality (Liu 2008) illustrates that for a stochastic variable X, it distributes within the interval [ X mV ( X ) , X mV ( X )] with a confidence probability over m2 1/ m2 , where X is the mean value and V ( X ) is the standard variance. Therefore, at each pixel, the average gray intensity is first computed. Then, the average Euclidean distance and PEDV are calculated to describe the pixel distribution. Based on the Chebyshev Inequality, if the distance between the pixel in the query image and that in the average pixel is within a certain range of the average distance, then this pixel is considered noiseless, otherwise, it is noisy. The discrimination criterion, therefore, is as follows:

L(unoise,i , j , ui , j ) L(un ,i , j , ui , j ) cPEDVi , j

(4)

442


Furthermore, for a noisy pixel, the noiseless pixels in its eight-neighborhood are selected. For each selected pixel, the Euclidean distances between it and the corresponding pixels in the training set are computed. Then the pixel with the minimum distance is picked for the noisy pixel recovery. This noisy pixel will be recovered by the weighted sum of the picked pixels in the training set with the minimum distances, where the weighted coefficients are inversely proportional to the distances. And if all the pixels in its eight-neighborhood are noisy, then this noisy pixel will be denoised by PCA recovery. Therefore, the final-denoised background image is˖

urec,i , j

upca,i , j , neighborhood all noisy ° ° ° ® ¦ wi , j ,k uL ,i , j , otherwise , noisy i , j ,k ® °w z0 ° ¯ i , j ,k °¯=unoisy,i , j , noiseless

˄5˅

where upca,i,j is the pixel (i,j) in the PCA-recovered image and unoisy,i,j is that in the query image. wi,j,k is the normalized weight-coefficient of the k-th noiseless pixel in the eight-neighborhood. 4. Foreground Image Denoising In the foreground images, the similar road scenes in the original images are excluded by PRCA. Therefore, the foreground images mainly contain the moving vehicles and the complanate gray background. KSVD is an approach for training an over-complete dictionary composed of prototype signal-atoms (Aharon 2006). Instead of adopting the classic dictionaries such as Contourlet set (Do 2005) and Curvelet set (Cands 2002), KSVD utilizes the characteristics and features of the query image and the dictionary is generated with iterative sparse decomposition. The denoised image is recovered by a linear combination of the atoms under strict sparse constraints (Aharon 2006). And the convergence tolerance, namely the noise power needs to be estimated for the iterative sparse decomposition. The background in the foreground traffic images is of complanate statistical characteristics, where the fluctuation is mainly brought by the noise. Therefore, the foreground image is segmented into blocks of a certain size. The variance of each block is calculated and the minimum value is considered the estimate of the noise power, And then KSVD algorithm is performed for the foreground image denoising. All of the procedures of our proposed algorithm are illustrated in Fig. 2.

Fig. 2. The procedures of our algorithm

5. Experiment Results Our experiments are conducted based on the traffic videos obtained under the same view and angle. 100 frames at different times are selected as the training set for RPCA. And the training set for PCA is constructed by the background images of those above-mentioned images. Other fifty traffic images are selected as the test set. And none of the selected images are under extreme illumination. Gaussian noise, Rayleigh noise, salt-and-pepper noise and mixed noise (a mixture of other three types of noise) are added to the test images, respectively. The low-rank decomposition is first carried out. Then the noisy pixel discrimination and the neighborhood interpolation is performed for the background images and KSVD is applied for the foreground images where the block size is set 16×16. The value of c in (4) is empirically set 2. BM3D, KSVD, and PCA recovery are compared to our algorithm.

443


PSNR index is adopted to evaluate the performances of these several algorithms. The corresponding results are illustrated below. Ga us s i a n N o i s e

Ray leigh No ise

35

35

P roposed

P roposed

K SVD

K SVD 30

BM3 D

30

BM3 D P CA

25

25

PSNR/d B

PSNR/d B

P CA

20

20

15

15

10

10

20

30

40

50

60

70

10

80

20

30

40

50

60

70

80

N o i s e P o we r

N o i s e P o we r

Mixed Noise

Sa l t - a n d - P e p p e r N o i s e

30 34

P roposed

P roposed

28

K SVD

32

K SVD BM3 D

BM3 D 30

26

P CA

P CA

PSNR/d B

PSNR/d B

28 26 24 22

24

22

20

20

18

18 16 0.05

0.1

Noise Densit y

0.15

16 10

20

30

40

50

60

70

80

N o i s e P o we r

Fig. 3. Denoising performance comparison for different algorithms under different kinds of noise.

It can be seen from the results that when the noise power is small, BM3D, KSVD and our proposed method all perform well. Furthermore, as the noise power increases, our algorithm performs better. Higher PSNR can be reached, as well as better visual effects while other methods fail, as illustrated in Fig. 4.: severe blurring occurs and great amounts of noise remains. That is due to the fact that other three methods mix the moving vehicles and the added noise together while our method can separate the foreground image from the background image under the low-rank and sparse constraints of RPCA. The noisy pixel discrimination can effectively detect the noisy pixel and neighborhood weight interpolation can preserve as much of the useful information in the query image as possible. The complanate gray in the foreground image guarantees the accuracy of noise power estimation and the performance of KSVD. In addition, our algorithm is without requiring prior knowledge about the noise and it is effective to various kinds of noise. Therefore the denoised image derived from our proposed method is with clearer scene, more useful information preserved, which is of great importance for the applications including vehicle orientation, object tracking and feature extraction.

444


Fig. 4. Denoised traffic images using different methods. The first row is with Gaussian noise, the second row is with Rayleigh noise, the third row is with salt-and-pepper noise and the last row is with mixed noise. The first column are the noise-corrupted images, denoised images obtained by BM3D, KSVD, PCA and our proposed method are listed respectively in the second to the last column.

6. Conclusions In this paper, a novel denoising method for traffic image based on the sparse and low-rank decomposition is proposed. RPCA is first carried out to divide the query image into a background image containing the road scenes and a foreground image containing the vehicles. Then KSVD is performed for the foreground image denoising and the noisy pixel discrimination and neighborhood interpolation is performed for the background image denoising. Moreover, our proposed method is compared with three state-of-the-art denoising methods, including BM3D, KSVD and PCA recovery. The experiment results illustrate that our proposed method can achieve higher PSNR, as well as better visual effects and is effective to different kinds of noise. Acknowledgements This work was supported in part by National Basic Research Program of China (973 Projext) 2012CB725405, Hi-Tech Research and Development Program of China (863 Project) 2011AA110405, National Nature Science Foundation China 61273238 and the Henry Fok Foundation 122010. References Aharon, M., Elad, M., & Bruckstein, A. (2006). K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. Processing of IEEE Transactions on Signal, 1047-3203. Candes, E., Li, X. D., & Ma, Y. (2010). Robust principal component analysis? Recovering low-rank matrices from sparse errors. Sensor Array and Multichannel Signal Processing Workshop, 201-204. Cands, E. J., & Guo, F. (2002). New multiscale transforms, minimum total variation synthesis: applications to edgepreserving image reconstruction. Processing of IEEE Transactions on Signal, 1519-1543.


445

Dabov, K., & Foi, A. (2006). Image denoising with block-matching and 3D filtering. In SPIE Electronic Imaging: Algorithms and Systems, San Jose, 607-616. Do, M. N., & Vetterli, M. (2005). The contourlet transform: an efficient directional multiresolution image representation. Processing of IEEE Transactions on Image, 2091-2106. Jiang, M., & Feng, J. (2011). Robust low-rank subspace recovery and face image denoising for face recognition. Processing of IEEE International Conference on Image, 3033-3036. Brussels. Kirby, M., & Sirovich, L. (1990). Application of the KL procedure for the characterization of human faces recognition using eigenfaces. IEEE Transaction on Pattern Analysis and Machine Intelligence, 103-108. Lipton, A., Fujiyoshi, H., & Patil, R. (1998). Moving target classification and tracking from real-time video. IEEE Workshop Applications of Computer Vision, 8-14. Liu, K. and Zhang, K. (2008). “Background modeling algorithm that uses Chebyshev inequaliy,” International Conference on Computational Intelligence for Modeling, Control and Automation, 838-843. Tan, X., Chen, S., & Zhou, Z. H. (2009). Face recognition under occlusions and variant expressions with partial similarity. IEEE Transactions on Information Forensics and Security, 217-230. Thierry, B., & Luisier, F. (2007). The sure-let approach to image denoising. Processing of IEEE Transactions on Image, 2778-2786. Wang, S. S., Xia, Y., & Liu, Q. G. (2012). Gabor feature based nonlocal means filter for textured image denoising. Journal of Visual Communication and Image Representation, 1008-1018. Wright, J., Ganesh, A., & Rao, S. (2009). Robust principle component analysis: exact recovery of a corrupted lowrank matrix. International Conference on Neural Information Processing Systems Foundation, 2106-2112. Vancouver, Canada.