Efficient DCT-Domain Blind Measurement of Blocking Artifacts
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1 ISSN , England, UK Journal of Information and Computing Science Vol. 5, No. 1, 21, pp Efficient DCT-Domain Blind Measurement of Blocing Artifacts Jagroop Singh 1 +, Suwinder Singh 2, Dilbag Singh 3 and MoinUddin 4 1Faculty department of Elec. & Comm. Engg., DAVIET, Jalandhar, Punjab, India 2 Faculty department of Computer Science & Engg., UIET, Chandigarh, Punjab, India 3 Faculty department of Elec. & Comm. Engg., Dr. B.R.Ambedar N.I.T, Jalandhar, Punjab, India 4 Director, Dr. B.R.Ambedar N.I.T, Jalandhar, Punjab, India. (Received June 3, 29, accepted August 6, 29) Abstract: It is well nown that low bit rate bloc-based discrete cosine transform coded images exhibits visually annoying coding artifacts. It is of interest to be able to numerically assess the degree of blocing artifacts as it plays an important role in the design, optimization and assessment of image and video coding systems. A novel algorithm for image blocing artifact detection is presented in this paper. Experimental results illustrating the performance of proposed method are presented and evaluated. Our experiment results show that the proposed method of measuring blocing artifacts exhibits satisfactory performance as compared to other post-processing method s/techniques and is very efficient and stable since the signal need not be compressed/decompressed. Keywords: Bloc discrete cosine transform, blocing artifacts, JPEG 1. Introduction Transform coding is the heart of several industry standards for image and video compression. In particular, the bloc based discrete cosine transform (B-DCT) is the basis for the JPEG image coding standard [1], the MPEG video coding standard [2], and the ITU TH. 261 [3] and H.263 recommendation s [4] for real time visual communication. BDCT coding has been successfully used in image and video compression applications due to its energy compacting property and relative ease of implementation. After segmenting an image in to blocs of size N N, the blocs are independently DCT transformed, quantized, coded and transmitted. One of the most noticeable degradation of the bloc transform coding is the blocing artifact. These artifacts appear as a regular pattern of visible bloc boundries.this degradation is the result of course quantization of the coefficients and of the independent processing of the blocs which does not tae in to account the existing correlations among adjacent bloc pixels. In order to reduce blocing artifacts, measurement of blocing artifacts is very necessary. Several methods have been proposed to measure the blocing artifacts in compressed images [5-1]. In [5], a model was obtained that gives the numerical value depending upon the visibility of the blocing artifacts in compressed images and thus requires original image for comparison with reconstructed image. In [6] the blocy image is modeled as a non blocy image interfering with a pure blocy signal. This method can be implemented only in the pixel domain and thus requires iterative DCT/IDCT operations with heavy computational burden [7]. The weaness of [8] is to assume that the difference of the pixel value across bloc boundary is caused only by blocing artifacts. This assumption decreases computation complexity but the measured value does not confirm to truth, particularly for the two adjacent blocs with a gradual change in pixel value. In [9] and [1] the variation of pixel value across bloc boundary was modeled as a linear function. This method may give error nous results especially for the adjacent blocs with a large change of pixel value across the bloc boundary.in this paper we propose a blind but accurate measurement algorithm for blocing artifacts by taing into account that the change in pixel value across bloc boundary is large as compared to adjacent pixels as we move away across bloc boundary. + Corresponding author. Tel: ; fax: address: roopasidhu@yahoo.com Published by World Academic Press, World Academic Union
2 48 2. Blocing Artifact Measurement System Jagroop Singh, et al: Efficient DCT-Domain Blind measurement of blocing Artifacts Blocing artifacts are introduced in the horizontal and vertical directions. Let us consider two adjacent blocs c 1 and c 2. Here we study the case of horizontally adjacent blocs, for the vertical adjacent blocs same principles apply. Let the right half of c 1 and left half of c 2 form a bloc denoted as bloc b. Bloc b is the 8x8 bloc which contains the boundary pixels. If any blocing artifacts occur between c 1 and c 2 the pixel value in b will be abruptly changed. In this paper we propose a novel DCT- domain method for blind measurement of blocing Artifacts, by modeling the abrupt change in b. Assume that the change in pixel value across the bloc boundary is very large as compared to pixel value away from bloc boundary. Then the change in pixel value in bloc b can be modeled as a two dimensional function f(x,y) given by Where x, y = N-1. In (1), f(x, y) is not constant in the vertical direction. Also the change in f(x, y) is large as x varies between 3 and 4. (1) Where Fig.1 Illustration of replacing the step function with a function f(x, y) in the 1-D case and Thus the eight pixels values on the function f(x,y) can be obtained as f( 3.5), f( 2.5), f( 1.5), f(.5), f(.5), f(1.5), f(2.5), f(3.5) The 2-D 8x8 bloc f can be constituted by simply stacing the vector row by row, i.e., Note that the bloc f is anti-symmetric horizontally and constant in the vertical direction. Therefore the, 8x8 DCT transform of f has only four non -zero elements in the first row. JIC for contribution: editor@jic.org.u
3 Journal of Information and Computing Science, Vol. 5 (21) No. 1, pp f Fig.2 JPEG compressed test images with Q=7, from top-left to bottom-right: pentagon, lena, peppers, and elaine,. The blocing artifacts between blocs c 1 and c 2 can be regarded as a 2-D step function in the bloc b given by 1, x,...,7; y...,3 N sxy (, ) 1, x,...,7; y 4...,7 N Let m the slope of f(x, y) and be the amplitude of s(x, y).then, bloc b can be modeled as bxy (, ) mf. ( xy, ). sxy (, ) rxy (, ) (5) (4) JIC for subscription: publishing@wau.org.u
4 5 Jagroop Singh, et al: Efficient DCT-Domain Blind measurement of blocing Artifacts Where is the average value of b representing local brightness and rxy (, ) represents the white Gaussian noise with zero mean [11-12]. Figure 2 show s a 1-D model of the pixel value difference across the bloc boundary. Let the difference between two pixels in horizontal direction be denoted by mxy (, ) bxy (, ) bxy (, 1) (6) Let the slope of left half of b is m L given by N1 /2 1 1 N 2 ml m( x, y) N x N 2 y1 Let the slope of me right half of b is mr The slope m (7) N1 1 1 N 12 mr m( x, y) N x N( N 2) yn/2 in bloc c can be computed by averaging ml and mr (8) ml mr m 2 (9) N1 / N N 1 6 mxy (, ) mxy (, ) N x N 2 y1 N( N 2) yn /2 Once and d are calculated the next part bxy ˆ(, ) composed of sxy (, ) and rxy (, ) can be obtained by bxy ˆ(, ). sxy (, ) rxy (, ) (1) bxy (, ) mf. ( xy, ) Using the blocing artifact can be measured/estimated quantitatively. 3. Fast Dct Domain Algorithm Denote the BDCT of c 1, c 2 and b by C 1, C 2 and B. Let us define two matrices q 1 and q 2 as follows:- q O O O I, q I4 4 O O44 O Where I is identity matrix and O is zero matrix ˆbcq 1 1 c2q2 (11) In DCT domain equation can be written as The 8x8 BDCT transform of the bloc Where =1, 2 c ( x, y) ˆBCQ C Q (12) is defined as 7 7 C ( u, v) c c c ( x, y) u v x y 2x 1u 2y1 v cos cos and c u (13) 1/8 for u, v cv (14) 2/8 otherwise Assume that the variation in pixel value of c is modeled by m. f( x, y) Here m represents the JIC for contribution: editor@jic.org.u
5 Journal of Information and Computing Science, Vol. 5 (21) No. 1, pp slope of 2-D function f(x, y) in c. For u =, v= 1 Substituting m. f ( x, y ) for c (x,y) in (13) gives 7 N 1 C(,1) 2 /8 m y 2 y (2y 1) cos 16 C (,1) m Where = according to par. [1] Then, by averaging the slopes of 2-D function f(x,y) in C 1 and C 2 we estimate m as m m C ( C (,1) m,1) (16) 2 2 The value m can be obtained from the above equation (16) with less computational complexity. Let us denote the first row of the 8x8 BDCT transform of f(x,y) by ˆ,,...,.In order to calculate we o 1 7 first compute the rest bloc ˆB by subtracting and f(x,y) from B as given below. B( i, j) m. j, i and Bˆ, i and j Bi (, j), otherwise j 1,...,7. Note that the 8x8 DCT transform of the 2-D step function defined in (4 ) has only four none zero elements in the first row. Let the vector v= [v o,v 2,.,v 7 ] be the first row of the 8x8 DCT transform of the 2-D step function, Then v o =v 2 =v 4 =v 6 =. By the unitary property of the DCT transform, we have (15) (17) Hence the Parameter can be computed as follows 7 vb j ˆ(, j ) jo vbˆ(,1) vbˆ(,3) vbˆ 5 (,5) vb ˆ(,7) (19) Because of the sparseness of DCT coefficients in the DCT bloc, the proposed method is far more efficient than the conventional IDCT-DCT methods such as [6]. It should be noted that if the magnitude of the blocing artifact is very small as compared to the original variation of pixel values across the bloc boundary then the blocing artifacts may not observed. 4. Discussion In the proposed method several ( lena,, pepper s, pentagon, and Elaine, ) 512 x512 images are coded at different bit rate. Fig. 3 shows the comparative results of the blocing artifact measurement done by proposed method and method in [1]. In addition to that the results are also compared with true blocing artifact which is measured by measuring the original pixel variation across the bloc boundary As shown in fig. 3 the measured (average) of the proposed method is more close to true blocing artifact as compared to the method in [1]. It should be noted that at low Q factor the blocing artifact is relatively small but as the Q factor increases the blocing artifact (Horizontal, vertical as well as average) also increases. JIC for subscription: publishing@wau.org.u
6 52 Jagroop Singh, et al: Efficient DCT-Domain Blind measurement of blocing Artifacts Average Blocing Artifact Par Proposed Original Peppers Average Blocing Artifact Par Proposed Original Elaine Fig. (4) shows the average deviation 1 2 m for different values of Q factor.the average deviation is different for different images and is maximum in case of lena, and is minimum for pentagon, image. The deviation is small for low values of Q but as the Q factor increases the deviation is large. The results indicate that the proposed method measures blocing artifacts more accurately than the method in [1] 3 Average Blocing Artifact Pentagon Proposed Par Original Average Blocing Artifact o b A 2 Original Par Proposed Lena QFactor Fig.3. Average blocing artifact comparison of different detection methods. Measure of deviation M.5 Average deviation Lena Peppers Pentagon Elain e Q Fact or Fig. 4. Average deviation comparison for different images. JIC for contribution: editor@jic.org.u
7 Journal of Information and Computing Science, Vol. 5 (21) No. 1, pp Conclusion Table I Measure of Blocing Artifacts of JPEG-Coded Lena Image Original Method in [1] Proposed β h β v β av β h β v β av β h β v β av Table II Measure of Blocing Artifacts of JPEG-Coded Peppers Image Original Method in [1] Proposed β h β v β av β h β v β av β h β v β av Table III Measure of Blocing Artifacts of JPEG-Coded Pentagon Image Original Method in [1] Proposed β h β v β av β h β v β av β h β v β av Table IV Measure of Blocing Artifacts of JPEG-Coded Elaine Image Original Method in [1] Proposed β h β v β av β h β v β av β h β v β av In this paper we proposed a DCT-domain blind measurement of blocing artifact s which is stable and can be applied to a wide variety of images in both pixel and DCT domain. Experimental results indicate that JIC for subscription: publishing@wau.org.u
8 54 Jagroop Singh, et al: Efficient DCT-Domain Blind measurement of blocing Artifacts the proposed method gives better results as compared to the method in [1] and is more accurate. The proposed method can be used to improve the performance (accuracy) of existing algorithms reducing the blocing artifacts. Due to its low computational cost, the technique can be integrated in to real- time image/video applications. 6. References [1] W. Pennebaer and J.Mitchell. JPEG Sill Image Data Compression Standard. New Yor: Van Nostrand, 1993 [2] J.L.Mitchel,W.B.Pannebaer, C.E.Fogg and D.J.LeGall. MPEG Video Compression Standard. New Yor: Chapman & Hall, [3] Video Codec s for Audiovisual Services at p 64 b/s. ITU-T Rec. H.261, Mar [4] Video Coding for Low Bitrate Communication. ITU- Rec. H.263, [5] S.A.Karunaseera and N.G.Kingsbury. A distortion measure for blocing artifacts in images based on human visual sensitivity. IEEE Trans. Image Processing. 1995, 4: [6] Z.Wang and A.C.Bovi. Blind measurement of blocing artifacts in images. in Proc. IEEE Conf. Image Processing. Vancouver, Canada. 2, pp [7] S.D.Kim and J.B.Ra. Efficient DCT domain prefiltering inside a video encoder. in Proc. SPIE Visual Communication and Image Processing. June 2, 467: [8] C.Wang, W.J.Zhang and X.Z Fang. Adaptive reduction of blocing artifacts in DCT domain for highly compressed images. IEEE Trans. Consum. Electr. 24, 5: [9] S.Z.Liu, and A.C.Bovi. Efficient DCT- domain blind measurement and reduction of blocing artifacts. IEEE Trans. Circuits Syst. Video Technol. 22, 12(12): [1] Chun-Su Par, Jun-Hyung Kim and Sung-Jea Ko. Fast blind measurement of blocing artifacts in both pixel and DCT domain. J Math Imaging Vis. 27, 28: [11] B.A.Wandell. Foundations of Vision. Sunderland, M.A.: Sinauer Assocites, [12] A.C. Bovi. Handboo of Image & Video Processing. San Diego, CA: Academic, 2. JIC for contribution: editor@jic.org.u
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