Performance Comparison of Ringing Artifact for the Resized Images Using Gaussian Filter and OR Filter

Home , Overshoot (signal), Ringing artifacts

ISSN: 2278 – 909X International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE) Volume 2, Issue 3, March 2013 Performance Comparison of Ringing Artifact for the Resized images Using Gaussian Filter and OR Filter

Jinu Mathew, Shanty Chacko, Neethu Kuriakose

developed for image sizing. Simple method for image resizing Abstract — This paper compares the performances of two approaches which are used to reduce the ringing artifact of the digital image. The first method uses an OR filter for the is the downsizing and upsizing of the image. Image identification of blocks with ringing artifact. There are two OR downsizing can be done by truncating zeros from the high filters which have been designed to reduce ripples and overshoot of image. An OR filter is applied to these blocks in frequency side and upsizing can be done by padding so that DCT domain to reduce the ringing artifact. Generating mask ringing artifact near the real edges of the image [1]-[3]. map using OD filter is used to detect overshoot region, and then In this paper, the OR filtering method reduces ringing apply the OR filter which has been designed to reduce artifact caused by image resizing operations. Comparison overshoot. Finally combine the overshoot and ripple reduced between Gaussian filter is also done. The proposed method is images to obtain the ringing artifact reduced image. In second computationally faster and it produces visually finer images method, the weighted averaging of all the pixels within a without blurring the details and edges of the images. Ringing window of 3 × 3 is used to replace each pixel of the image. The artifact reduction technique is first applied to the downsized weights are determined by Gaussian function. The result image with truncation operation and then it is applied to the obtained in these two methods is compared in this paper. upsized image by zero padding. The proposed method Index Terms — DCT (discrete cosine transform), OD reduces the artifact and preserves the details and edges of the (Overshoot Detector), OR (overshoot-ripple) filter image. In Section II, the ringing artifact of the resized images is analyzed when resizing operations are performed in the DCT I. INTRODUCTION domain. In Section III, the ringing artifact reduction method using OR filter is given. In Section IV, filtering of ringing Ringing artifact appears as bands, ghosts near edges or artifact using OR filter has been explained and the echos when sharp transition takes place. Mathematically, this comparison between Gaussian filter are given in Section VI. artifact is called the Gibbs phenomenon. Ringing artifact can Experimental results are discussed in VII. Concluding be reduced by using various methods. These methods cannot remarks are given in Section VIII. remove serious artifact. Many computations have to be performed in order to estimate the ringing artifact and it II. RESIZING OPERATION causes serious blurring at edges and details of the image. Image resizing is the operation used to change the size of In frequency domain description, there is a possibility for the image. Truncation and zero padding can be used in DCT the generation of ringing artifact when the signal is domain for downsizing and upsizing of the image bandlimited or passed through a low-pass filter. In the time respectively. In truncation operation, the high frequency domain, ripples on sinc function produce ringing. Ringing coefficients of the image are discarded and in upsizing, occurs when a non-oscillating input yields an oscillating zeroes are added to the high frequency side. output. Ringing is closely related to overshoot which is when The resizing of the image in DCT domain [8] is explained the output takes on values higher than the maximum input below. The DCT operation has been used for resizing the value. image where block size of the DCT is chosen as 8X8. The Image resizing is done due to the advances of digital ringing artifact generated by the resizing operation is image processing. It is needed for various applications like analyzed here. image transmissions through the networks having varying In order to perform downsize operation on 8X8 DCT bandwidth. There are number of approaches have been block, take 8 sample sequences and apply type-II DCT. Then truncate high frequency coefficients of the image. Then apply 4-point IDCT. The same operations will be done for the Manuscript received March, 2013. upsizing operation also. Jinu Mathew , Electronics and Communication Karunya university, Coimbatore, Thamilnadu Shanty Chacko , Assistant Professor, Electronics and Communication, Karunya University, Coimbatore, Thamilnadu . Neethu Kuriakose , Electronics and Communication Karunya university, Coimbatore, Thamilnadu .

III. RINGING ARTIFACT REDUCTION METHOD USING OR new low-pass filter, called as overshoot-ripple (OR) filter is FILTER used to reduce the ringing artifact. Figure 1 shows the block diagram of the ringing artifact The main-lobe width of the OR filter is to preserve the reduction method using OR filter. Image resizing includes details and edges on the resized images. The main-lobe width both downsizing and upsizing of the image in block-DCT is the distance from the location where the main-lobe domain is the first step, so that due to the transitions of this amplitude is equivalent to the maximum side-lobe amplitude image size ringing artifact will be produced near the edges of in the impulse response. The ratio of the main-lobe amplitude the image. The ringing artifact will be reduced only in the to the maximum side-lobe amplitude is called as ripple ratio. image blocks having the artifact above a threshold value. If it The main-lobe width can be calculated [9] as below, is below the threshold value, then the IDCT of image is taken ω = 2cos −1 (x / x ) (1) directly without filtering. R a β The blocks having ringing artifacts are filtered by the OR where, the parameter xa is found using this eqn filters with 1and 2.The image with artifact will be given as D (y ) − a input to a filter, called as OR filter. The ripples will be n k (2) yk +1 = yk − β −1 reduced using the OR filter with 1. In order to detect the 2βCn−1 (yk ) overshoot region, an OD filter is designed and is used to which uses the inputs µ = , n = N − 1, and ε = 10 -6 generate a mask. After finding the overshoot regions, OR filter with the designed value of 2 is applied in that region . D µ (x) is calculated using the following algorithm : The overshoot and ripples of the image is identified and n remove separately. • Step 1 Input µ, n, and ε. Image resizing in block µ , x π/ n DCT domain If = 0 then output = cos( 2 ) and stop. Set k = 1 , and compute n 2 + 2nµ − 2µ −1 No y = 1 n + µ ERinging ˃ E th • Step 2 Yes Compute D µ (y ) y = y − n k k+1 k 2µD µ+1 OR filter, OR filter, n−1 OD filter 1 2 • Step 3

If |yk+1 – yk| ≤ ε, then output x= yk+1 and stop. Set k = k + 1 , and repeat from Step 2. IDCT IDCT IDCT IDCT Similarily, Ripple ratio can be calculated using the equation

Mask-map generation a Dn (yk ) − r yk+1 = yk − β −1 2βCn−1 (yk ) Overshoot region correction (3)

ε -6 where the inputs µ= , n=N-1, and = 10

Ringing artifact reduced image V. DESIGN OF OVERSHOOT -DETECTOR (OD) FILTER

Figure 1. Block diagram of the ringing-artifact reduction method Overshoot detector filter can be designed using the using OR -filter following figure 2. The candidate OD filters can be obtained as follows The OR filter design includes the steps to find out the main-lobe width which will reduce the overshoot caused by F(n) > F N ' < n < N '  the increased value of . The ripple ratio is also decided by  th 1 2  for 0 n LN-1 (4 ) the value of which should be chosen so as to reduce the F(n)

In this paper, the ringing artifact reduction using OR filter H (k) = is explained. Ringing artifact is analyzed when zero-padding OR|DFT 2RN and truncation operations are performed in DCT domain. A

ISSN: 2278 – 909X International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE) Volume 2, Issue 3, March 2013 will be the result when the low-pass filter is a Gaussian. In U α (k ) N 0 ≤ k ≤ N − 1  order to estimate the parameters from signals running 0 N ≤ k ≤ 2RN − N )5(  averages to estimate parameters from signals with U α 2( RN − k ) 2RN − N + 1 ≤ k ≤ 2RN − 1 characteristics that vary with space and time. Gaussian filtering in one, two or three dimensions is among

Mask map is generated by using an overshoot detector (OD) filter. Generated mask map which is a binary image the most commonly needed tasks in signal and image with 1 for the overshoot regions and 0 for the normal regions. processing. Finite impulse response filters in the time domain In the image domain, the ringing-artifact reduced image is with Gaussian masks are easy to implement in either floating composed as follows: or fixed point arithmetic, because Gaussian kernels are strictly positive and bounded.

VII. EXPERIMENTAL RESULTS yOR (α )1 (m,n) for mask (m,n) =1 l(m,n) =  The ringing artifact reduction technique is applied to the yOR (α )2 (m,n) for mask (m,n)=0 resized images that are initially downsized with truncation and then upsized with zero-padding operations in high frequency levels in the block-DCT domain. Since the high 0 m,n N 1 )6( ≤ ≤ − frequency coefficients are removed, the ringing artifact is produced near the edges of the image as shown in figure 2. where l (m,n) is ringing artifact reduced image, The image with artifact is given to an OR filter which is α yOR (α ) (m,n) denotes OR-filtered image with , and designed to reduce the ringing artifact. Mask map is generated using OD filter in order to detect the overshoot mask(m, n) denotes the mask map, respectively. region. The ripples can be reduced by using OR filter with Mask map can be generated as follows: 1. This filter is designed with the values of mu=0.402 and  ,1 F(m,n) ≥ Fth Xmu=1.042369 will give the better result for the ripple mask (m,n)=  0 m,n N-1 (7)  ,0 otherwise reduction of image. OD filter uses mu=9.629, Xmu=0.78221 for the mask map generation and the new OR filter with 2 is where F(m,n) is the difference between the OR-filtered designed for the image, and the OD filtered image . values mu=2.579, Xmu=0.92817 to remove overshoot effectively. The output with reduced ringing artifact using VI. GAUSSIAN FILTER OR filter is obtained and is shown in figure 3. The obtained Image will be initially downsized and then upsized then PSNR using OR filter is 34.7868. apply the filter. A Gaussian filter is a filter whose impulse The comparison is also done with Gaussian filter with response is a Gaussian function. A Gaussian filter modifies various values of sigma. The PSNR values for different the input signal by convolution with a Gaussian function. values of sigma are tabulated in table 1. The PSNR value is Gaussian filter is applied to the resized image in order to found to be maximum when sigma value is at 1 and is given reduce the ringing artifact. Initially, downsized the image and by 33.0749. The ringing artifact is not removed effectively then upsized. Due to the resizing operation the ringing when sigma value is less than 1. The output obtained after artifact is produced at the edges of the image. Gaussian filter applying the Gaussian filter is shown in figure 4. is applied to the whole image where the OR filtering is done based on block by block analyses of image. In this filtering method, each pixel in the image is replaced TABLE 1. PSNR VALUES DIFFERENT VALUES OF SIGMA by the weighted average of all the within a window. The weights are determined by the Gaussian function. Gaussian function is given by [10], SIGMA PSNR value 1 33.0749 1.5 32.5476  2 2   (x − x ) (y − y )  2 32.3712 F(x, y) = Aexp −  0 + 0  (8)   2σ 2 σ 2  2.5 32.2915   y  3 32.2066 where A=1, σ x = σ y =1 3.5 32.2231 4 32.2066 in the filtering of image (x,y) represent the location of the pixel to be replaced and (x-x0) and (y-y0) represent the location of the pixel within the window. F(x,y) represent the new intensity of pixel at (x,y). There are two different contexts like low pass filtering and computing running averages in digital signal processing where the Gaussian filter can apply. Gaussian filter will attenuate high-frequency noise. A smooth impulse response

with OR filter and found the OR filtering method is an efficient technique to remove ringing artifact from the resized images.

REFERENCES

[1] H. W. Park, Y. S. Park, and S. K. Oh, “L/M-fold image resizing in block-DCT domain using symmetric convolution,” IEEE Trans. Image Process., vol. 12, no. 9, pp. 1016–1034, Sep. 2003. Figure 2. Image with ringing artifact [2] J. Mukherjee and S. K. Mitra, “Image resizing in the compressed domain using subband DCT,” IEEE Trans. Circuits Syst. Video Technol., vol. 12, no. 7, pp. 620–627, Jul. 2002. [3] R. Dugad and N. Ahuja, “A fast scheme for image size change in the compressed domain,” IEEE Trans. Circuits Syst. Video Technol., vol. 11, no. 4, pp. 461–474, Apr. 2001 [4] Hyungjun Lim and HyunWook Park, “A Ringing Artifact Reduction Method for Block- DCT- Based Image Resizing” IEEE transactions on circuits and

systems for video technology, vol.21, no.7,july 2011 Figure 3. Image after filtering the ringing artifact is reduced [5] Stuart W.A.Bergen and Andreas Antoniou, “ Design of using OR filter. ultraspherical windows with prescribed spectral characteristics [6] Stuart W.A.Bergen and Andreas Antoniou, Generation of ultraspherical window functions [7] D.Gottlieb and C. W. Shu, “On the Gibbs phenomenon and its resolution,” Soc. Ind. Appl. Math., vol. 39, no. 4, pp. 644–668, 1997 [8] A. Krylov and A. Nasonov, “Adaptive total variation deringing method for image interpolation,” in Proc. IEEE Int. Conf. Image Process., Oct.2008, pp. 2608–261 [9] Stuart W. A. Bergen and Andreas Antoniou, “on the ultraspherical family of window functions’’, university of Victoria october 2003 [10] http://en.wikipedia.org/wiki/Gaussian_function

Figure 4. Image after filtering the ringing artifact is reduced using Gaussian filter.

The ringing artifact is removed for both using OR filter and Gaussian filter. Visually OR filter is showing good result comparing with Gaussian filter. The PSNR value comparison is also done and found OR filter has more PSNR value than Gaussian filter. In short, the artifact reduction method using OR filter is an efficient technique to remove ringing artifact from the resized images.

VIII. CONCLUSION This paper proposed a DCT-domain filtering approach that reduces the ringing artifact on the resized images in block-DCT domain. A ringing-artifact reduction technique for the removal of ringing artifact from the resized image is implemented. The OR filter technique reduces the ringing artifact and preserves the details or edges by combining overshoot-reduced image and ripple-reduced image. The ringing-artifact reduced image is constructed using the OR-filter. The OD filter is used for to detect overshoot region of an image. The Gaussian filter is designed and compared