Modified Quaternion Based Impulse Noise Removal with Adaptive Threshold from Color Video Sequences and Medical Images

Transcription

1 Middle-East Journal of Scientific Research 3 (7): , 05 ISSN IDOSI Publications, 05 DOI: 0.589/idosi.mejsr Modified Quaternion Based Impulse Noise Removal wi Adaptive Threshold from Color Video Sequences and Medical Images 3 G. Elaiyaraja, N. Kumaraaran and C. Rama Prapau Department of ECE, Adhiparasaki College of Engineering, Anna University, Chennai, Tamilnadu, India Department of Information Technology, Sri Venkateswara College of Engineering, Anna University, Chennai, Tamilnadu, India PG Scholar M.E., Applied Electronics, Department of ECE, Adhiparasaki College of Engineering, Anna University, Chennai, Tamilnadu, India Abstract: In is paper, we present a modified quaternion vector filter to removal of random valued impulse noise from color video sequences. First e quaternion based meods are effectively representing e color distance of two color pixels. Then, based on is new color distance mechanism, e adaptive reshold used for identifying isolated noisy pixels. By analyzing e spatiotemporal order statistics information of e samples along horizontal, vertical and diagonal directions in current frame and e samples adjacent frames on motion trajectory, e video pixels are classified into noisy and noise free. Finally, e proposed filter is performed on e pixels at are judged as noisy and e oer pixels remain unchanged. Simulation results show at e proposed filter yields e superior performance in comparison to oer filtering meods. Key words: Color images Impulse noise Quaternions Video denoising CT scan image INTRODUCTION temporal domain meods more effective an e spatial domain meod [4]. Accurate motion estimation is Images and videos belong to e most important necessary for utilizing e temporal domain information. information carriers in today s world (eg. traffic Thus e video filters wi e use of motion observations, surveillance systems, autonomous information are usually called motion-compensated filters. navigation, etc). The impulse noise is often introduced Among ose filters, a few video filters can be found for into color video sequences during e process of bad removal of impulse noise, especially for color video acquisition, transmission or recording, malfunctioning sequences. pixels in camera sensors or faulty memory locations in In is paper, e noise is filtered step by step wi hardware []. Furer e impulse noise can be classified e help of fuzzy rules. There are ree types of meods into salt and pepper noise and random valued impulse to removal of impulse noise in color video sequences. noise and more difficult to remove e random valued The first step is component wise meod, which perform impulse noise. Noise removal in video is necessary for grayscale video denoising on individual color channels video application system. Video denoising meods can separately. It can provides a better estimate for magnitude be classified into spatial domain, temporal domain and of filtered vector and prevents blurring caused by spatiotemporal domain []. In spatial video denoising changes in noise free component. The second meod is image noise reduction is applied to each to frame to apply e algorim of -D color image filtering to each individually. In temporal video denoising meods, noise frames. The ird meod is to extend e -D color image between frames is reduced. Spatial-temporal video filtering to 3-D video data. The directional weighted denoising meods use a combination of spatial and median filter is much better for brightness restoration temporal video denoising meods [3]. The strong because of its ability of edge preservation along wi correlation between adjacent frames makes e spatial- brightness restoration [3-0]. Corresponding Auro: G. Elaiyaraja, Department of ECE, Adhiparasaki College of Engineering, Anna University, Chennai, Tamilnadu, India elaiyarg@gmail.com. 38

2 Middle-East J. Sci. Res., 3 (7): , 05 Most filters in literatures at are developed for It has one real component (a) and ree orogonal video, which are corrupted by impulse noise. For example, imaginary components (b, c, d).the modulus and e fast and efficient median filter (FEMF), e noise conjugate of quaternion ( ) are represented by. q adaptive fuzzy switching median filter (NAFSMF), FEMF uses prior information to get natural pixels for restoration. q = a + b + c + d The NAFSMF utilizes e histogram of e corrupted () image to identify noise pixels and employs fuzzy reasoning to handle uncertainty present in e extracted local information as introduced by noise []. The median (3) q = a-b i-c j-d k filters are very efficiency. There are different types of vector filters are used to removal of impulse noise include A quaternion wi unit modulus is called a unit weighted vector filter, switching vector filter, non linear quaternion. Addition of two quaternion is commutable, vector filter and similarity based vector filter. Effective but e multiplication is not commutable. meods for removal of impulse noise is mainly based on T A RGB color pixels x= [r, g, b] are represented in component wise meod [-7]. In is meod filtering quaternion form as, of detected pixels is done by block matching based on noise adaptive mean absolute difference. Block matching q=r i+g j+b k (4) for blocks of pixels and to filter e noisy pixels at e same time instead of applying e block matching for each Color pixels q and RqR* are positioned opposite each noisy pixels separately [8]. This meod is superior to oer at equal distances from e gray line =i+j+k. vector filtering for noisy pixels. Latter e noise free pixels Assume two color pixels q =ri+g j+bk and q =ri+gj+bk. will be change. In is paper, a new quaternion-based The quaternion is to express e chromaticity meod is used to measure color distance mechanism, e difference of color vectors q and q : proposed meod first uses e adaptive reshold value to detect e noisy pixels and noise free pixels, by r g b r g b r g b Q( q,q ) (r )i (g )j (b = )k analyzing e order statistics information about e color samples along e five directional lines. Then e (5) proposed filter is applied to noisy channels and remains unchanged. Compare to oer state-of-e-art meods, This equation does not include luminance difference. noticeable performance improvements have been But e color distance mechanism should include bo e achieved by e proposed solution [9]. chromaticity difference and luminance difference. So e color distance of q and q is using e formula as to Proposed Meod: he quaternion based meods are used measure e color distance between two color pixels: to removal of impulse noise. It would be more efficient in color image denoising. So in is paper, e quaternion CD(q,q )=w Q(q,q ) +(-w) I(q,q ) (6) based meods is using to represents e color distance of two color pixels. Then based on adaptive reshold where Q(q,q ) and I(q,q ) denotes e differences of q detecting noisy pixels and noise free pixels, by analyzing and q in chromaticity and luminance difference and w e order statistics information about e color samples [0,] gives e importance of chromaticity difference and aligning wi five directional lines. Finally, e proposed luminance difference. filter is performed on detected noisy pixels and remains unchanged. The difference of q and q in luminance variation as: Quaternions Model: Quaternions, which were discovered I(q,q )=k (r-r )+k (g-g )+k 3(b-b ) (7) by Hamilton in 843, are an extension of -D complex numbers to four dimensions. A quaternion ( ) form is where ki (i=,, 3 ) represent e contributions of red, q represented by. green, blue channels to luminance and we can set k =k =k 3=/3, which denotes e image luminance is e () average of ree color channels. q = a + b i + c j + d k 383

3 Middle-East J. Sci. Res., 3 (7): , 05 Fig. : Directional Pixels Along Vertical (Blue Line Color), Horizontal (Yellow Line Color) and Diagonal Direction (Black Line Color) in Current Frame and Adjacent Frames on e Motion Trajectory(Red Color) Impulse Detection: There are many techniques are used to process e pixels along four directional lines and detect noise in gray scale images. Such as weighted difference [9] and fuzzy reasoning [0]. For color images, several color image filtering approaches based on e directional pixels, such as CIELAB uniform color space [5]. In is paper, we are considering e pixels on motion trajectory to detect e noisy pixels, due to strong correlation between neighboring frames. Thus e pixels along e horizontal, vertical and diagonal directions in current frames and e pixels in adjacent frames on motion trajectory is used to detect wheer e pixels is noisy or not as shown in Fig.. Let I(x,y,t) and Y(x,y,t) denote e color vectors at position (x,y) in e t frame of e original(noisy) and e filtered color image sequences. The 3-D positions of e current pixels(x,y,t) along e five directional lines as ={p, p,., p,, p } (8) h h, h, h,l/ h,l h= to 5 represent e five directional lines, L and p h,i(i= to L) denotes e number of pixels and e position of i color pixels in directional lines h. p h,l/ as: represent e current 3-D position (x,y,t). The original noisy pixels in e five directional lines ={I(p ),, I(p ),., I(p )} (9) h h, h, h,l The following directional pixels to detect e current pixel I(x,y,t) is noisy or not: * h={y(p h,),..., Y(p h,-+l/),i(p h,l/),..., I(p h,l) } (0) Y(p ) (h=to5) represents filtered video on e h,i observed samples I(ph,i). In quaternion form: = {q(p ),..., q(p ),..., q(p )} () * h h, h,l/ h,l The pixel q(p h,i) wi e number of possible outlier is judged to be noisy, if e color distance between it and * e vector median of e color vectors in h is greater an or equal to a given adaptive reshold: Noised (q(p )) = h,i VM h q = argmin q(p ) q w L i= 0 L l= VM ( ( h,l/) l ), CD q p,q ADTOL 0,oerwise () VM ADTOL represent e adaptive reshold and q h is e vector median of e color vectors in directional line h as: h,l diff = w5*5 nd(w5 * 5 VM ( ( h,l/) l ) (3) The pixels along e direction wi e minimum number of possible outliers are used to judge wheer e current pixel q(p ) is corrupted by impulse noise or not. h,l/ Noised (q(p )) = h,l/, CD q p,q ADTOL 0,oerwise (4) where l denotes e directional line wi e minimum number of possible outliers (impulses): l = argmin Noised(q(p h,i)) for h= to 5 (5) For impulse detection, e reshold is varied adaptively as per e order statistics information of e frame and take a w n*n detection window separately for each channel for e impulse detection. First e median med (w 5*5) is subtracted from each pixel in window w to obtain difference as: 5*5 a ) for k= to 3 (6) Now for each channel ese differences are arranged in ascending order as { d,d,d,...d }. Then a parameter () () (3) (5) r, defining e roughness of filtering window is computed as: 384

4 5 i= (i) Middle-East J. Sci. Res., 3 (7): , 05 d `r = (7) 4 Now an adaptive reshold, which depends on statistical characteristics of pixels wiin e window 5 5 for each channel, is empirically obtained for natural images as: T=5+.6r*exp( r ) (8) The same reshold is appropriate for natural videos and it is used in Equ. () and Equ. (4) to find e output of e detector. Noise Removal: During noise removal only e pixels which are found noisy are filtered. There are different types of filters are existed for removal of impulse noise in color video sequences. Such as MF, VMF, AVNF etc. For removal of impulse noise, e most widely used filter is VMF. And e median filter is a non linear digital filtering technique.vmf introduces e maximum amount of smooing, when noise contamination is heavy. In smooing, e data signal structures are disordered. To overcome at problem, e weighted vector median filter is used to removal of impulse noise in color video sequences. But e weights are very crucial and significally affect e filtering performance. The proposed filter meod is denoted as q filtered (x, y,k) as: N M/ N/ m n,t +. s ( m+ x k t,n yk t, k t) ss t argmin G q q l= M/m= N/ N n = (9) where (x k+t, y k+t) is e motion trajectory in e frame k + t, W denotes e pixels inside e 3-D support window of size N N M, G σ σ s s t (s,t) = exp + t σs σt (0) where G s t(s, t) denotes e -D Gaussian weighted function. The weight of spatial filter and temporal filter are determined by e parameters s and t of e -D Gaussian function, en e more accurate motion estimation is needed in is meod. Experimental Results: The performance of e proposed meod is compared wi existing meods including VMF, AVMF, VAVDMF and WVMF. We use e peak signal to noise ratio (PSNR), mean absolute error (MAE), normalized color difference (NCD) to evaluate performance of different meods. Peak signal to noise ratio is computed from average MSE. PSNR and MAE are defined in e RGB color space and used to measure e performance of noise suppression and structural content preservation. NCD is computed in e perceptually uniform CIELAB color space. PSNR = 0log0 t H 55 y x,y,t 3HW x= y= W x y H W ( ) o( x,y,t) MAE t = y( x, y,t) o( x, y, t) 3HW () = = () NCD = t H W LAB LAB x= y= H W LAB o ( x,y,t ) x= y= ( ) ( ) y x, y,t o x, y,t (3) 385

5 Middle-East J. Sci. Res., 3 (7): , 05 Fig. : Matlab Simulation Results of Proposed Meod for color video sequence Fig. 3: (a) Lung CT Scan Image(b) Noise Corrupted Image wi 30% (c) Median Filtered Image(d) Proposed Meod Image Fig. 4: (a) MRI Brain Image(b) Noise Corrupted Image wi 0% (c) Median Filtered Image(d) Proposed Meod Image 386

6 Middle-East J. Sci. Res., 3 (7): , 05 Table : Comparison of PSNR for various image filtering meods for 5 frame of video sequence Noise density% VMF AV MF VAVD MF WV MF Proposed Approach Table : Comparison of MAE for various image filtering meods for 5frame of video sequence Noise density% VMF AVMF VAVDMF WVMF Proposed Approach Table 3: Comparison of NCD for various image filtering meods for 5frame of video sequence Noise density% VMF AVMF VAVDMF WV MF Proposed Approach Fig. 5: Graph Model for Comparison of PSNR Value for Various Image Filtering Meods for 5 frame of Video Sequence Fig. 6: Graph Model for Comparison of MAE Value for Various Image Filtering Meods for 5 frame of Video Sequence 387

7 Middle-East J. Sci. Res., 3 (7): , 05 Fig. 7: Graph Model for Comparison of NCD Value for Various Image Filtering Meods for 5 frame of Video Sequence Fig. 8: Matlab Simulation Results of Proposed Meod for CT Scan Brain Image where t denotes e t frames, H and W denotes e video are tabulated in Table, 3. Table shows e PSNR frame size, o(x,y,t) and y(x,y,t) represents e noise free values for different filters dealing wi different levels of LAB LAB and filtered frames respectively. O (x,y,t) and y (x,y,t) random valued impulse noise and us e PSNR value is are e expressions of o(x,y,t) and y(x,y,t) in e CIELAB high compared to e oer existing filtering meods. color space. Table shows e MAE values for different filters Fig. and Fig. 8 shows at matlab simulation results dealing wi different levels of random valued impulse of proposed meod for color video sequence and CT noise and us e MAE value is less compared to e scan brain image. Fig. 3 and Fig. 4 shows at results of oer existing filtering meods. Table III shows e NCD median filterd and proposed meod for CT and MRI scan values for different filters dealing wi different levels of medical images. From e results e proposed meod random valued impulse noise and us e NCD value is remove high density noise image compard to existing less compared to e oer existing filtering meods. meods. The results of ese experiments in terms of MAE, The performances are calculated for proposed PSNR and NCD are respectively presented in Table -3. algorim by varying e noise densities from 0% to 50% A graph of performance values against noise densities for 388

8 Middle-East J. Sci. Res., 3 (7): , 05 5 frame of video sequence is shown in Fig. 5, Fig Dong, Y. and S. Xu, 007. A new directional and Fig. 7. From at table it is observed at e weighted median filter for removal of random-valued performance of e proposed algorim is better an impulse noise, IEEE Signal Process. Lett., e existing algorims at bo low and high noise 4(3): densities. 9. Kang, C.C. and W.J. Wang, 009. Fuzzy reasoningbased directional median filter design, Signal CONCLUSION Process., 89(3): M elange, T., M. Nachtegael and E.E. Kerre, 0. The proposed filtering frame work for color videos Fuzzy random impulse noise removal from color corrupted wi random valued impulse noise is presented image sequences, IEEE Trans. Image Process., in is paper. The proposed algorim first combined e 0(4): two differences and at are represented in quaternion. Varghese, G. and Z. Wang, 00. Video denoising form to measure color distances. Then, based on adaptive based on a spatiotemporal Gaussian scale mixture reshold detecting noisy pixels, by analyzing e order- model, IEEE Trans. Circuits Syst. Video Technol., statistic information about e samples along e 0(7): horizontal, vertical and diagonal directions in e current. M elange, T., M. Nachtegael, S. Schulte and E.E. frame and e samples on motion trajectory, e video Kerre, 0. A fuzzy filter for e removal of random pixels were classified as noisy and noise free. Finally, e impulse noise in image sequences, Image Vis. proposed filter was employed to remove e detected Comput., 9(6): noisy pixels. It provides e better performance, when 3. Jin, L., H. Liu, X. Xu and E. Song, 0. Color compared to oer existing filters. impulsive noise removal based on quaternion representation and directional vector order- REFERENCES statistics, Signal Process., 9(5): Jin, L., H. Liu, X. Xu and E. Song, 00. Quaternion-. Boncelet, C., 005. Image noise models, in based color image filtering for impulsive noise Handbook of Image and Video Processing, A. C. suppression, J. Electron. Imag., 9(4): nd Bovik, Ed., ed. New York: Academic Press, 5. Jin, L. and D. Li, 007. A switching vector median pp: filter based on e CIELAB color space for color. Kim, J.S. and H.W. Park, 00. Adaptive 3-D median image restoration, Signal Process., 87(6): filtering for restoration of an image sequence 6. Yiqiu Dong and Shufang Xu, 007. A New corrupted by impulse noise, Signal Process.: Image Directional Weighted Median Filter for Removal of Commun., 6: Random Valued Impulse Noise, IEEE Signal 3. Rosales-Silva, P.A. and V. Golikov, 006. Processing Letters, 4(3): Adaptive and vector directional processing 7. Rajoo Pandey, 008. An Improved Switching applied to video colour images, Electron. Lett., Median Filter for Uniformly Distributed Impulse 4(): Noise Removal, World Academy of Science, 4. Deergna Rao, K., M.N.S. Swamy and E.I. Plotkin, Engineering and Technology, 38: Adaptive Filtering Approach for Colour Image 8. Yu, S., M.O. Ahmad and M.N.S. Swamy, 00. Video and Video Restoration, Proc. IEEE Conference on denoising using motion compensated 3-D wavelet Image Signal Process, 50(3): transform wi integrated recursive temporal 5. Ponomaryyov, V., A. Rosales-Silva and V. Golikov, filtering, IEEE Trans. Circuits Syst. Video Technol., 006. Adaptive and Vector Directional Processing 0(6): Applied to Video Colour Images, Electronic Letters, 9. Hsieh, M.H., F.C. Cheng, M.C. Shie and S.J. Ruan, 4(): Fast and efficient median filter for removing 6. Luo, W., 006. Efficient removal of impulse noise -99% levels of salt-and-pepper noise in images, from digital images, IEEE Trans. Consum. Electron., Eng. Applicat. Artif. Intell. 5(): Toh, K.K.V. and N.A.M. Isa, 00. Noise adaptive 7. Celebi, M.E., H.A. Kingravi and Y.A. Aslandogan, fuzzy switchingmedian filter for salt-and-pepper 007. Nonlinear vector filtering for impulsive noise noise reduction, IEEE Signal Process. Lett., removal from color images, J. Electron. Imag., 7(3): (3):