International Journal of Computer Engineering and Applications, Volume XII, Issue I, Jan. 18, ISSN

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1 International Journal of Computer Engineering and Applications, Volume XII, Issue I, Jan. 18, ISSN A STUDY ON STATISTICAL METRICS FOR IMAGE DE-NOISING A.Ramya a, D.Murugan b, S.Vijaya Kumar c,v.murugan d a, b Department of Computer Science & Engineering, Tirunelveli, Tamilnadu, India c Departmnent of Computer Application,NPR Arts and Science College,Natham, Tamilnadu, India d Department of Computer Science, MSU Constituent College, Tirunelveli, Tamilnadu, India ABSTRACT The statistical quality measure for an image is a mandatory field for digital image processing for evaluating the noise and the efficiency of the algorithm over an image. In many ways, the quality of an image gets degrade such as during physical interference, acquisition process, transmission, compression and also sometimes by human error with the devices. This work reported the several metrics that dealt with the pre-processing stage of an image. The Pre-processing is an important stage that should be concentrated carefully before processing an image to any mid or post-processing stages like segmentation and reconstruction to yield the better outcome. Therefore proper metrics should be undertaken and evaluate the pre-processing algorithm. In this paper, we have briefly comprehended the various quality assessment metrics related to the full reference Image Quality Assessment (IQA). We clustered IQA metrics clustered according to their strategies. Therefore, it is mandatory to establish the empirical measure for image de-noising for evaluating an image quality. Key words: Image quality, Performance Metric, Image De-noising, pre-processing, Quality Index. 1. INTRODUCTION Digital image processing is the realistic synthesis process for the creation of accurate, high-quality image. Image processing method arises with the two major principle application areas such as improvement of image feature for human interpretation and processing of image data for machine learning. The ultimate goal is the quality assessment is to create an image which is indistinguishable from an actual scene. Image Quality Assessment (IQA) has an important role numerous image processing applications such as medical imaging technology, Forensic Science, fake biometric detection, image enhancement. A. Ramya, D. Murugan, S.Vijaya Kumar And V. Murugan 241

2 A STUDY ON STATISTICAL METRICS FOR IMAGE DE-NOISING The advance in image synthesis methods allows improving the distribution of contrast image with good perception. But it does not ensure that the displayed image with high fidelity with visual perception. There exists much reason for the distortion of image quality they are limited dynamic display, residual short comings of the rendering process and physical interference. Apart from this problem there exist problems like the low-contrast image, blurred image, noise affected image, noise occurred during transmission, during the conversion process, manipulation and storage [9]. The trade-off between hardware resources and visual quality are involved in designing such advance system and accurate quality measurement techniques in order to make the trade-off efficiently [10]. The subjective evaluation is a tedious process, expensive and also they cannot be incorporated into the automatic system usually called Computer Aided System (CAD) that adjusts them to the real-time environment. The Great progress has been made in the past decade for the full reference IQA. But no work has been reported to measure and compare the performance of the preprocessing algorithm [11]. In this paper, we comprehend the full reference quality measurement for image de-noising, enhancement and restoration process. The main goal of Quality Assessment (QA) research is to discover automatic ways of accurately measuring visual quality. Apart from the traditional method of performance metrics like PSNR, MSE and SSIM, many new metrics that evaluate the image quality, contrast and structure better than this methods. This paper is organized as, in section 2; the brief information of various performance metrics is described and formulated. The conclusion is derived in section PERFORMANCE METRICS The Image Quality Assessment access the quality of image and video in very consistent manner. The full reference quality factors attempt to achieve the consistent in an image quality and psycho-visual features of Human Visual System (HVS) or by fidelity criteria. 2.1 Peak-Signal to Noise Ratio The Peak Signal-to-Noise Ratio (PSNR) is a term of expression for the ratio between maximum possible power value of a signal and the power of distorting signal (noise) that affects the quality of an image. PSNR usually will be an approximation to human perception of the de-noised image. The PSNR is usually expressed in terms of the logarithmic decibel scale. The higher the value of PSNR indicates that the reconstructed or enhanced image is of higher quality. The lower value of PSNR indicates the reconstructed image is not reconstructed properly and there may be a chance of noise present in it. The PSNR has two blocks of calculation, the first is the evaluating the Mean-Square Error (MSE). The MSE indicates the cumulative squared error between reconstructed and original image and PSNR represent the measure of peak error. To compute the PSNR, first MSE should be formulated: MSE 1M 1N 1 g(u,v) f (u,v) 2 (1) MN u 0 v PSNR 10log10 MSE (2) Here f (u,v)and g(u,v) are the original and reconstructed image respectively. A. Ramya, D. Murugan, S.Vijaya Kumar And V. Murugan 242

3 International Journal of Computer Engineering and Applications, Volume XII, Issue I, Jan. 18, ISSN Noise Quality Measure The Noise Quality Measure (NQM) is the effect of additive noise. It is based on Peli s contrast with the properties such as variation in contrast sensitivity with distance, image dimension, spatial frequency, variation in local luminance mean, contrast interaction between spatial frequency and contrast masking effects [1]. If G s (u,v) and F s (u,v) are the model of the processed and original image then NQM is formulated by the equation given below: Gs2(u,v) u v NQM 10log10 u v (Gs(u,v) Fs(u,v))2 (3) 2.3 Universal Quality Index The Universal Quality Index (UQI) is modelled for distortion of an image with the combination of three factors such as loss of correlation, luminous distortion and contrast distortion [2]. Let x and y be the original and processed image respectively. The quality index is measured by, x,y UQI. (x)2 2 x y. x y (y)2 2 x y 2 2 x y (4) The dynamic range of UQI ranges from [-1, +1]. The UQI consists of three components which are mentioned in equation (5). The first component is the correlation co-efficient between x and y which measures the degree of linear correlation between x and y and its dynamic range is [-1, +1]. The second component value ranges between [0, 1] which measures the closeness of mean luminance between original and processed image respectively. The third component measures the similarity between the contrast images. Its value is also between [0, 1]. 2.4 Structural Similarity Index Measure The Structural Similarity index Measure (SSIM) is a metrics for determining the similarity between reconstructed and corrupted image [3]. The SSIM is an improved version of UQI. This measurement of image quality is based on an initial uncompressed or distortion-free image as a reference. It is of the design that the picture element has strong inter-dependencies when they are spatially close enough. The dependency carries the details about the structure of the object in an image. The SSIM is based on the luminance, contrast and structure. (2 i j C1)(2 i, j C2) SSIM ( 2 2j C1)( i2 2j C2) (6) i Here i j are the local means, i and j are the standard deviation, i, j is the cross variance of an UQI 4 xy x y (5) image i,j. C 1 (0.01* L) 2,C 2 (0.03* L) 2. Where L is the specified dynamic range value lie between [-1, +1]. 2.5 Multi-Scale Structural Similarity Index Measure The Multi-Scale Structural Similarity Index Measure (MS-SSIM) provides flexibility ( x2 2y)[(x)2 (y)2] than single scale SSIM. The MS-SSIM is advanced of SSIM which is performed over multi-scale through multiple stages of A. Ramya, D. Murugan, S.Vijaya Kumar And V. Murugan 243

4 A STUDY ON STATISTICAL METRICS FOR IMAGE DE-NOISING sampling and reminiscent of multi-scale processing in the early vision system. It has been shown to perform equally well or better than SSIM on different subjective image and video databases [8]. Like SSIM, MS-SSIM has to satisfy the three condition such as symmetry, boundary and unique maximum. The MS-SSIM is formulated below: MS SSIM l(x, y) M y) M. c (x, y) j (7) j 1 j. s(x, Where M, j and j are used to adjust the relative importance of the different component. l(x, y), c(x, y) and s(x, y) are the luminance, contrast and structure factors and they are determined by the equation given below: l(x, y) 22 x y C1 (8) x 2y C1 c(x, y) 2 x2 x y2y CC22 (9) 2.6 Information Fidelity Criteria Information Fidelity Criteria (IFC) is based on the natural statistic model. In IFC the quality assessment problem is defined as the information fidelity problem, whereas the image source communicates with the receiver through a channel. This channel is responsible for the signal transmission [6]. It has fundamental limits on how much information should transmit from source (reference image) through the channel (image degradation process) to the receiver (psycho-visual observation). The IFC quantifies the statistical information, shared between the original and degraded image. The IFC does not involve parameters associated with a display device, information from psychology visual experiment. The IFC does not require training data either. IFC I(CNk,K ; DNk,K SNk,K ) (11) k subband The reference image in the k-th sub-band as C k, distorted image as D k. C Nk,K denotes N k is the coefficient from the radio frequency RFC k of the k-th subband and similarity for D Nk,K an S Nk,K image. Assume C k are independent of each other. If C is obtained by summing over all sub-band. x,y C 3 s(x, y) (10) x y C3 Where C 1, C 2 and C 3are the small constant. 2 C1 (K1L)2, C2 (K2L)2andC3 C 2, where L is the dynamic range of pixel value (L=255 for 8-bit grey scale image).k is the scalar constant. 2.7 Visual Signal to Noise Ratio The quantitative Visual Information Fidelity (VSNR) of the natural image based on nearthreshold and distance threshed properties. The VSNR operates through a two-stage approach. The initial stage is the contrast threshold for detection of distortion in the presence of a natural image. VSNR is efficient in terms of computational complexity and operated based on luminous parameter The VSNR, in decibels, is accordingly given by A. Ramya, D. Murugan, S.Vijaya Kumar And V. Murugan 244

5 International Journal of Computer Engineering and Applications, Volume XII, Issue I, Jan. 18, ISSN Where c is constant, d iis the similarity between VSNR 10log10 C VD2(2I) 20log10 C(I) (12) Where VD denotes the visual distortion of an image and it is represented by dgp VD d pc (1 ) 2 (13) Where d pcis the measure of perceive contrast of the distortion, d gc is the measure which is extended to global precedence that has been disrupted. C(I) denotes the RMS contrast of the source image I. 2.8 Riesz Transform Based Feature Similarity The Riesz-transform basedfeature Similarity metric (RFSIM) is one of the image quality assessment metrics based on the human visual perception. The 1storderand 2nd-order Riesztransform coefficients of theimage are taken as image features [7]. The similarityindex between the reference and distorted images ismeasured by comparing the two feature maps at keylocations marked by the feature mask. 5 RFSIM D i (14) i 1 D i di (x M, y().xm, y()x, y) (15) Here M is the mask for an image. 2 f di 2(ix(,xy,)y ).ggii2(x(,x,y)y) cc (16) fi d pc 2 ( 1 d gp ) two feature maps and f i,g iis the source and enhanced image. 2.9 Feature Similarity Index Measure The Feature Similarity Index Measure (FSIM) is the full reference of the image quality assessment and it is based on the human visual effect. In FSIM two kinds of features exist they are the phase congruency (PC) and the gradient magnitude (GM) they represent complementary aspects of the image visual quality [5]. The PC value is also used to weight the contribution of each point to the overall similarity of two images. X S FSIM L(X ).(PCm(X )) (17) X (PCm(X )) Where is the spatial domain of the whole image. PC is the phase congruent structure and is given by the formula: PCm(X) max(pc1(x),pc2(x)) (18) SL(X) is the overall similarity between f1 and f2, where f1 and f2 are the original and enhanced image. S L(X) is formulated and given below. SL(X ) SPC(X ).Sg (X ) (19) Here G is the gradient magnitude and it is formulated by: A. Ramya, D. Murugan, S.Vijaya Kumar And V. Murugan 245

6 A STUDY ON STATISTICAL METRICS FOR IMAGE DE-NOISING G G x 2 G 2 y (20) The above equation (20), represent the partial derivatives of an image f(x). 3. CONCLUSION In this paper, we have briefly comprehended the various validation metrics for image preprocessing, especially for noise reduction. This statistical measure assists us to evaluate the efficiency of the algorithm and quality of the enhanced noisy free image. In this work, we have presented nine full-reference image quality assessment metrics for preliminary stage of image processing which will be useful for further processing stages of any image without any degradation in their quality. The main aim of the quality assessment is to design an algorithm for the evaluation of an image quality respective with the human visual perception. Image quality metrics prove the testing and used for monitoring the application related to images and video. 4. REFERENCE 1. Damera-Venkata, N., Kite, T.D., Geisler, W.S., Evans, B.L. and Bovik, A.C., Image quality assessment based on a degradation model. IEEE transactions on image processing, 9(4), pp Z. Wang and A.C. Bovik, A universal image quality index, IEEE Signal Process. Lett., vol. 9, pp , Wang, Z., Bovik, A.C., Sheikh, H.R. and Simoncelli, E.P., Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4), pp Chandler, D.M. and Hemami, S.S., VSNR: A wavelet-based visual signal-tonoise ratio for natural images. IEEE transactions on image processing, 16(9), pp Zhang, L., Zhang, L., Mou, X. and Zhang, D., FSIM: A feature similarity index for image quality assessment. IEEE transactions on Image Processing, 20(8), pp Sheikh, H.R., Bovik, A.C. and De Veciana, G., An information fidelity criterion for image quality assessment using natural scene statistics. IEEE Transactions on image processing, 14(12), pp Zhang, L., Zhang, L. and Mou, X., 2010, September. RFSIM: A feature based image quality assessment metric using Riesz transforms. In Image Processing (ICIP), th IEEE International Conference on (pp ). IEEE. 8. Wang, Z., Simoncelli, E.P. and Bovik, A.C., 2003, November. Multiscale structural similarity for image quality assessment. In Signals, Systems and Computers, Conference Record of the Thirty-Seventh Asilomar Conference on (Vol. 2, pp ). IEEE. 9. NATARAJ, K. and PATNEKAR, N., Neural Networks for Image Analysis and Processing in Measurements, Instrumentation and Related Industrial Applications. Neural Networks for Instrumentation, Measurement and Related Industrial Applications, 185, p Sheikh, H.R. and Bovik, A.C., Image information and visual quality. IEEE Transactions on image processing, 15(2), pp Zhang, L., Zhang, L., Mou, X. and Zhang, D., 2012, September. A comprehensive evaluation of full reference image quality assessment algorithms. In Image Processing (ICIP), th IEEE International Conference on (pp ). IEEE. A. Ramya, D. Murugan, S.Vijaya Kumar And V. Murugan 246