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medical image computing is proposed in this article. Globally accepted .... Department of Biomedical Engineering, Vel Tech Multi Tech Engineering College, Chennai,. India. ..... Journal of Elect and Electron Eng 2014; 2:47-51. 13. Jang WD ...
Elsevier Editorial System(tm) for Biocybernetics and Biomedical Engineering Manuscript Draft Manuscript Number: BBE-D-15-00239R2 Title: A full reference morphological edge similarity index to account processing induced edge artefacts in magnetic resonance images Article Type: Original Research Article Keywords: Edge similarity Index; Blur Metric; Image quality analysis; Pratt's figure of merit; Edge Strength. Corresponding Author: Dr. Sivaraman Jayaraman, Corresponding Author's Institution: VTMT First Author: Kuppusamy PG Order of Authors: Kuppusamy PG; Justin Joseph; sivaraman jayaraman Abstract: An objective measure of edge similarity between the original and processed images to quantify the processing induced artefacts in medical image computing is proposed in this article. Globally accepted Image Quality Analysis (IQA) indices such as Peak Signal Noise Ratio (PSNR) and Structural Similarity Index (SSIM) measure the structural similarity between the original and processed image and do not specifically reflect the resemblance of the edge content. Most of the IQA indices either do not comply with the subjective quality ratings or they are prone to noise level. In the proposed Morphological Edge Similarity Index (MESI), the binary edge maps of the reference and processed images are generated via gradient based threshold and these edge maps are objectively compared to yield a reliable edge quality metric. The index is found superior to Edge Preservation Index (EPI), Edge Strength Similarity based Image quality Metric (ESSIM) and SSIM in terms of dynamic variability, correlation with subjective quality ratings, robustness to noise and sensitivity to degradation in edge quality caused by blockiness artefacts in image compression. MESI exhibits a correlation of 0.9985, very close to unity, with the subjective quality ratings. It is useful for objectively evaluating the performance of denoising, sharpening and enhancement schemes and for the selection of optimum value of the arbitrary parameters used in them. Suggested Reviewers: Opposed Reviewers: Response to Reviewers: Reply to Reviewer The authors would like to thank the reviewer for his As a result, a number of substantial improvements to been made. Authors are really thankful to reviewer’s bringing quality to the manuscript. We have promptly corrections suggested by the reviewer. Reviewers' comments: Reviewer #3: Figures 2,4,5 still are not readable.

helpful comments. the manuscript have precious advices for incorporated the

Reply: Authors agree with the expert suggestion of the reviewer and regret that the readability of the figures were poor previously. We noticed that the text is legible in the figures and the issue is with compressed Y axis and line style. In the figures, lines were plotted in different colours and Y axis was expanded. Authors corrected the fig. 3 also as reviewer’s suggestion is quite true. The corrected figures and the figures before the correction are furnished below for the evaluation of reviewer. Obeying reviewer’s comments we have supplied all the images in uncompressed .tif format also, along with the manuscript. Fig. 2 before correction Fig. 2: Variation of quality indices with respect to variation in compression quality in JPEG 2000 compression algorithm

Fig. 2 after correction Fig. 2: Variation of quality indices with respect to variation in compression quality in JPEG 2000 compression algorithm Fig. 5 before correction Fig. 5: Variation of quality indices between the reference and smoothened images with respect to variation in window size of the median filter

Fig. 5after correction Fig. 5: Variation of quality indices between the reference and smoothened images with respect to variation in window size of the median filter Fig. 3before correction Fig. 3: Variation of quality indices with respect to variation in noise variance in the contextual image

Fig. 3after correction Fig. 3: Variation of quality indices with respect to variation in noise variance in the contextual image The restored images with diminishing edge quality, depicted in fig. 4, are produced by smoothening the reference image by a median filter with different window sizes. These images with poor edge quality are deliberately produced for the experimental purpose. The pattern of variation of edge quality in these figures is gradually decreasing. These poor quality images are furnished in the manuscript to offer an opportunity to the readers to appreciate the variation in the edge quality indices are in correspondence with the subjective evaluation of edge quality performed on these images. Authors request the reviewer for his expert opinion in this regard.We have supplied these images also in uncompressed .tif format.

*Financial support (NO Author details)

Financial Support One of the authors would like to thank the fund from the DST-FIST, Govt of India, vide Ref.: SR/FST/College-189/2013, Dated: 6th August 2014.

*Detailed Response to Reviewers (NO Author details)

Reply to Reviewer The authors would like to thank the reviewer for his helpful comments. As a result, a number of substantial improvements to the manuscript have been made. Authors are really thankful to reviewer’s precious advices for bringing quality to the manuscript. We have promptly incorporated the corrections suggested by the reviewer. Reviewers' comments: Reviewer #3: Figures 2,4,5 still are not readable. Reply: Authors agree with the expert suggestion of the reviewer and regret that the readability of the figures were poor previously. We noticed that the text is legible in the figures and the issue is with compressed Y axis and line style. In the figures, lines were plotted in different colours and Y axis was expanded. Authors corrected the fig. 3 also as reviewer’s suggestion is quite true. The corrected figures and the figures before the correction are furnished below for the evaluation of reviewer. Obeying reviewer’s comments we have supplied all the images in uncompressed .tif format also, along with the manuscript. Fig. 2 before correction 1

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Fig. 3: Variation of quality indices with respect to variation in noise variance in the contextual image The restored images with diminishing edge quality, depicted in fig. 4, are produced by smoothening the reference image by a median filter with different window sizes. These images with poor edge quality are deliberately produced for the experimental purpose. The pattern of variation of edge quality in these figures is gradually decreasing. These poor quality images are furnished in the manuscript to offer an opportunity to the readers to appreciate the variation in the edge quality indices are in correspondence with the subjective evaluation of edge quality performed on these images. Authors request the reviewer for his expert opinion in this regard.We have supplied these images also in uncompressed .tif format.

*Title Page (WITH Author Details and Acknowledgements)

A full reference morphological edge similarity index to account processing induced edge artefacts in magnetic resonance images P.G. Kuppusamya, Justin Josephb, J. Sivaramanc* a

Department of Electronics and Communication Engineering, Vel Tech Multi Tech Engineering

College, Chennai, India, b

Department of Applied Electronics & Instrumentation, St. Joseph’s College of Engg. &

Technology, Kerala, India. c

Department of Biomedical Engineering, Vel Tech Multi Tech Engineering College, Chennai,

India.

*

Corresponding Author

Dr. Sivaraman Jayaraman Assistant Professor Department of Biomedical Engineering Vel Tech Multi Tech Engineering College Avadi, Chennai 600062. Ph: +919840968282 Email: [email protected] Conflict of Interest: None of the authors have any conflict of interest to declare. Acknowledgements One of the authors would like to thank the fund from the DST-FIST, Govt of India, vide Ref.: SR/FST/College-189/2013, Dated: 6th August 2014.

*Blinded Manuscript (NO Author Details)

A full reference morphological edge similarity index to account processing induced edge artefacts in magnetic resonance images Abstract An objective measure of edge similarity between the original and processed images to quantify the processing induced artefacts in medical image computing is proposed in this article. Globally accepted Image Quality Analysis (IQA) indices such as Peak Signal Noise Ratio (PSNR) and Structural Similarity Index (SSIM) measure the structural similarity between the original and processed image and do not specifically reflect the resemblance of the edge content. Most of the IQA indices either do not comply with the subjective quality ratings or they are prone to noise level. In the proposed Morphological Edge Similarity Index (MESI), the binary edge maps of the reference and processed images are generated via gradient based threshold and these edge maps are objectively compared to yield a reliable edge quality metric. The index is found superior to Edge Preservation Index (EPI), Edge Strength Similarity based Image quality Metric (ESSIM) and SSIM in terms of dynamic variability, correlation with subjective quality ratings, robustness to noise and sensitivity to degradation in edge quality caused by blockiness artefacts in image compression. MESI exhibits a correlation of 0.9985, very close to unity, with the subjective quality ratings. It is useful for objectively evaluating the performance of denoising, sharpening and enhancement schemes and for the selection of optimum value of the arbitrary parameters used in them. Keywords: Edge similarity Index, Blur Metric, Image quality analysis, Pratt’s figure of merit, Edge Strength.

1. Introduction Well-defined boundaries among distinct structures are one of the primary characteristics of a good quality medical image. In some cases edge quality may be adversely affected during the processing. Objective measures of edge similarity between the original and processed images are necessary to quantify the processing induced artefacts, quality degradation and information loss,in medical image processing. They are useful for objectively evaluating the performance of denoising, sharpening and enhancement schemes and for the selection of optimum value of the arbitrary parameters used in them. Generally, the edge quality metrics fall under either of the two types, ‘no reference / reduced reference’ and full reference metrics. No reference edge metrics are useful in multimedia communication where the original image or video would not be available at the receiver end. But in image processing, the original image prior to the transformation is always available as reference. Hence, no reference edge content metrics have less significance in this context. Despite the preeminent applications of edge quality metrics in image processing, a rational and viable metric is not known to be available. Molina et al. [1], after a comprehensive review on objective measures of edge content, concluded that there is no reliable metric to compare the edge quality in different images. Existing pixel-based metrics such as Mean Square Error (MSE), Signal-to-Noise Ratio (SNR), Peak Signal to Noise Ratio (PSNR), Feature Similarity Index (FSIM) [2] and Structural Similarity Index Metric (SSIM) are similarity measures between reference and the processed images and do not specifically reflect any information regarding the similarity of the edge content. Universal Quality Index (UQI) [3], which is the previous version of SSIM also does not account for edge similarity. MSE and PSNR are not in good correspondence with the subjective evaluation [2]. Only SSIM and FSIM have a standard dynamic range between 0 and 1. The MSE, SNR and PSNR do not have a finite range so that judging the

level of similarity from their numerical values is difficult. Many of the recently used edge content metrics are extensions of the conventional pixel based metrics. Edge Weighted PSNR (EWPSNR) introduced by Lu et al.[4] is a mere extension of the PSNR. Similarly, Edge Based Structural Similarity (EBSSIM) [5], Mean-Edge Structural Similarity (MESSIM) [6], Mean Dual-scale Edge Structure Similarity Matrix (MDESSIM) [7], Multi-Scale Structural Similarity Index (MS-SSIM) [8], Corner SSIM (C-SSIM), EdgeSSIM (E-SSIM), Symmetry SSIM (S-SSIM) [9] and Weighted Structural Similarity Index (WSSI) are modifications of SSIM. Corner SSIM (C-SSIM), Edge-SSIM (E-SSIM) and Symmetry SSIM (S-SSIM) [10], respectively, are the similarity, measured by the SSIM itself between corner, edge and symmetry maps of the images being compared. But the SSIM and MS-SSIM are less effective in blurred and noisy images. Modified versions of SSIM and MS-SSIM, called ‘three component SSIM’ (3-SSIM) and ‘three component MS-SSIM’ (3MS-SSIM) [11] were introduced to resolve this issue. However, none of the extensions of SSIM could tackle noise susceptibilityof SSIM. The full reference IQA indices available in literature are primarily of two categories; the former category which measures the structural or feature similarity [2-3] and the latter exclusively based on the edge similarity [4-28]. Some of the edge similarity indices are extensions of PSNR and SSIM [4-11] as already mentioned. Unlike the conventional metrics and their extensions, Directional Edge Metric (DEM) [12] was based on directional edges obtained using Scharr filter. A similar metric, termed as Structural Edge Quality Metric (SEQM) [13] was the sum of matching costs between the pixels in the binary edge maps of the contextual image and the corresponding pixel in the edge map of the reference. The matching cost accounts for both the dislocation of the edge pixels and the discrepancy between the local structures around the pixels being compared. The use of graph-cut optimization involved in the estimation of the matching cost hampers the computational

feasibility of SEQM. Another metric, Gradient Magnitude Similarity Deviation (GMSD) introduced in literature [14] is the standard deviation of the pixel-wise Gradient Magnitude Similarity (GMS) between the reference and processed images. The standard deviation of the pixel-wise GSM does not have a standard range and do not comply with the subjective quality rating. Moreover, gradient is so badly sensitive to noise. A full reference visual quality index, based on the local edges and edge gradients in the wavelet domain was introduced in [15]. Another approach in wavelet domain, the Visual Signal-to-Noise Ratio (VSNR) [16] attempted to quantify the fidelity of natural images based on near-threshold and supra-threshold properties of human vision. Following this, Sampatet al. [17] proposed Complex Wavelet SSIM (CW-SSIM). As PSNR, the numerical value of VSNR [16] also does not have a standard limit and its computation is as tedious as FSIM and CW-SSIM [17]. The information fidelity criterion reported in literature in [18] express the Shannon information, shared between the reference and the distorted images, relative to the information in the reference itself, using Natural Scene Statistics (NSS) modelling, in concert with image degradation and HVS models. The difference between four motifs of each edge pixel between the reference and distorted images was used to evaluate the amount of distortion in literature [19]. This distortion measure was computationally complex as the difference between the reference and distorted images was computed by comparing the motifs of four overlapping grids in each 3×3 block. The perceptual quality was expressed as the ratio of the binary Non-shift Edge (NSE) maps of the reference and processed images, obtained using Laplacian of Gaussian (LOG) in Zhang et al. [20] and Xue and Mou [21]. The spaghetti effect degrades the quality of the edge map derived by LOG. Continuity and thinness of the detected local edges were used for evaluating edge detectors in literature [22]. Except the edge detectors, the method may not be useful for

evaluating denoising and enhancement schemes. Strickland and Chang [23] defined an edge metric as a weighted sum of six edge characteristics, continuity, smoothness, thinness, localization, detection and noisiness. The principal limitation of the Strickland’s metric was that, it was defined only for straight edges lying in vertical or horizontal directions. Khvorostov et al. [24] later extended the Strickland’s metric as suitable for arbitrarily defined edge contours. Edge Enhancement Index (EEI) introduced in [25] is the ratio of absolute difference in intensity of the pixels on the two sides of the edge in the filtered image and absolute difference in intensities of the pixels on both sides of the edge in the original image. But same as PSNR, the index has no standard limits. Ni et al. [26] recently introduced a metric for the edge quality assessment in screen content images. Initially, the edge information in the reference and contextual images had been modelled with a parametric model in which local contrast, local edge width and the local luminance were the model parameters. The metric was derived based on the concordance of the model parameters in the reference and contextual images. Edge Preservation Index (EPI) [27-28] is a statistical index in common use. Laplacian kernel was used to produce the binary edge maps of the contextual and reference images. But, second derivatives exaggerate noise and detect negligibility weak edges also.Edge Strength Similarity based Image quality Metric (ESSIM) [29] is another edge similarity metric extensively used as EPI. ESSIM is a metric derived from the map of local edge strength in the reference and contextual images. Resultant edge strength at each pixel location was determined from the orthogonal and diagonal edge strengths at that location. Orthogonal and diagonal edge strength was computed from the directional derivatives at the eight connected neighbours of the contextual pixel. The directional derivatives were computed by convolving the reference and contextual images with kernels derived from the Scharr operator. Numerous steps involved in the computation of ESSIM itself reveal its complexity.

Pratt’s Figure of Merit (PFOM) [30-35] is an index usually used to compare the performance of different edge detection methods. PFOM is an index which indicates the concordance of the pixels in two binary edge maps and cannot directly account for the edge quality in medical images. Most of the edge similarity indices available in literature are not computationally feasible, do not have a standard dynamic range, do not match with the subjective quality ratings and are sensitive to noise. Hence, this article proposes a novel metric for evaluating the edge similarity in medical images termed as Morphological Edge Similarity Index (MESI). During the forthcoming discussions, mathematical formulation of MESI is explained in detail followed by its comparative evaluation with respect to ESSIM, SSIM, EPI and Subjective quality ratings. 2. Methodology The MESI between the reference image ‘X’ and processed image ‘Y’ can be computed as,

where ‘NR’and ‘NP’are the total number of strong edge pixels present in ‘X’ and ‘Y’, respectively.

In (2) M*N is the dimension of the reference and processed images. ‘BR’ and ‘BP’ are the binary edge maps of the reference and processed images, respectively. To generate the binary maps of dominating edges ‘BR’ and ‘BP’in the reference and processed images, corresponding gradient images ‘GR’ and ‘GP’ are ‘thresholded’ with respect to a gradient threshold ‘GT’ as,

where the threshold ‘GT’ is the mean of local gradients of the reference image‘X’ given as,

‘GR’and ‘GP’in (3) are the gradient maps of reference and processed images, respectively.The gradient mapsare computed using standard ‘Sobel’ operator [36]. The convention followed for the generation of binary edge maps is that, the pixels with local gradients above the mean of local gradients in the reference image are true edge pixels and not noise contributed ones. In (1) d(u,v) is the spatial distance between the edge pixel ‘u’ in the binary edge map ‘BR’ of the reference image and the nearest edge pixel in the binary edge map ‘BP’ of the processed image. The spatial distance between ‘u’ and ‘v’ is,

‘α’ in (1) is an arbitrary penalty parameter which penalizes the misplaced edge pixels during the ‘processing’. The value of this arbitrary scaling constant is set to unity to make the dependency of MESI on the coincidence of the edge pixels in the reference and processed images more significant. As evident in (1), the edge similarity expressed by MESI accountsfor the number of edge pixels, diminished and dislocatedduring the processing. For a perfect match of maps of dominating edges in the reference and processed images, the value of MESI is unity and ‘0’indicates completely deteriorated edge similarity. The value of MESI, equal to one, denotes that none of the dominating edge pixels in the reference image is degraded or misplaced during processing.

The correlation of MESI with the subjective fidelity ratings, robustness to noise and its response to quality of compression are compared with that of ESSIM, EPI and SSIM. To investigate the noise robustness of MESI, the reference image is corrupted to different levels by adding zero mean White Gaussian Noise (WGN) with different values of variance between 0.01 and 0.1. The consistency of MESI, ESSIM, EPI and SSIM between the reference image and the images obtained by adding WGN of different values of noise variance to the reference image is studied to evaluate their robustness to noise. To investigate the correlation of MESI with the subjective fidelity ratings, contextual images of different levels of edge similarity with respect to the reference image were created by smoothening the reference image by a median filter with different window sizes. The kernel size of the median filter was continuously varied from 3*3 to 21*21. The blur in edges increases with the kernel size. The smoothened images which are completely different in their edge strength were presented to 25 observers with in the age limit 18-35 on a computer screen of 96 dpi resolution and they were asked to rate the edge strength in comparison with the edge strength in the reference image, with a subjective score between one and five. The Mean Opinion Score (MOS) of each image was considered as its subjective quality rating. The Pearson correlation between MOS and the image quality indices were computed to analyse their correspondence with the subjective fidelity ratings. To investigate the dependency of MESI on the quality of compression, contextual images of degraded edge similarity with respect to the reference image were produced by compressing the reference image via lossy JPEG compression algorithm using Huffman coding. The quality of compression was continuously varied from 5 to 100. MESI, ESSIM, EPI and SSIM were computed between the reference image and contextual images obtained by compressing the reference image. The compression induced blockiness artefacts increases with decreasing values of quality of compression. The ability of the quality indices to quantify the

degradation in edge similarity caused by blockiness is qualitatively analysed by visually inspecting the compressed images in concert with numerical values of the indices. The reference images used in the study belong to Axial Plane Spin Echo Fast Spin Contrast MR images of the study Magnetic Resonance Spectroscopy (MRS) series. The experimental study is performed in Matlab®, Version 7.12.0.635 (R2011a)License Number: 161052, Operating System: Microsoft Windows 7 Version 6.1 (Build 7601: Service Pack 1), 64 bit on a Personal Computer with Processor, Intel (R), Pentium (R), CPU B950 @ 2.10GHz with installed Memory (RAM) 4GB. As pointed earlier the performance of MESI is compared with ESSIM, EPI and SSIM.The ESSIM between the reference image ‘X’ and processed image ‘Y’ can be computed as [29],

where ‘C’ is an arbitrary constant with best defined value [29] equal to 2550. Ex(i,j) and

EY(i,j)in (6) respectively denote the local edge strengths in the reference and processed images. The edge strength at a location defined by the coordinates (i,j) in the reference image ‘X’ is the maximum of the orthogonal and diagonal edge strengths at that location such that,

The diagonal edge strength in the reference image ‘X’ at the location specified by the coordinates (i,j),

Similarly, the orthogonal edge strength at this location,

X(i-1,j+1), X(i-1,j-1), X(i,j+1) and X(i-1,j) are the directional derivatives at the north east, north west , east and north neighbors of the contextual pixel X(i,j), notated respectively as, XNE, XNW, XEand XN.

where, 0 0 h

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,

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if

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EPI between the reference image ‘X’ and processed image ‘Y’ [27-28],

PI

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mean of these second derivatives. The SSIM between the reference image ‘X’ and processed image ‘Y’ [37],

where C1= (K1L)2&C2= (K2L)2, K1,K2≪1. K1 and K2 are two arbitrary constants with values 0.01 and 0.03 respectively. μx, μy, σx2, σy2 and σxy are the mean brightness of the reference image, mean brightness of the processed image, global variance of the reference image, global variance of the processed image and covariance between reference and processed images, respectively. 3. Results To highlight the merits of MESI, it is compared with the existing metrics, EPI, SSIM and ESSIM interms of its sensitivity to degradation in edge quality causedby compression, robustness to noise and compliance to the subjective rating. It can be noticed in the fig. 1 (b) fig. 1 (c) that the compressed image is prone to ‘blockiness’ when the compression quality is below 15. For the values of compression quality greater than 15, no significant difference is apparent between the compressed image (fig. 1 (d-f)) and the original image (fig. 1 (a)). original

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Fig. 1:(a) Original image (b) Compressed image with quality =5 (c) Compressed image with quality =10 (d) Compressed image with quality =15 (e) Compressed image with quality =20 (f) Compressed image with quality =25 Variation of MESI, ESSIM, EPI and SSIM with respect to variation in compression quality in JPEG 2000 compression algorithm is demonstrated in fig. 2. ESSIM is not sensitive enough to the degradation in edge similarity between the original or reference image and the compressed images, caused by the blockiness artifact. Even if SSIM looks sensitive to the

degradation in edge similarity caused by blockiness, its dynamic range is insufficient to account for the visually apparent difference between reference image and the compressed images. EPI exhibits good dynamic range. But its variation is random, especially at higher values of quality of compression, which is not appreciable as far as an edge similarity metric is concerned. Value of the proposed edge similarity metric, MESI considerabily deminishes when the edge similarity between the reference and compressed images is degraded by the blockiness artifacts. Its value tends to unity with the increase in compression quality and edge similarity between the reference image and the compressed images. For the values of compression quality above 15, the compressed images are free from blockiness and no aparant difference is visible between the reference and compressed images. The numerical values of MESI is close to unity for compression quality above fifteen and is in par with the subjective evaluation.

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Fig. 2: Variation of quality indices with respect to variation in compression quality in JPEG 2000 compression algorithm The variation of EPI, SSIM, ESSIM and MESI between the reference image and the contextual images, produced by corrupting the reference images with WGN at different

levels, is observed (fig. 3) to demonstrate the robustness of MESI to noise. The standard deviation of EPI, ESSIM, SSIM and MESI between the reference image and contextual images corrupted at different noise levels are 0.0233, 0.0756, 0.1500 and 0.0013, respectively, corresponding to the change in variaince of WGN between 0.01 and 0.1. It is evident from fig. 3 also that MESI is robust to noise variance than EPI, SSIM and ESSIM. MESI remains constant regardless of the change in the variance of WGN which corrups the contextual image. It can be noted that the standard deviation of MESI is less than that of the other three indices. The MESI takes only the true edge pixels into account while quantifying the edge similarity. Only the pixels with local gradient magnitude above the mean of local gradients are considered as true edge pixels. The MESI is robust to noise in contrarily to EPI, ESSIM and SSIM as the noise pixels are excluded during the screening via gradient based threshold. The mean of local gradients increases with the level of noise corruption. As the true edge pixels are detected by thresholding the local gradient map with respect to the mean of local gradients, the traced binary edge map is robust to noise. The Laplacian involved in the computation of EPI exagerate the noise. Similarly, the Scharr based convolution kernels used for the computation of directional derrivatives in ESSIM are also suceptable to noise. The global variance used in the computation of SSIM increases along with the noise variance. These facts make SSIM, ESSIM and EPI sensitive to noise.

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Fig. 4: MR images filtered by median filter with different window sizes (a) Window size=3×3 (b)Window size=5×5 (c) Window size=7×7 (d)Window size=9×9 (e)Window size=11×11 (f)Window size=13×13 (g)Window size=15×15 (h)Window size=17×17 (i)Window size=19×19 (j) Window size=21×21

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Fig. 5: Variation of quality indices between the reference and smoothened images with respect to variation in window size of the median filter

The restored images with diminishing edge quality produced by smoothening the reference image by a median filter with different window sizes are depicted in fig. 4. It can be noted that the blurr in edges increases with the kernel size. It can be seen from the fig. 5 that the dynamic range of ESSIM and SSIM is insufficient to accommodate the abruptly reducing edge strength in the smoothened images presented in fig. 4 (a) to fig. 4 (j). Both EPI and MESI exhibit appreciable dynamic range. The Pearson’s correlation between the quality indices and Mean Opinion Score are as follows: MESI-MOS= 0.9985, EPI-MOS=0.993, ESSIM-MOS=0.9456, SSIM-MOS=0.8844. MESI is correlated well with MOS than other indices.The above experiments was repeated on 50 different MR images of distinct MR series and planes. The observation was found consistent regardless of the origin i.e. series to which the MR images belong to and the imaging plane and the information content. 4. Discussions FSIM [2], fidelity criterion reported in literature [18], SSIM [37], MSE, SNR and PSNR express the visual similarity between two images and do not compare the strength of edges in them. But the proposed index, MESI objectively account for the concordance of edges in the reference and processed image. The metric introduced in literature [22] and PFOM [30-35] are meant only to evaluate the performance of the edge detection methods as they operate directly on binary edge maps and cannot be used to compute the edge quality in greyscale medical images like MRI or CT. MESI is fully comprehensive in this respect. It comprises analytical methods to extract of binary edge map of the reference and contextual images and for the quantification of the concordance of these edge maps. In MESI, the binary edge maps of the reference and contextual images in grey scale space are generated by gradient based threshold. GMSD [14], MSE and PSNR do not exhibit appreciable correspondence with subjective fidelity ratings. MESI exhibits a correlation of 0.9985, very close to unity, with the subjective

quality ratings. The MSE, SNR, PSNR, EWPSNR [4], GMSD [14], VSNR [16] and EEI [25] do not have a finite range. MESI has a definite range of 0-1. SSIM itself and its extensions, ESSIM [5], MESSIM [6], MDESSIM [7], MS-SSIM [8], C-SSIM, E-SSIM, S-SSIM [9-10], 3-SSIM and 3-MS-SSIM [11] are less effective in blurred and noisy images.GMSD [14] and the visual quality index reported by Rao and Reddy [15] are gradient based which is so badly sensitive to noise. In MESI, the binary map of true edges is generated via gradient based threshold. The threshold is adaptively computed and it is the mean of the local gradients in the reference image. When the level of noise increases, naturally the mean of the local gradients and in turn the threshold also increases. Hence, in MESI, the detected edge map is not sensitive to the level of noise and it comprises only true morphological edges. This makes the process of generating the binary edge map, superior to Laplacian and LOG. Laplacian kernel employed in [27-28] to compute EPI enhances noise and detect negligibility weak edges as well as noise pixels, rather than the true edge map. LOG operator used by Zhang et al. [20] and Xue and Mou [21] to generate the binary NSE maps introduces spaghetti effect and degrades the quality of the generated map. The global variance involved in the computation of SSIM [37] and the directional derivatives used in ESSIM [29] makes them sensitive to noise. The standard deviation of MESI between the reference image and the images generated by corrupting the reference image with WGN at different levels of variance (0.0 ≤ σ ≤ 0. ) was found to be negligibly small (0.013). This exhibits the robustness of MESI to noise. The computation of all the wavelet domain approaches, the metric in literature [15], VSNR [16] and CW-SSIM [17] is tedious as FSIM. Similarly, the use of graph-cut optimization involved in the estimation of the matching cost hampers the computational feasibility of SEQM [13]. The method based on motifs in literature [19] was computationally intense as the difference between the reference and distorted images was computed by comparing the

motifs of four overlapping grids in each 3×3 block. The computation of MESI is simple as the entire operations are performed in spatial domain itself. Different from the Strickland’s metric [23] which considers only straight edges lying in vertical or horizontal directions, MESI takes the entire edge pixels into account, regardless of their direction. MESI is found superior to EPI, ESSIM and SSIM in terms of dynamic variability, correlation with subjective quality ratings, robustness to noise and sensitivity to degradation in edge quality caused by blockiness artefacts in image compression. 5. Conclusion An Objective measure of edge similarity between the original and processed images to quantify the processing induced artefacts in medical image processing was proposed in this article. The proposed index, MESI objectively account for the concordance of edges in the reference and processed image. The index was found superior to EPI, ESSIM and SSIM in terms of dynamic variability, correlation with subjective quality ratings, robustness to noise and sensitivity to degradation in edge quality caused by blockiness artefacts in image compression. MESI is useful for objectively evaluating the performance of denoising, sharpening and enhancement schemes and for the selection of optimum value of the arbitrary parameters used in them.

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