AN IMPROVED NO-REFERENCE SHARPNESS METRIC BASED ON THE PROBABILITY OF BLUR DETECTION. Niranjan D. Narvekar and Lina J. Karam

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1 AN IMPROVED NO-REFERENCE SHARPNESS METRIC BASED ON THE PROBABILITY OF BLUR DETECTION Niranjan D. Narvekar and Lina J. Karam School of Electrical, Computer, and Energy Engineering Arizona State University, Tempe, AZ ABSTRACT In this work, a no-reference objective image sharpness metric is presented based on the cumulative probability of blur detection (CPBD). In order to obtain a discrete number of quality classes that can be easily mapped into qualitative scores, a classification-based metric, which corresponds to a discretized version of the, is proposed. The proposed and classification-based metric are tested using Gaussian-blurred images and JPEG2000- compressed images. It is shown that the proposed metrics are able to predict well the quality of the tested images. Compared to existing sharpness metrics, the proposed CPBD-based metrics are found to correlate significantly better with subjective scores. 1. INTRODUCTION Objective quality assessment is becoming an important part of multimedia applications, be it audio, image, video or a combination of these. This can be noticed by the increasing interest of the research community and also industry towards including objective quality assessment techniques for multimedia applications and products [1]. Among the various assessment techniques, no-reference objective quality assessment is quite important and also challenging, since it does not require any reference information as opposed to the full-reference and reduced-reference techniques. This paper deals with no-reference objective assessment of the perceived blur in an image. Blur distortions occur due to the loss of high frequency information which could be caused during acquisition, processing or compression. Several sharpness/blurriness metrics have been proposed [2, 3, 4, 5, 6, 7]. It was found that the metric proposed in [7] correlates very well with subjective scores for general natural images but this correlation decreases significantly when only images with significantly varying background and foreground blur qualities are considered. As a result, a visual attention based metric was proposed in [8] for images with attentive regions but with only a slight improvement in performance. Then, in [9], a sharpness metric based on the cumulative probability of blur detection (CPBD) was proposed which significantly improved the metric performance for images with both uniform and non-uniform saliency content. In this work, the interest is in developing a discretized visual sharpness metric that can be mapped into a finite number of distinct quality classes or qualitative scores. The proposed metric builds upon the results obtained for the. A training-based method is proposed to determine the centroids of the quality classes for the CPBD scores, where each quality class represents a perceived quality level. The proposed classification-based metric is obtained by first classifying an input image into one of the quality classes based on its CPBD score and the precomputed class centroids, and then assigning the index of the corresponding quality class as the metric value for that image. This paper is organized as follows. Section 2 describes the proposed in [9]. Its performance is analyzed for Gaussian-blurred and JPEG2000-compressed images. Section 3 presents the proposed discrete classification-based metric. The performance of the metric for Gaussian blurred images with uniform and non-uniform saliency content and JPEG2000 compressed images is also presented in Section 3. A conclusion is given in Section CPBD SHARPNESS METRIC This section describes the CPBD sharpness metric proposed in [9]. The basis of the proposed CPBD sharpness metric is the Just Noticeable Blur (JNB) concept as proposed in [7]. JNB can be defined as the minimum amount of perceived blurriness given a contrast higher than the Just Noticeable Difference (JND). As explained in [7], the probability of blur detection (P BLUR ) at an edge given a contrast C can be modeled as a psychometric function given by: w(e i ) P BLUR = P (e i ) = 1 exp( w JNB (e i ) β ) (1)

2 (a) sigma = (b) sigma = Fig. 1. Block diagram summarizing the computation of the proposed CPBD sharpness metric [9]. where w JNB (e i ) is the JNB edge width which depends on the local contrast C and w(e i ) is the measured width of the edge e i. The block diagram summarizing the calculation of the CPBD sharpness metric is shown in Fig. 1. The image is first divided into blocks and then each block is characterized as edge block or non-edge block as in [7]. The non-edge blocks are not processed further, whereas, for each edge block, the width of each edge in the block is determined. The probability of blur detection at each edge is estimated using (1), in which w JNB depends on the contrast C of the edge block to which the edge belongs. It should be noted that when w(e i ) = w JNB (e i ) then P BLUR = 63% = P JNB. It follows that the blur is not detected at an edge if P BLUR P JNB. Finally, the cumulative probability of blur detection (CPBD) is calculated as: CP BD = P (P BLUR P JNB ) = P BLUR =P JNB P BLUR =0 P (P BLUR ) (2) where P (P BLUR ) denotes the value of the probability distribution function at a given P BLUR. The CPBD sharpness metric was tested using Gaussianblurred and JPEG2000-compressed images from the LIVE image database [10]. The LIVE database [10] consists of 29 high-resolution 24-bits/pixel RGB color images (typically ). The images are distorted using different distortion types: JPEG2000, JPEG, Gaussian blur in RGB components, white noise in the RGB components, and bit errors in the JPEG2000 bitstream when transmitted over a simulated fast-fading Rayleigh channel. The test sets from (c) sigma = Fig. 2. Sample images from Set 1 of the LIVE image the LIVE database used to validate the metric performance are given as follows: Set 1: 174 Gaussian blurred images are used which are taken from the LIVE These images have been generated using a circular-symmetric 2-D Gaussian kernel of standard deviation σ blur ranging from 0 to 15. Fig. 2 shows some of the sample images from this set. Set 2: 30 Gaussian blurred images taken from the LIVE database, which are blurred using a 2-D Gaussian kernel of standard deviation ranging from 0 to 15, are used. These images are chosen such that they have varying foreground and background blur quantities. Fig. 3 shows some of the sample images from this set. Set 3: 227 JPEG2000 compressed images taken from the LIVE database are used. This set is chosen because JPEG2000 compression introduces blurring and ringing. Fig. 4 shows some of the sample images from this set.

3 Table 1. E VALUATION OF THE PROPOSED CPBD METRIC PERFORMANCE W. R. T. MOS SCORES FOR THE LIVE DATABASE. Sets Set 1 (a) sigma = (b) sigma = Set 2 Set 3 Metrics Pearson Spearman (c) sigma = 0. MOS Scores Bad Poor Fair Good Excellent Centroids 20 Fig. 3. Sample images from Set 2 of the LIVE image CPBD Scores Fig. 5. Classification into 5 quality classes and corresponding class centroids. (a) bit-rate = bits/pixel.(b) bit-rate = bits/pixel. (c) bit-rate = bits/pixel. Fig. 4. Sample images from Set 3 of the LIVE image The resulting performance of the is shown in Table 1 using the Pearson correlation coefficient and the Spearman rank-order correlation coefficient. The Pearson correlation coefficient determines how well the metric can predict the subjective scores and the Spearman rank-order correlation coefficient determines the degree of monotonicity of the metric. For comparison, Table 1 also shows the resulting Pearson and Spearman coefficients for the metrics proposed in in [7] and [2]. From Table 1, it can be clearly seen that the correlates with the subjective scores much better than the metrics proposed in [7] and [2], for all sets of images. It can also be noted that the proposed performs significantly better than the metrics of [7] and [2] for Set 2 and Set 3, which correspond to images with non-uniform saliency content and JPEG2000 compressed images, respectively.

4 Table 2. CENTROID VALUES FOR THE CORRESPONDING QUALITY CLASSES. Quality Cluster Centroid Value Bad Poor Fair Good Excellent CLASSIFICATION-BASED METRIC The proposed in [9] gives a quality score in the continuous range of 0 to 1. A high CPBD value indicates a sharp image and a low CPBD value indicates a blurred image. In some cases, it might be useful to obtain a discrete qualitative score corresponding to a quality class, instead of a continuous quantitative score. For example, an image can be classified into one of 5 quality classes, corresponding to the 5 discrete quality scores commonly used for subjective assessment namely, Bad, Poor, Fair, Good, and Excellent. In order to obtain a discretized version of the CPBD metric, the MOS and CPBD scores of a selected set of images (training set) were used to classify the images into 5 quality classes. In this work, a total of 210 images, consisting of 90 Gaussian blurred images and 120 JPEG2000 compressed images from the LIVE database, are used. These images are selected such that they span the entire quality range. For each image in the set, the corresponding CPBD value is calculated. The images are then initially classified into 5 quality intervals based on the MOS scores. The MOS scores provided in the LIVE database are in the range of The intervals used for classification are 1-20, 21-40, 41-60, and corresponding to Bad, Poor, Fair, Good, and Excellent, respectively. Then, for each quality interval (class), the centroid of the CPBD values is calculated. These initial centroids can be further refined using the k-means clustering algorithm. Fig. 5 illustrates the resulting centroid locations for the quality intervals corresponding to the selected training set and Table 2 summarizes the centroid values. It should be noted that, in our case, the performance results that were obtained using the initial centroids (without refinement with k-means) were not significantly different from the results obtained when using the refined centroids. Once the centroids of the various quality classes are determined, the classification-based metric value can be obtained, for a given image, by simply classifying the considered image into one of the quality classes. For this purpose, the value is first calculated for the considered image. The image is then classified into one of the 5 quality classes based on the proximity of its value to (a) Score = 1 (Bad) (c) Score = 3 (Fair) (e) Score = 5 (Excellent) (b) Score = 2 (Poor) (d) Score = 4 (Good) Fig. 6. Scores obtained for sample images from the LIVE

5 Table 3. EVALUATION OF THE PROPOSED CLASSIFICATION-BASED METRIC PERFORMANCE W.R.T. MOS SCORES FOR THE LIVE DATABASE. Sets Metrics Pearson Spearman Classification based Metric Set Classification based Metric Set Classification based Metric Set the class centroid values. Hence, the image gets a quality score of 1, 2, 3, 4 or 5 based on whether it belongs to the class Bad, Poor, Fair, Good or Excellent, respectively. Fig. 6 illustrates the scores obtained for some of the images taken from the LIVE Table 3 presents the correlation results for the proposed discretized classification-based metric along with the CPBD metric and the metrics proposed in [7] and [2] for images taken from the LIVE As indicated in Section 2, Set 1 consists of Gaussian blurred images, Set 2 consists of Gaussian blurred images having non-uniform saliency content, and Set 3 consists of JPEG2000 compressed images. However, the sets of Table 3 do not include images that were used as part of the training set. It can be seen that the proposed discretized classification-based metric performs better as compared to the metrics proposed in [7] and [2] but its performance is slightly worse than the continuous-range. 4. CONCLUSION A discretized classification-based no-reference sharpness metric based on the cumulative probability of blur detection is presented in order to classify the visual quality of images into a finite number of quality classes. Its performance is evaluated for both Gaussian-blurred and JPEG2000- compressed images. It is shown that the proposed metric performs significantly better than the other existing metrics. Future work includes investigating the development of a discretized metric that does not require an initial training step for determining the quality classes. 5. REFERENCES the Issue on Visual Media Quality Assessment, IEEE Journal on Selected Topics in Signal Processing, Special Issue on Visual Media Quality Assessment, vol. 3, no. 2, pp , Apr [2] P. Marziliano, F. Dufaux, S. Winkler and T. Ebrahimi, Perceptual blur and ringing metrics: Applications to JPEG2000, Signal Processing: Image Communication, vol. 19, no. 2, pp , Feb [3] J. Caviedes and S. Gurbuz, No-reference sharpness metric based on local edge kurtosis, IEEE international Conference on Image Processing, vol. 3, pp , June [4] N. Zhang, A. Vladar, M. Postek and B. Larrabee, A kurtosis-based statistical measure for two-dimensional processes and its application to image sharpness, in Proceedings of Section of Physical and Engineering Sciences of American Statistical Society, 2003, pp [5] E. Ong, W. Lin, Z. Lu, X. Yang, S. Yao, F. Pan, L. Jiang, and F. Moschetti, A no-reference quality metric for measuring image blur, in Seventh IEEE International Symposium on Signal Processing and its Applications, July 2003, vol. 1, pp [6] R. Ferzli and L. J. Karam, No-reference objective wavelet based noise immune image sharpness metric, IEEE international Conference on Image Processing, vol. 1, pp , Sept [7] R. Ferzli and L. J. Karam, A no-reference objective image sharpness metric based on the notion of Just Noticeable Blur (JNB), IEEE Transactions on Image Processing, vol. 18, pp , Apr [8] N. G. Sadaka, L. J. Karam, R. Ferzli, and G. P. Abousleman, A no-reference perceptual image sharpness metric based on saliency-weighted foveal pooling, IEEE International Conference on Image Processing, pp , Oct [9] N. D. Narvekar, and L. J. Karam, A No-Reference Perceptual Quality Metric based on cumulative probability of blur detection, First International Workshop on Quality of Multimedia Experience-09, pp , July [10] H. R. Sheikh, A. C. Bovik, L. Cormack and Z. Wang, LIVE image quality assessment database, 2003, [1] L. J. Karam, T. Ebrahimi, S. Hemami, T. Pappas, B. Safranek, Z. Wang, and A. B. Watson Introduction to