AN IMPROVED NO-REFERENCE SHARPNESS METRIC BASED ON THE PROBABILITYOF BLUR DETECTION

Niranjan D. Narvekar and Lina J. Karam

School of Electrical, Computer, and Energy EngineeringArizona State University, Tempe, AZ 85287-5706

nnarveka@asu.edu, karam@asu.edu

ABSTRACTIn this work, a no-reference objective image sharpness met-ric is presented based on the cumulative probability of blurdetection (CPBD). In order to obtain a discrete number ofquality classes that can be easily mapped into qualitativescores, a classification-based metric, which corresponds toa discretized version of the CPBD metric, is proposed. Theproposed CPBD metric and classification-based metric aretested using Gaussian-blurred images and JPEG2000-compressed images. It is shown that the proposed met-rics are able to predict well the quality of the tested im-ages. Compared to existing sharpness metrics, the proposedCPBD-based metrics are found to correlate significantly bet-ter with subjective scores.

1. INTRODUCTION

Objective quality assessment is becoming an important partof multimedia applications, be it audio, image, video or acombination of these. This can be noticed by the increas-ing interest of the research community and also industry to-wards including objective quality assessment techniques formultimedia applications and products [1]. Among the var-ious assessment techniques, no-reference objective qualityassessment is quite important and also challenging, since itdoes not require any reference information as opposed tothe full-reference and reduced-reference techniques.

This paper deals with no-reference objective assessmentof the perceived blur in an image. Blur distortions occurdue to the loss of high frequency information which couldbe 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 generalnatural images but this correlation decreases significantlywhen only images with significantly varying backgroundand foreground blur qualities are considered. As a result,a visual attention based metric was proposed in [8] for im-ages with “attentive” regions but with only a slight improve-ment in performance. Then, in [9], a sharpness metric based

on the cumulative probability of blur detection (CPBD) wasproposed which significantly improved the metric perfor-mance for images with both uniform and non-uniformsaliency content.

In this work, the interest is in developing a discretizedvisual sharpness metric that can be mapped into a finitenumber of distinct quality classes or qualitative scores. Theproposed metric builds upon the results obtained for theCPBD metric. A training-based method is proposed todetermine the centroids of the quality classes for the CPBDscores, where each quality class represents a perceivedquality level. The proposed classification-based metric isobtained by first classifying an input image into one of thequality classes based on its CPBD score and the pre-computed class centroids, and then assigning the index ofthe corresponding quality class as the metric value for thatimage.

This paper is organized as follows. Section 2 describesthe CPBD metric proposed in [9]. Its performance isanalyzed for Gaussian-blurred and JPEG2000-compressedimages. Section 3 presents the proposed discreteclassification-based metric. The performance of the metricfor Gaussian blurred images with uniform and non-uniformsaliency content and JPEG2000 compressed images is alsopresented in Section 3. A conclusion is given in Section 4.

2. CPBD SHARPNESS METRIC

This section describes the CPBD sharpness metric proposedin [9]. The basis of the proposed CPBD sharpness metric isthe “Just Noticeable Blur” (JNB) concept as proposed in [7].JNB can be defined as “the minimum amount of perceivedblurriness given a contrast higher than the Just NoticeableDifference (JND)”. As explained in [7], the probability ofblur detection (PBLUR) at an edge given a contrast C canbe modeled as a psychometric function given by:

PBLUR = P (ei) = 1− exp(−| w(ei)wJNB(ei)

|β) (1)

Fig. 1. Block diagram summarizing the computation of theproposed CPBD sharpness metric [9].

where wJNB(ei) is the JNB edge width which depends onthe local contrast C and w(ei) is the measured width of theedge ei.

The block diagram summarizing the calculation of theCPBD sharpness metric is shown in Fig. 1. The image isfirst divided into 64 × 64 blocks and then each block ischaracterized 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 blockis determined. The probability of blur detection at eachedge is estimated using (1), in which wJNB depends onthe contrast C of the edge block to which the edge be-longs. It should be noted that when w(ei) = wJNB(ei)then PBLUR = 63% = PJNB . It follows that the blur isnot detected at an edge if PBLUR ≤ PJNB . Finally, the cu-mulative probability of blur detection (CPBD) is calculatedas:

CPBD = P (PBLUR ≤ PJNB)

=PBLUR=PJNB∑

PBLUR=0

P (PBLUR) (2)

where P (PBLUR) denotes the value of the probability dis-tribution function at a given PBLUR.

The CPBD sharpness metric was tested using Gaussian-blurred and JPEG2000-compressed images from the LIVEimage database [10]. The LIVE database [10] consists of29 high-resolution 24-bits/pixel RGB color images (typi-cally 768 × 512). The images are distorted using differentdistortion types: JPEG2000, JPEG, Gaussian blur in RGBcomponents, white noise in the RGB components, and biterrors in the JPEG2000 bitstream when transmitted over asimulated fast-fading Rayleigh channel. The test sets from

(a) sigma = 2.1666. (b) sigma = 7.6666.

(c) sigma = 0.5625

Fig. 2. Sample images from Set 1 of the LIVE imagedatabase.

the LIVE database used to validate the metric performanceare given as follows:

• Set 1: 174 Gaussian blurred images are used whichare taken from the LIVE database. These images havebeen generated using a circular-symmetric 2-D Gaus-sian kernel of standard deviation σblur ranging from 0to 15. Fig. 2 shows some of the sample images fromthis set.

• Set 2: 30 Gaussian blurred images taken from theLIVE database, which are blurred using a 2-D Gaus-sian kernel of standard deviation ranging from 0 to15, are used. These images are chosen such that theyhave varying foreground and background blur quan-tities. Fig. 3 shows some of the sample images fromthis set.

• Set 3: 227 JPEG2000 compressed images taken fromthe LIVE database are used. This set is chosen be-cause JPEG2000 compression introduces blurring andringing. Fig. 4 shows some of the sample imagesfrom this set.

(a) sigma = 7.6666. (b) sigma = 11.3333.

(c) sigma = 0.

Fig. 3. Sample images from Set 2 of the LIVE imagedatabase.

(a) bit-rate = 0.1119 bits/pixel.(b) bit-rate = 0.1227 bits/pixel.

(c) bit-rate = 0.1254 bits/pixel.

Fig. 4. Sample images from Set 3 of the LIVE imagedatabase.

Table 1. EVALUATION OF THE PROPOSED CPBD MET-RIC PERFORMANCE W.R.T. MOS SCORES FOR THE LIVEDATABASE.

Sets Metrics Pearson Spearman

Set 1

CPBD metric 0.9211 0.9449JNBM metric [7] 0.8475 0.8291

marziliano metric [2] 0.8561 0.8672

Set 2

CPBD metric 0.8708 0.8986JNBM metric [7] 0.71 0.604

marziliano metric [2] 0.6752 0.6423

Set 3

CPBD metric 0.8807 0.8443JNBM metric [7] 0.6967 0.6629

marziliano metric [2] 0.7577 0.7185

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

10

20

30

40

50

60

70

80

90

100

CPBD Scores

MO

S S

core

s

BadPoorFairGoodExcellentCentroids

Fig. 5. Classification into 5 quality classes and correspond-ing class centroids.

The resulting performance of the CPBD metric is shownin Table 1 using the Pearson correlation coefficient and theSpearman rank-order correlation coefficient. The Pearsoncorrelation coefficient determines how well the metric canpredict the subjective scores and the Spearman rank-ordercorrelation coefficient determines the degree of monotonic-ity of the metric. For comparison, Table 1 also shows theresulting Pearson and Spearman coefficients for the metricsproposed in in [7] and [2]. From Table 1, it can be clearlyseen that the CPBD metric correlates with the subjectivescores much better than the metrics proposed in [7] and [2],for all sets of images. It can also be noted that the pro-posed CPBD metric performs significantly better than themetrics of [7] and [2] for Set 2 and Set 3, which correspondto images with non-uniform saliency content and JPEG2000compressed images, respectively.

Table 2. CENTROID VALUES FOR THE CORRESPONDINGQUALITY CLASSES.

Quality Cluster Centroid ValueBad 0.0206Poor 0.1579Fair 0.3334

Good 0.5320Excellent 0.7266

3. CLASSIFICATION-BASED METRIC

The CPBD metric proposed in [9] gives a quality score inthe continuous range of 0 to 1. A high CPBD value indicatesa sharp image and a low CPBD value indicates a blurred im-age. In some cases, it might be useful to obtain a discretequalitative score corresponding to a quality class, insteadof a continuous quantitative score. For example, an imagecan be classified into one of 5 quality classes, correspondingto the 5 discrete quality scores commonly used for subjec-tive assessment namely, “Bad”, “Poor”, “Fair”, “Good”, and“Excellent”.

In order to obtain a discretized version of the CPBDmetric, the MOS and CPBD scores of a selected set of im-ages (training set) were used to classify the images into 5quality classes. In this work, a total of 210 images, consist-ing of 90 Gaussian blurred images and 120 JPEG2000 com-pressed images from the LIVE database, are used. Theseimages are selected such that they span the entire qualityrange. For each image in the set, the corresponding CPBDvalue is calculated. The images are then initially classi-fied into 5 quality intervals based on the MOS scores. TheMOS scores provided in the LIVE database are in the rangeof 1-100. The intervals used for classification are “1-20”,“21-40”, “41-60”, “61-80” and “81-100” corresponding to“Bad”, “Poor”, “Fair”, “Good”, and “Excellent”, respec-tively. Then, for each quality interval (class), the centroidof the CPBD values is calculated. These initial centroidscan be further refined using the k-means clustering algo-rithm . Fig. 5 illustrates the resulting centroid locations forthe quality intervals corresponding to the selected trainingset and Table 2 summarizes the centroid values. It shouldbe noted that, in our case, the performance results that wereobtained using the initial centroids (without refinement withk-means) were not significantly different from the resultsobtained when using the refined centroids.

Once the centroids of the various quality classes are de-termined, the classification-based metric value can be ob-tained, for a given image, by simply classifying the consid-ered image into one of the quality classes. For this purpose,the CPBD metric value is first calculated for the consideredimage. The image is then classified into one of the 5 qualityclasses based on the proximity of its CPBD metric value to

(a) Score = 1 (Bad) (b) Score = 2 (Poor)

(c) Score = 3 (Fair) (d) Score = 4 (Good)

(e) Score = 5 (Excellent)

Fig. 6. Scores obtained for sample images from the LIVEdatabase.

Table 3. EVALUATION OF THE PROPOSEDCLASSIFICATION-BASED METRIC PERFORMANCE W.R.T.MOS SCORES FOR THE LIVE DATABASE.

Sets Metrics Pearson Spearman

Set 1

Classification based Metric 0.8949 0.9292CPBD metric 0.9211 0.9449

JNBM metric [7] 0.8475 0.8291marziliano metric [2] 0.8561 0.8672

Set 2

Classification based Metric 0.8358 0.89488CPBD metric 0.8708 0.8986

JNBM metric [7] 0.71 0.604marziliano metric [2] 0.6752 0.6423

Set 3

Classification based Metric 0.8347 0.8326CPBD metric 0.8807 0.8443

JNBM metric [7] 0.6967 0.6629marziliano metric [2] 0.7577 0.7185

the class centroid values. Hence, the image gets a qualityscore of 1, 2, 3, 4 or 5 based on whether it belongs to theclass “Bad”, “Poor”, “Fair”, “Good” or “Excellent”, respec-tively. Fig. 6 illustrates the scores obtained for some of theimages taken from the LIVE database.

Table 3 presents the correlation results for the proposeddiscretized classification-based metric along with the CPBDmetric and the metrics proposed in [7] and [2] for imagestaken from the LIVE database. As indicated in Section 2,Set 1 consists of Gaussian blurred images, Set 2 consists ofGaussian blurred images having non-uniform saliency con-tent, and Set 3 consists of JPEG2000 compressed images.However, the sets of Table 3 do not include images that wereused as part of the training set. It can be seen that the pro-posed discretized classification-based metric performs bet-ter as compared to the metrics proposed in [7] and [2] butits performance is slightly worse than the continuous-rangeCPBD metric.

4. CONCLUSION

A discretized classification-based no-reference sharpnessmetric based on the cumulative probability of blur detectionis presented in order to classify the visual quality of imagesinto a finite number of quality classes. Its performance isevaluated for both Gaussian-blurred and JPEG2000-compressed images. It is shown that the proposed metricperforms significantly better than the other existing metrics.Future work includes investigating the development of a dis-cretized metric that does not require an initial training stepfor determining the quality classes.

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