No-Reference Image Quality Assessment Using Euclidean Distance

No-Reference Image Quality Assessment Using Euclidean Distance Matrices 1 Chuang Zhang, 2 Kai He, 3 Xuanxuan Wu 1,2,3 Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing, 2144, zhch_76@163.com 1 State Key Laboratory for Novel Software Technology, Nanjing University, 2193, zhch_76@163.com Abstract Image quality assessment (IQA) methods play important roles in many applications such as image communication, reception, compression, restoration, and display. No-reference IQA metrics are required to resolve an image when there is a lack of a reference image that is required for fullreference IQA metrics. We propose a no-reference IQA method to evaluate the image quality by using the difference between the distribution width of the recorded block pixel correlative matrix (PCM) and the distribution width of the recorded block Euclidean distance matrix (EDM) of the PCM (EDM PCM). Euclidean distance is generally used to measure the similarity between two pixels, and an image EDM is built by calculating the Euclidean distance between two same-size image blocks centered on two different pixels. Images with different noise have different PCM distribution widths, and the original image has a wider PCM distribution width as well as a noised image with narrower PCM distribution width. The calculated EDM PCMs suggest that noised images have a narrower EDM PCM distribution width. Therefore, the distribution widths of the EDM PCM and the image PCM can be used as an image quality assessment index. The assessment results suggest that the proposed method is effective in evaluating the quality of images with Gaussian blur, global contrast decrements, and JPEG2 compressed noise. Keywords: No-Reference Image Quality Assessment, Euclidean Distance Matrix, Pixel Correlative Matrix 1. Introduction Recently, image quality assessment (IQA) has played an important role in image acquisition, compression, communication, and display. Full-reference IQA metrics have been fully developed and used in practical applications to retrieve reference images. However, the original reference images are not always available to equipment used to process received images in many cases. In such cases, noreference IQA (NRIQA) metrics are required to overcome the lack of reference images. The NRIQA method is based on image quality evaluation results that are consistent with human visual perception [1] using the information within an image itself. In the image acquisition and processing field, not only are reference images not obtained in many cases, but also the imaging quality is different using different image acquisition devices under various environmental conditions. It is difficult to measure the image quality simply using several original copies of an image. In addition, the original reference images are not easily determined where special imaging systems are used, such as thermal infrared imaging devices, low light level night vision systems, etc. To retrieve the above mentioned images, IQA methods are applied using mature image processing algorithms [2-4]. The NRIQA method only uses the information in an image to measure the difference between itself and a real scene [5-6]. The NRIQA method can be easily embedded into a variety of image processing software to adjust the parameters of the image processing algorithm and the system at any time. The NRIQA method has the advantage of being a convenient application without being limited by the imaging system or landscape characteristics. At the same time, because of the diversity of measuring parameters and the uncertainties of human vision, the NRIQA method has the following problems. First, some image quality indices are difficult to quantify, such as deformation, aesthetics, context, and knowledge links. Second, it is difficult to establish a mode for IQA that is in accordance with the characteristics of human vision [7]. This is mainly limited by the lower level of understanding Advances in information Sciences and Service Sciences(AISS) Volume6, Number1, February 214 89

of the human visual system. Third, the NRIQA algorithm has strong dependences and is difficult to apply generally. This is mainly due to the different image distortions caused by different external factors. At present, different NRIQA methods are designed according to different types of image distortion [8-11]. Existing NRIQA methods have the following characteristics. First, the development of a general NRIQA method is limited by the specified image feature extractions, such as fuzzy effect, block effect, and the effects of noise. Second, the algorithm becomes stronger when combined with human visual characteristics, especially in color IQA [12-13]. Third, the algorithm based on machine learning is gradually improved to supplement visual subjectivity in order to provide a sufficiently comprehensive image [14-16]. The research of the NRIQA method has yielded specific applications [17-19], but there is a lack of general-purpose NRIQA methods. This paper proposes a general NRIQA method using a Euclidean distance matrix (EDM) to measure the correlation between an original image and its EDM so as to obtain a useful NRIQA metric. The proposed method is able to provide an image quality index without a reference image. And the evaluated results are consistent with human vision perception. At the same time, the necessary computations are accomplished quickly. 2. Euclidean distance matrix and image quality Given an image, the Euclidean distance is generally used to measure the similarity between two pixels. A shorter distance implies a higher correlation and a longer distance implies a lower correlation. The correlation between two pixels is measured by the similarity of their neighborhood, and is expressed as a function [2],. In the function, and denote the intensity of gray level vectors, and would denote a square neighborhood with fixed size and centered at the pixel k. Four image blocks are shown in the image in Figure 1[21], the Euclidean distance between blocks 1 and 2 is 577, between blocks 1 and 3 is 4536, and between blocks 1 and 4 is 683. Figure 1 illustrates that the pixels with similar gray level neighborhoods have smaller Euclidean distances. 3 4 1 2 Figure 1. Pixel blocks used to illustrate the similarity between two pixels using the Euclidean distance 2.1. Image Euclidean distance matrix By calculating the Euclidean distance between each pixel and other pixels that are in the same gray level neighborhood, an image Euclidean distance matrix is built. Each value in the EDM denotes the similarity of a pixel with its neighborhood pixels. An image and its EDM are shown in Figure 2. 9

Original image EDM Figure 2. An image and its Euclidean distance matrix 2.2. IQA using EDM If the original image quality were to decrease, the EDM would also change in accordance with the image quality. Figure 3 illustrates this fact, where Gaussian noise is added to the original image, causing the EDM to blur. Original image - Gaussian noise added Resulting EDM Figure 3. A noisy image and its Euclidean distance matrix 3. Image quality assessment method The relationship between the image and its EDM can be observed from the Figure 3, but the IQA method based on the EDM requires further study. There is a method to evaluate the image quality using an image pixel correlative matrix (PCM), and the quality index of an image is given by the standard variation of the PCM [7]. Although the PCM method has its shortcomings, where the assessment results are not accurate sometimes, the decreasing quality of an image should provide useful assessment results. In our study, the distribution width of the image PCM and the EDM PCM are used to measure the image quality, where the image quality is evaluated by the difference between the two widths. 3.1. Image pixel correlative matrix The image PCM is shown in Figure 4, and the PCM can be obtained by the following steps: (1) Build a matrix with a size of 256 256; (2) The grayscale of pixel (i, j) is g1 and the grayscale of pixel (i, j+l) is g2, the point (g1, g2) in the matrix is defined as set 1, where the l is the distance between the two pixels. 91

Original image PCM Gaussian noise added PCM Figure 4. Images and their pixel correlative matrices From Figure 4, where l belongs to set 1, the different noised images have different PCM distribution widths. And the original image has a wider PCM distribution width and the noised image has a narrower PCM distribution width. 3.2. Euclidean distance matrix correlation The EDM PCM is obtained by following the method to build the image PCM, and the resulting matrices are shown in the Figure 5. From Figure 5, note that both image have narrower distribution widths in the EDM PCMs than those of the PCMs in Figure 4. Then, the distribution widths of the EDM PCMs and the image PCMs are used to determine the IQA index. EDM of the original image PCM 92

EDM with Gaussian noise added PCM Figure 5. EDMs of the original and the noisy images and their pixel correlative matrices 3.3. No-reference IQA method From Figures 4 and 5, the distribution widths of the original image PCM and its EDM PCM are obviously different, and the distribution widths of the noised image PCM and its EDM PCM follow a similar relationship. Therefore, the difference in distribution widths between the image PCM and its EDM PCM is used as the no-reference index to evaluate the image quality. The purpose of IQA is to provide a quality index that reflects the degree to which an image s quality has decreased. Then, the complete IQA index must be obtained by processing a number of images subjected to different types of noise. The CSIQ image database [22] is used to obtain the IQA index, and the index extraction method is accomplished by the following steps. First, build the image PCMs of each image and all noised images with different types of noise. To simplify the following calculation, the image is divided into blocks of 32 32. Then, the block PCMs are built and the block with the largest distribution width is recorded and becomes the reference block for other calculations. An example is shown in Figure 6, where the block PCMs are shown and the largest distribution width can be extracted by simple geometric operations. Original image Block PCMs 93

Reference block Largest width block PCM Figure 6. Block PCMs and the largest width block Second, calculate the EDM of the reference block and build its PCM, as shown with the example blocks in Figure 7. Reference block EDM Largest width EDM PCM Figure 7. EDM of the reference block and its PCM Third, calculate the difference between the distribution width of the reference block PCM and the distribution width of the reference block EDM PCM, and record the differences in a spreadsheet, such as Excel. Figure 8 shows the differences using different noised images. From Figure 8, the decrease in image quality is reflected by the decreased difference in all content images. 15 flower leave 1 5 Figure 8. Difference in blurring of four images due to Gaussian noise Fourth, calculate the difference between the distribution width of the reference block PCM and the distribution width of the reference block EDM PCM for all types of noised images. According to the calculated results, build the look up table. 94

4. Experiments and Discussions Following the proposed method, four images with several types of noise were analyzed. The results are shown in Figures 9 to 13. In Figure 9, additive Gaussian white noise is present in the images. In Figure 1, additive Gaussian pink noise is present. In Figure 11, Global contrast decrements are added as noise. In Figure 12, JPEG compression causes noise in the images. In Figure 13, JPEG 2 compression causes the noise. 15 14 flowers leave 13 12 11 1 9 Figure 9. Differences in additive Gaussian white noised images 15 14 flower leave 13 12 11 1 9 Figure 1. Differences in additive Gaussian pink noised images 95

15 flower leave 1 5 Figure 11. Differences in global contrast decrements noised images 16 15 14 flower leaves 13 12 11 1 9 8 7 Figure 12. Differences in JPEG compressed images 15 flower leave 1 5 Figure 13. Differences in JPEG2 compressed images 96

From Figures 8 to 13, note that the proposed method is used to evaluate the images with Gaussian blur, global contrast decrements, JPEG compressed noise, and JPEG2 compressed noise. We are then able to obtain a lookup table to assess the various noise effects on the images. The image quality is divided into six grades, as shown in Tables 1 to 3 for three of the noise types. For images with Gaussian blurring noise, the difference from 15.3595 to 256 is the first grade, the difference from 72.4784 to 15.359 is the second grade, the difference from 41.7193 to 72.47845 is the third grade, the difference from 21.92 to 41.71935 is the fourth grade, the difference from 8.485281 to 21.923 is the fifth grade, and the difference from to 8.4852 is the sixth grade. Similarly, Tables 2 and 3 show the differences used to assess the images with global contrast decrements and the JPEG2 compressed images, respectively. Table 1. Gaussian blur assessment indices Noise grade The smallest difference is The largest difference is 1 2 3 4 5 6 1.492 61.51829 38.18377 28.99138 8.485281 1.414214 15.3595 72.4784 41.7193 21.92 8.485281 142.8356 11.387 83.4386 45.25483 14.84924 5.656854 256 15.359 72.47845 41.71935 21.923 8.4852 Table 2. Global contrast decrements indices Noise grade The smallest difference is The largest difference is 1 2 3 4 5 1.492 74.24621 46.6695 4.242641 3.535534 18.18735 8.257 51.6187 26.163 142.8356 115.9655 86.2673 56.56854 48.8326 256 18.1873 8.2566 51.618 26.162 Table 3. JPEG2 compressed indices Noise grade The smallest difference is The largest difference is 1 2 3 4 5 6 1.492 96.16652 94.452 91.21677 6.81118 5.656854 122.33 118.9 114.91 12.53 53.39 142.8356 144.2498 14.71 135.7645 113.8442 45.96194 256 122.32 118.8 114.9 12.52 53.38 5. Conclusion We calculated the difference between the distribution width of the recorded block PCM and the distribution width of the reference block EDM PCM for several types of noised images. The results show that the proposed method is effective to evaluate the quality of images with Gaussian blur, global contrast decrements, and JPEG2 compressed noise, and may work equally well on other types of noise, although additional research must be conducted to confirm this possibility. To achieve a truly general method, a higher quantity of original images will likely be required to obtain generalized quality indices for different noise types and potentially for images that include more than one noise type. Acknowledgements The present study is supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions project, Jiangsu Key Laboratory of Meteorological Observation and Information Processing open project (kdxs123), and State Key Laboratory for Novel Software Technology (Nanjing University) project (KFKT212B2). 97

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