Experimental Images Analysis with Linear Change Positive and Negative Degree of Brightness

Experimental Images Analysis with Linear Change Positive and Negative Degree of Brightness 1 RATKO IVKOVIC, BRANIMIR JAKSIC, 3 PETAR SPALEVIC, 4 LJUBOMIR LAZIC, 5 MILE PETROVIC, 1,,3,5 Department of Electronic and Computer Engineering Faculty of Technical Sciences, University of Prishtina Kneza Milosa 7, 380 Kosovska Mitrovica SERBIA 4 State University of Novi Pazar Vuka Karadzica, 36300 Novi Pazar SERBIA 1 ratko.ivkovic@ymail.com, branimir.jaksic@pr.ac.rs, 3 petar.spalevic@pr.ac.rs, 4 llazic@np.ac.rs, 5 mile.petrovic@pr.ac.rs Abstract: - In this paper we presented an analysis of the image that is applied to the linear rate of increasing and decreasing of brightness on image. The analysis of the results are presented in tabular and graphical form. The analysis used the parameters of the Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM), Different Structural Similarity Index (DSSIM). It was found that the different degrees of linear brightness changes the parameters PSNR and MSE have approximately the same value, and the mathematical changes to the image can only be analyzed through SSIM and DSSIM parameters. Analysis of the impact of positive and analyzed through histograms for the RGB channels. Key-Words: - Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Structural similarity index (SSIM), Different Structural similarity index (DSSIM), brightness, brightness parameter (BP) 1 Introduction Brightness is one of the most significant pixel characteristics, and like this represent attribute of visual perception in which a source seems to be radiating or reflecting a specific amount of light. It is involved in many image-editing algorithms such as contrast or shadow/highlight. Currently, there is no conventional formula for brightness calculation, and the same image-processing tool may employ several different brightness measures. However, stimuli, equi-bright according to one measure, may differ more, than ten times according to another [1]. Usually, term Brightness should be used only for nonquantitative references to physiological sensations and perceptions of light. Wyszecki and Stiles define Brightness as an attribute of a visual sensation according to which a given visual stimulus appears to be more or less intense; or, according to which the area in which the visual stimulus is presented appears to emit more or less light, and range variation in Brightness from bright to dim. Given definition is useless for digital image processing, because provides no foundation for image editing. Developers of algorithms for digital image processing are obliged to find a way to describe Brightness quantitatively. However, currently, there is no conventional numerical description for this stimulus characteristic []. This paper proposes a review and analysis of the most popular values used for Brightness representation and discusses the effectiveness of those values in image editing algorithms heavily dependent on the choice of Brightness measure [3]. Parameters for Image Quality Analysis.1 Mean Square Error (MSE) and Peak Signal to Noise Ratio (PSNR) A method for the estimation of image quality is needed in order to give a view about how lossy compression methods modify image quality. We may treat an image as a matrix whose elements are image pixels. The estimation process is then based on the calculation of distances between appropriate elements of input and output matrices. In this way, not only comparison of quality of different ISBN: 978-960-474-350-6 116

compression methods is enabled, but also comparison of the results of the same method using different compression ratios [4]. We denote the matrix A at the input of the compression system with elements a ij, with i{1...m}, j{1...n}, where M is the number of image elements in the vertical and N is the number of image elements in horizontal direction]. MxN is the total number of image elements. The output of the compression system is the matrix A' with elements a' ij. The distance between the elements of matrices A and A' represents the error or the loss of image quality. Usually, the error is larger for higher compression ratios. A user can set the compression ratio according to the desired image quality, and hence directly influence the data size of the compression image. m1 n1 ' aij aij (1) i0 j0 E The distance between matrices A and A' is frequently calculated using the Mean Square Error (MSE) [4]: m1 n1 E 1 ' MSE aij aij () MN MN i0 j0 where MxN is the total number of image pixels, and the sum is applied to all image elements. The amplitudes of image elements are in the range [0, n -1], where n is the number of bits needed for binary representation of amplitude of each element in the original image. MSE does not consider amplitudes of image elements (it only considers differences between amplitudes) and it is the reason for introducing the Peak Signal to Noise Ratio (PSNR). MAX I MAX I PSNR 10 log 10 0 log 10 (3) MSE MSE The variable MAX I is the maximum amplitude value of image element (pixel). When the amplitude of the image pixel is represented by B bits, MAX I is B -1. With n=8 bits/image element we can define: 55 PSNR 10 log 10 (4) MSE Typical values for PSNR for lossy compressed images are between 30 and 50 db.. Structural similarity index (SSIM), Different Structural similarity index (DSSIM) Structural similarity index (SSIM) represents perceptual image quality based on the structural information. SSIM is an objective image quality metric and is superior to traditional quantitative measures such as MSE and PSNR [5]:,,,, SSIM x y l x y c x y s x y (5) where α>0, β>0 and γ >0 are parameters used to adjust the relative importance of the three components. Symbols x,y are image patches and l(x,y) is luminance comparison, c(x,y) is contrast comparison, and s(x,y) is structural comparison [6]. When DSSIM calculate: 1 SSIM x, y DSSIM x, y (6) DSSIM is a distance metric derived from SSIM (though the triangle inequality is not necessarily satisfied) [7]. 3 System Model For the analysis of the objective image quality were used 8-bit uncompressed images saved in bmp format, with a original resolution of 51x51 pixels available on the website http://sipi.usc.edu/database/misc.zip. The analyzed images are bright with varying degrees of positive and by using Matlab software package. Positive brightness corresponding with increasing brightness in image, and a negative corresponding with decreasing brightness in image. The brightness of the image is controlled through the Brightness parameter (BP), so that to increase the brightness BP ranges from 1 to 55 (positive brightness), and to decrease the brightness of -1 to -55 (), and 0 corresponds to the value the original image. A change in the brightness and a change in the value of BP is directly related to the changing value of the pixels in the image. Fig. 1 shows one of the analyzed image with varying degrees of positive brightness, and in Fig. analyzes the images with various degrees of. By using the Matlab software it has taken the ability to present the picture with matrix expression [m n].it is allowed that the pixel values may change depending on some functions. This attribute of the MATLAB software provides a great opportunity to directly manipulate pixel values to a specific function. ISBN: 978-960-474-350-6 117

Fig. 1: Image with a positive brightness: a) BP=5 b) BP=100 c) BP=175 Fig. : Image with : a) BP=-5 b) BP=-100 c) BP=-175 Changing the level of brightness is not just for one or a group of pixels, but for the total number of pixels in the image. With applied linear functions and increasing of the BP leads to increasing the pixel values. This increasing leads to a shift of the entire histograms to the right, respectively, to the right border of the spectrum (white). According to that it doesn t come to changing the number of pixels and the form of histograms to RGB channels [8]. In case of reduction of brightness, i.e. using a negative brightness, the pixel values are reduced and there is a shift to the left side of the histogram, as shown in Fig. 3. Based on the definition MSE, equation (), the values of parameter m and n represent the value of pixel, expressed in basis RGB parameters. In this case there exist two identical linear functions (positive and ), and the values of the pixels will be changed by the same law. According to the definition of MSE where the absolute value exists, the results will be the same values for positive and negative picture brightness. Fig. 3: Histogram of the RGB channels of a) original image, b) image with a positive light BP = 5, c) image with a negative light BP = -5 ISBN: 978-960-474-350-6 118

Based on the differential between the original and brightness images computed mean squared error (MSE), Structural Similarity Model (SSIM), Different Structural Similarity Model, Peak Signalto-Noise Ratio (PSNR).. with different degrees of brightness of the analyzed image. On the x-axis is given absolute value of the parameter lighting (BP). Positive values (1 to 55) refer to picture brightness, and negative values on the darkening of the image. 4 Results Results of the analysis for different values of positive and images are given in Table 1 and Table. Table 1: Values of PSNR, MSE, SSIM and DSSIM for positive brightness BP PSNR MSE SSIM DSSIM 1 48.1314 0.999856 0.99996 13465.8 5 0.558 613.053 0.96851 31.7565 50 14.5083 30.78 0.900657 10.0661 75 11.311 4797.03 0.816795 5.45835 100 9.14973 7908.74 0.73968 3.74488 15 7.5518 1147.5 0.646493.888 150 6.487 14798. 0.548368.1419 175 5.737 17353. 0.451085 1.8178 00 5.40936 18713 0.399966 1.66657 5 5.603 19366.4 0.38117 1.61596 55 5.188 1955.4 0.373995 1.59743 Table : Values of PSNR, MSE, SSIM and DSSIM for BP PSNR MSE SSIM DSSIM -1 48.1308 1.0 0.9999 1877-5 0.3 616.4 0.934987 15.3816-50 14.3536 386.3 0.781113 4.56858-75 11.0369 511.43 0.56508.998-100 8.96371 854.86 0.373966 1.59736-15 7.61039 173 0.3786 1.31111-150 6.67849 13971.1 0.145085 1.16971-175 5.97513 1647.4 0.07601 1.088-00 5.46991 18453.9 0.080764 1.0889-5 5.19333 19667.4 0.004351 1.00437-55 5.1371 1993.7 0.0004494 1.00045 In Fig. 4, Fig. 5 and Fig. 6 shows a graph of changes in PSNR, MSE, SSIM and, respectively, PSNR [db] 50 40 30 0 10 0 Fig. 4: PSNR for different degree of positive and MSE 0000 15000 10000 5000 0 Fig. 5: MSE for different degree of positive and In graphs there can be seen that in lower absolute values BP, PSNR there is a higher value, while with the increase of BP, PSNR there is very fast decrease. Value of PSNR is almost the same for positive, as well as for negative contrast of the image. Similar to PSNR, MSE is identical for the same amount of positive and negative contrast of the image, white MSE is growing with the increase of positive brightness, i.e. in the image. Based on the change of parameter PSNR and MSE for different degree of positive and negative brightness in the Fig. 3 and Fig. 4, respectfully, ISBN: 978-960-474-350-6 119

there is no possibility to see the difference in brightness and darkness of the image. SSIM 1.0 0.8 0.6 0.4 0. 0.0 Fig. 6: SSIM for different degree of positive and Therefore there is new parameter SSIM and DSSIM. In the Fig. 5 there is decrease of SSIM with increase of positive and, but for the difference in PSNR and MSE that are identical with the increase of BP. In this case decreasing of SSIM is much more visible with negative than in positive brightness [9]. 4 Conclusion Apart from the visual appearance, based on PSNR and MSE could not be mathematically determined difference between the original image and the image with increasing/decreasing brightness. SSIM is a parameter that mathematically confirms the difference when it is impossible to determine with other parameters. Based on the above, the SSIM can be established in conditional different values of BP for the same image and the same values of MSE and PSNR, SSIM parameter values demonstrate the diversity of images. These results show that the SSIM and decreases in positive and in a, such as the decrease in is significantly expressed, as a consequence of the properties of SSIM compares pictures by illumination and reflection. References: [1] S. Bezryadin, P. Bourov, D. Ilinih, Brightness Calculation in Digital Image Processing, Symposium on Technologies for Digital Photo Fulfillment, pp. 10-15(6), 007. [] S. Bezryadin, P. Bourov, Color Coordinate System for Accurate Color Image Editing Software, The International Conference Printing Technology SPb 06 proceedings, p. 145 148, St. Peterburg State University of Technology and Design, 006. [3] B. Jaksic, R. Ivkovic, M. Petrovic, Analisys brightness effect on quality pictures after compression with JPEG and SPIHT compression method, Matematicke i informaticke tehnologije, September 013. [4] Z. Wang, Alan C. Bovik, Mean Squared Error: Love It or Leave It?, Signal Processing Magazine, IEEE, Vol. 6, No. 1, January 009, pp. 98 117. [5] Z. Wang, A. C. Bovik, H, R. Sheikh, Structural Similarity Based Image Quality Assessment, Chapter 7 in Digital Video Image Quality and Perceptual Coding (H. R. Wu, and K. R. Rao, eds.), Marcel Dekker Series in Signal Processing and Communications, November 005. [6] T. O. Aydın, R. Mantiuk, H. P. Seidel, Extending Quality Metrics to Full Luminance Range Images, Human Vision and Electronic Imaging XIII, January 008. [7] A. Loza, L. Mihaylova, N. Canagarajah, David Bull, Structural Similarity-Based Object Tracking in Video Sequences, 006. [8] Z. Wang, A. C. Bovik, IEEE transactions on image processing, VOL. 13, NO. 4, April 004. [9] B. Jaksic, R. Ivkovic, M. Petrovic, Analysis of different influence of compression algorithm on the image filtered Laplcian, Prewitt and Sobel operator, International Journal of Darshan Institute on Engineering Research and Emerging Technology, Vol., No. 1, 013 Acknowledgment This work was done within the research project of the Ministry of Science and Technological Development of Serbia TR3506, entitled as: Software Development Environment for optimal software quality design.. ISBN: 978-960-474-350-6 10