IMAGE ZOOMING USING WAVELET COEFFICIENTS Dissertation submitted in partial fulfillment of the requirements for the award of degree of Master of Technology in Computer Science and Applications Submitted By Himanshu Jindal (Roll No. 651103003) Supervised By Dr. Singara Singh Assistant Professor SCHOOL OF MATHEMATICS AND COMPUTER APPLICATION THAPAR UNIVERSITY PATIALA – 147004 July 2014 CERTIFICATE I hereby certify that the work being presented in the dissertation entitled, "Image Zooming Using Wavelet Coefficients", in partial fulfillment of the requirements for the award of degree of Master of Technology in Computer Science and Applications submitted to the School of Mathematics and Computer Applications of Thapar University, Patiala, is a authentic record of my own work carried out under the supervision of Dr. Singara Singh and refers other researcher's work which are duly listed in the reference section. The matter presented in the dissertation has not been submitted for the award of any other desree of this or anv other university. _ .. \,. ->- PL*"*?irf t (Himanshu Jindal) This is to certify that the above statement made by the student is correct and true to the best of my knowledge. ffi1,, (Dr. Singara Singh) Assistant Professor, School of Mathematics and Computer Applications, Thapar University, Patiala Countersigned By - n r / /t I T" \^--Y H4W-- Dr. Rajesh Kumar Dr. S.K. Nlohdpatfa Head, Dean School of Mathematics and Computer Applications, (AcademicAffairs) Thapar University, Patiala Thapar University, Patiala ACKNOWLEDGMENT I would like to acknowledge everyone who supported me during my experience at Thapar University and my work on this dissertation. First and foremost I would like to thank God for providing me with faith, self-confidence and ability to complete the dissertation. It would be a great pleasure for me to acknowledge the guidance, assistance and help received from Dr. Singara Singh, Assistant professor, SMCA, Thapar Univeristy, Patiala. I am very grateful for his continual support, encouragement and invaluable suggestions. His enthusiasm and optimism made this experience both rewarding and encourageable. I extend my deep gratitude towards Dr. Rajesh Kumar, Head, SMCA, Thapar University, Patiala for providing the timely facilities and infrastructure that helped in completion of the dissertation. I would like to take this opportunity to express my sincere appreciation and thanks to my friends and family for their strong moral support and constant encouragement throughout this research. I am also thankful to all staff members of SMCA for their kind cooperation and sincere help. Ir 5;& W*urindar Roll No: 651103003 M.Tech (CSA) ABSTRACT The work in this dissertation involves an algorithmic approach to zoom a given image in wavelet domain and to get a sharper image using with various interpolation techniques. The exploration is an attempt to develop quantitative measures that can automatically predict perceived image quality. An objective image quality metric can play a variety of roles in image processing applications. First, it can be used to dynamically monitor and adjust image quality; second, it can be used to optimize algorithms and parameter settings of image processing systems. Second, it can be used to benchmark image processing systems and algorithms as zoomed images are sharper as compared to other methods. Hence keeping all this in mind on this source of information, Discrete Wavelet Transform (DWT) with various interpolation techniques had been applied upon variances to obtain their values. Performance is measured by calculating Peak Signal to Noise Ratio (PSNR), and the proposed method gives much better PSNR compared to other methods. This algorithm can help in medical science to get the minutest details for detection of cancer. iii TABLE OF CONTENTS Certificate........................................................................................................ i Acknowledgement........................................................................................... ii Abstract............................................................................................................ iii List of Figures……………………………………………………………...... vi List of Tables…………………………………………................................... vii Chapter I: Introduction …………………………………………….……....... 1-26 1.1 Introduction......................................................................................... 1 1.2 Image.................................................................................................... 1 1.3 Image Zooming.................................................................................... 3 1.3.1 Need of Zooming................................................................................. 4 1.4 Types of Zooming................................................................................ 5 1.4.1 Pixel Replication.................................................................................. 5 1.4.2 Interpolation........................................................................................ 7 1.4.2.1 Linear Interpolation...................................................................... 8 1.4.2.2 Bilinear Interpolation................................................................... 10 1.4.2.3 Bi-Cubic Interpolation.................................................................. 11 1.4.2.4 Nearest Neighbour Interpolation................................................... 12 1.5 Discrete Wavelet Transform................................................................ 13 1.5.1 Inverse Discrete Wavelet Transform................................................... 17 1.6 Types of Wavelets............................................................................... 17 1.6.1 Haar wavelets...................................................................................... 17 1.6.2 Daubechies wavelets........................................................................... 17 1.6.3 The Dual-Tree Complex Wavelet Transform...................................... 17 1.7 Properties of Discrete Wavelet Transform.......................................... 18 1.8 Time Complexity of Discrete Wavelet Transform.............................. 18 1.9 Applications of Discrete Wavelet Transform...................................... 18 1.10 Image Quality...................................................................................... 19 1.11 Image Quality Factors......................................................................... 20 1.12 Scanning Factors.................................................................................. 22 iv 1.13 Image Quality Parameters................................................................... 23 1.14 Conclusion........................................................................................... 26 Chapter II: Literature Survey …………………………………….……......... 27-39 2.1 Introduction.......................................................................................... 27 2.2 Literature Survey.................................................................................. 27 2.3 Conclusion........................................................................................... 38 Chapter III: Image Zooming Algorithm Using Wavelet Coefficients.......... 40-49 3.1 Introduction.......................................................................................... 40 3.2 Proposed Algorithm............................................................................. 40 3.3 Implementation.................................................................................... 40 3.4 Results.................................................................................................. 42 3.5 Comparison with Existing Algorithm……....……………………….. 48 3.6 Conclusion........................................................................................... 49 Chapter IV: Conclusion and Future Scope …………………….……........... 50 4.1 Conclusion........................................................................................... 50 4.2 Future Scope........................................................................................ 50 References …………………….……................................................................. 52 v LIST OF FIGURES FIGURE DESCRIPTION PAGE NO Figure 1.1 An image arranged in array of columns and rows 2 Figure 1.2(a) Pixel having various colors based on gray scale 2 Figure 1.2(b) Each pixel has value from 0 to 255 on gray scale 3 Figure 1.3 Image of a Rose 4 Figure 1.4 Zoomed image of rose 5 Figure 1.5 Pixel Replication 6 Figure 1.6 Original image of a Boy 6 Figure 1.7 Zoomed image of Boy 7 Figure 1.8 Output Image of bilinear interpolation 11 Figure 1.9 Output Image of bi-cubic interpolation 12 Figure 1.10 Output Image of nearest neighbour interpolation 13 Figure 1.11(a) First level decomposition showing subbands of DWT 14 Figure 1.11(b) Second level decomposition showing subbands of DWT 14 Figure 1.11(c) Third level decomposition showing subbands of DWT 14 Figure 1.12 Output image of DWT 16 Figure 3.1(a) Image of Football 41 Figure 3.1(b) Image of Airplane 41 Figure 3.1(c) Image of Baboon 41 Figure 3.1(d) Image of Tape 41 Figure 3.1(e) Image of Office 41 Figure 3.1(f) Image of Lena 41 Figure 3.1(g) Image of Onion 41 Figure 3.1(h) Image of Pears 41 Figure 3.1(i) Image of Peppers 41 Figure 3.1(j) Image of Sailboat 42 Figure 3.1(k) Image of Trees 42 Figure 3.1(l) Image of Canoe 42 Figure 3.2(a) Zoomed Image by 2 of Football 42