Compression of the Mammography Images using Quadtree based Energy and Pattern Blocks Spideh Nahavandi Gargari M.S., Electronics Engineering, IS¸IK UNIVERSITY, 2017 Submitted to the Graduate School of Science and Engineering in partial fulfillment of the requirements for the degree of Master of Science in Electronics Engineering IS¸IK UNIVERSITY 2017 Compression of the Mammography Images using Quadtree Based Energy and Pattern Blocks Abstract Medical images, like any other digital data, require compression in order to reduce disk space needed for storage and time needed for transmission. This thesis offers , a novel image compression method based on generation of the so-called classified energy and pattern blocks (CEPB) is introduced and evaluation results are presented. The CEPB is constructed using the training images and then located at both the transmitter and receiver sides of the communication system. Then the energy and pattern blocks of input images to be reconstructed are determined by the same way in the construction of the CEPB. This process is also associated with a matching procedure to determine the index numbers of the classified energy and pattern blocks in the CEPB which best represents (matches) the energy and pattern blocks of the input images. Encoding parameters are block scaling coefficient and index numbers of energy and pattern blocks determined for each block of the input images. These parameters are sent from the transmitter part to the receiver part and the classified energy and pattern blocks associated with the index numbers are pulled from the CEPB. Moreover, in the second part of our method we used Quadtree too. By this way, all CEPB from quadtree results determined for each block of the input images too. input image is reconstructed block by block in the receiver part using a mathematical model that is proposed by 2 different method: • Reconstruct Based on one block size • Reconstruct Based on Quadtree Evaluation results show that the method provides considerable image compression ratios and image quality even at low bit rates. Test result have shown that Compression ratio and PSNR results is acceptable, moreover, Quadtree method gives better results that fix based block size. ii Quadtree Tabanlı Enerji ve Desen Bloklarını Kullanarak Mamografi G¨or¨unt¨ulerininSıkı¸stırılması Ozet¨ Tıp g¨or¨unt¨uleri,di˘gerdijital veriler gibi, depolama i¸cingerekli disk alanını ve ile- tim i¸cingerekli zamanı azaltmak i¸cinsıkı¸stırmagerektirir. Bu tez, sınıflandırılmı¸sen- erji ve desen blokları (CEPB) olarak adlandırılan yeni bir g¨or¨unt¨usıkı¸stırmay¨ontemi Tanıtılır ve de˘gerlendirmesonu¸clarısunar. CEPB, e˘gitimg¨or¨unt¨ulerinikullanarak in¸sa edilmi¸sve daha sonra ıleti¸simsisteminin verici ve alıcı taraflarnda kullanilir. Daha sonra giri¸sg¨or¨unt¨ulerininenerji ve desen blokları yeniden yapılanmasinda, CEPB'nin yapımı gibi aynı ¸sekildebelirlenir.Bu i¸slemaynı zamanda girdi g¨or¨unt¨ulerininenerji ve desen bloklarını da buluyor. Kodlama parametreleri giri¸sg¨or¨unt¨ulerininher blo˘gui¸cin, blok ¨ol¸ceklendirmekatsayısı, enerji endeksi sayıları, ve kalıp bloklarıdır. Bu parame- treler, verici b¨ol¨um¨undenalıcının par¸casıve endeks numaraları ile ili¸skilisınıflandırılmı¸s enerji ve desen blokları CEPB'den ¸cekilir. Dahası, y¨ontemimizin ikinci b¨ol¨um¨unde Quadtree'yi de kullandık. Bu y¨ontem ile, Quadtree metodina ba˘glı,girdi g¨or¨unt¨ulerinin her blo˘gui¸cinCEPB'leri de belirlendi. Giri¸sg¨or¨unt¨us¨u,2 farkl y¨ontem tarafından ¨onerilenmatematiksel bir model kullanarak alıcı par¸ca i¸cerisinde blok blok olarak yeniden olu¸sturulmu¸stur: • Sabit blok boyuna g¨ore, • Quadtree metoduna g¨ore. De˘gerlendirmesonu¸cları y¨ontemin d¨u¸s¨ukbit hızlarında bile ¨onemlig¨or¨unt¨usıkı¸stırma oranları ve g¨or¨unt¨ukalitesi sa˘gladı˘gınıg¨ostermektedir.Test sonucu, sıkı¸stırmaoranı ve PSNR sonu¸clarınınkabul edilebilir oldu˘gunu, ayrıca Quadtree y¨onteminin, blok boyu- tunu sabitleyen daha iyi sonu¸clarverdi˘ginig¨ostermi¸stir. iii Acknowledgements The author would like to thank to Professor Umit Guz, Hakan Gurkan (Isik Uni- versity, Engineering Faculty, Department of Electronics Engineering), Assistant Professor Murat Gezer (Istanbul University, Engineering Faculty, Department of Electronics Engineering), the many helpful discussions on this work during this thesis. The author also would like to thank the anonymous reviewers for their valuable comments and suggestions which substantially improved the quality of this paper. iv List of Tables 6.1 Energy and signature values metrics size . 83 6.2 CPB and CEB matrices sizes for different frame lenght . 84 7.1 Bit allocation table for the experiments . 95 7.2 CR values for different block size . 95 7.3 Fixed block size method average results . 96 7.4 Fixed block size method average time results . 96 7.5 Results for fix block size method, i=j=2 . 97 7.6 Results for fixed block size method, i=j=4 . 98 7.7 Results for fixed block size method, i=j=8 . 99 7.8 Results for fixed block size method, i=j=16 . 101 7.9 Time results for fixed block size method, i=j=2 . 102 7.10 Time results for fixed block size method, i=j=4 . 103 7.11 Time results for fixed block size method, i=j=8 . 104 7.12 Time results for fixed block size method, i=j=16 . 105 7.13 Quadtree method average results,max block size=8,min block size=2105 7.14 Quadtree method average results,max block size=16,min block size=2106 7.15 Quadtree method average results,max block size=4,min block size=2106 7.16 Quadtree method average time results,max block size=8,min block size=2 . 106 7.17 Quadtree method average time results,max block size=16,min block size=2 . 106 7.18 Quadtree method average time results, max block size = 4, min block size = 2 . 108 7.19 Quadtree method results, th=2, min block size=2, max block size=8109 7.20 Quadtree method results, th=5, min block size=2, max block size=8110 7.21 Quadtree method results, th=10, min block size=2, max block size=8111 7.22 Quadtree method results, th=15, min block size=2, max block size=8112 7.23 Quadtree method results, th=20, min block size=2, max block size=8113 7.24 Quadtree method results, th=30, min block size=2, max block size=8114 7.25 Quadtree method results, th=2, min block size=2, max block size=16115 7.26 Quadtree method results, th=5, min block size=2, max block size=16116 7.27 Quadtree method results,th=10, min block size=2,max block size=16117 7.28 Quadtree method results,th=15,min block size=2, max block size=16118 7.29 Quadtree method results,th=20,min block size=2,max block size=16119 ix List of Figures 3.1 Examples of gamma-ray images . 16 3.2 Examples of magnetic resonance images . 16 3.3 Examples of breast ultrasound images . 17 3.4 Mammography unit. 19 3.5 Mammography Screening . 20 3.6 Mammography Image . 21 4.1 General scheme for lossy compression. 29 4.2 Regular scalar quantization . 31 4.3 Compression system model in rate-distortion theory . 32 4.4 The relationship between bit rate and distortion in lossy compression 34 4.5 Self similarity in real images . 37 4.6 Quadtree partitioning of a range. Four iterations . 42 4.7 Horizontal-vertical partitioning of a range. Four iterations . 45 4.8 Region edge maps and context modeling . 49 4.9 Performance of compression methods with irregular partition . 50 4.10 Probability density function of block offset . 53 4.11 Spiral search . 54 4.12 Distributions of scaling and offset coefficients (second order poly- nomial intensity transformation . 63 5.1 Three clusters of given . 70 5.2 Segmented image using K-Means . 73 5.3 Block Diagram of K-Means Process. 74 5.4 Typical K-Means algorithm . 75 6.1 CEPB construction . 84 6.2 Partitioning of an image into the image blocks and reshaping as vector form . 85 6.3 Blocked Image by Quadtree method, max block size=16, min block size=2 . 86 6.4 Encoding . 87 6.5 Decoding . 89 7.1 Data set images . 91 7.2 Main mdb014 Image . 100 xi Chapter 1 Introduction 1.1 Background More and more fields of humans life are becoming computerized nowadays. This determines generation of huge, and further increasing, amount information stored in digital form. All this is possible thanks to technological progress in registration of different kinds of data. This progress is also being observed in wide field of digital images, which covers scanned documents, drawings, images from digital or video cameras, satellite images, medical images, works of computer graphics and many more. Many disciplines, like medicine, e-commerce, e-learning or multimedia, are bounded with ceaseless interchange of digital images. A live on-line transmis- sion of a sport event, or a surgery with a remote participation of one or more specialist, teleconference in a world wide company constitute great examples. Such utilization of technology related to digital images becomes nowadays very popular. Long-lasting storage of any data often can be very profitable. In medicine, Hospital Information Systems contain a large number of medical examination results. Thanks to them doctors can familiarize themselves with the case history and make a diagnosis based on many different examination results. Such systems are also very useful for the patients because they gain access to their 1 medical data. A very good example is IZIP Czech system, which gives Internet access to patients health records. Unfortunately, these hospital databases are growing rapidly each day tens or hundreds of images are produced and most of them, or even all, are archived for some period.