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Texture, Nonogram, and Convexity Priors in Binary Tomography

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Texture, Nonogram, and Convexity Priors in Binary Tomography PH.D. THESIS Texture, Nonogram, and Convexity Priors in Binary Tomography Author: Supervisor: Judit SZUCS˝ Péter BALÁZS, Ph.D. Doctoral School of Computer Science Department of Image Processing and Computer Graphics Faculty of Science and Informatics University of Szeged, Hungary Szeged, 2021 iii Acknowledgements First of all, I would like to say a special thank you to my supervisor, Péter Balázs, who always supported me throughout the years of my PhD studies, even during hard times. I would like to thank the following people for helping me in my research: Gábor Lékó, Péter Bodnár, László Varga, Rajmund Mokso, Sara Brunetti, Csaba Olasz, Gergely Pap, László Tóth, Laura Szakolczai, and Tamás Gémesi. I would also like to thank Zsófia Beján-Gábriel for correcting this thesis from a linguistic point of view. Last but not least, I would like to thank my family, especially my mother, my father, my grandmother, and my significant other for supporting me dur- ing my studies. Without their support, this PhD thesis would not have been possible. Finally, I would like to thank the Doctoral School of Computer Science and the Department of Image Processing and Computer Graphics of the University of Szeged for providing me with a productive work environment. This research presented in this thesis was supported by the following: • NKFIH OTKA K112998 grant, • ÚNKP-18-3 New National Excellence Program of the Ministry of Human Capacities, • ÚNKP-19-3 New National Excellence Program of the Ministry for Innovation and Technology, Hungary, • ÚNKP-20-4 New National Excellence Program of the Ministry for Innovation and Technology from the Source of the National Research, Development and Innovation Fund, • The project “Integrated program for training new generation of scientists in the fields of computer science“, no. EFOP-3.6.3-VEKOP- 16-2017-00002 (European Union and co-funded by the European Social Fund), • Grant 20391-3/2018/FEKUSTRAT of the Ministry of Human Capacities, Hungary, • Grant TUDFO/47138-1/2019-ITM of the Ministry for Innovation and Technology, Hungary. Judit Sz˝ucs,January 2021. v Contents Acknowledgements iii Contentsv List of Figures ix List of Tables xiii List of Abbreviations xv List of Symbols xvii 1 Preliminaries1 1.1 Problem Outline, Definitions.................... 1 1.2 Reconstruction Algorithms..................... 4 1.2.1 Analytical Methods..................... 4 1.2.2 Algebraic Reconstruction Methods............ 5 Algebraic Reconstruction Technique........... 7 Simultaneous Iterative Reconstruction Technique... 7 Simultaneous Algebraic Reconstruction Technique... 8 1.3 Discrete Tomography........................ 8 1.3.1 Discrete Algebraic Reconstruction Technique...... 8 1.4 Binary Tomography......................... 10 1.4.1 Ryser’s Algorithm ..................... 10 1.4.2 Binary Reconstruction by Optimization......... 13 Simulated Annealing.................... 13 1.4.3 Quality Measurement in Binary Tomography . 15 2 Binary Tomography with Local Binary Pattern Priors 17 2.1 Local Binary Patterns as Texture Descriptors .......... 17 2.1.1 Local Binary Patterns (LBP)................ 18 vi 2.1.2 Fuzzy Local Binary Patterns (FLBP) ........... 18 2.1.3 Shift Local Binary Patterns (SLBP) ............ 20 2.1.4 Dominant Rotated Local Binary Patterns (DRLBP) . 21 2.2 Preliminary Studies......................... 21 2.3 Comparison of the LBP Variants.................. 27 2.4 Results ................................ 28 2.4.1 Experimental Setup..................... 28 2.4.2 Synthetic Image Classes .................. 29 2.4.3 Software Phantom Images................. 33 2.4.4 Real Images ......................... 34 2.5 Conclusion.............................. 39 3 Binary Tomography Based on Nonograms 41 3.1 Problem Outline........................... 41 3.2 Proposed Methods ......................... 44 3.2.1 Constraint Satisfaction................... 44 3.2.2 Variants of Simulated Annealing............. 45 The Basic Method...................... 45 Starting from a Precalculated Number of Object Pixels . 45 Initialization with Ryser’s Algorithm........... 46 SA with Curveball Algorithm............... 46 3.3 Implementation Details....................... 47 3.3.1 Deterministic Methods................... 47 3.3.2 Stochastic Methods..................... 48 Local Update of the Strip Vectors............. 48 3.4 Experimental Results........................ 49 3.4.1 Random Matrices of Different Densities......... 49 3.4.2 Web Paint-by-Number................... 57 3.4.3 TomoPhantom Images................... 58 3.5 Conclusion.............................. 60 4 Global and Local Quadrant-Convexity 63 4.1 Global Quadrant-Convexity.................... 64 4.1.1 Obtaining Enlacement Descriptors by Normalization . 66 4.1.2 Object Enlacement and Interlacement .......... 68 4.1.3 Experiments......................... 69 4.2 LQH for Image Classification ................... 72 4.2.1 Comparison of the LQH Variants............. 75 4.2.2 Experiment with the Retina Dataset ........... 79 4.2.3 Appropriate Window Size and Quantization Level . 84 4.3 LQH for Binary Image Reconstruction.............. 86 4.3.1 Fast LQH Calculation.................... 87 Dynamic Programming .................. 87 Random Sampling ..................... 90 Local Update ........................ 91 4.3.2 Results............................ 92 vii 4.4 Conclusions ............................. 95 5 Conclusions of the Thesis 97 A Summary in English 99 A.1 Key Points of the Thesis ...................... 100 B Summary in Hungarian 103 B.1 Az eredmények tézisszer˝uösszefoglalása . 104 C Publications of the Author 107 D Images 111 E Tables 125 Bibliography 129 ix List of Figures 1.1 Sample images. ........................... 1 1.2 Parallel beam geometry. ...................... 2 1.3 A sample image and its projection (q = 20◦). .......... 3 1.4 Sample image (a) and its sinogram (b)............... 4 1.5 Sample for backprojection (a) and for filtered backprojection (b) of Fig. 1.4.............................. 5 1.6 Sample for binary image with parallel beams (a) and a projec- tion value calculation (b)....................... 6 1.7 Sample for ART (a), SIRT (b), and SART (c) reconstruction of Fig. 1.4................................. 7 1.8 Sample for DART of Fig. 1.4..................... 9 1.9 Image representations with black and white pixels (a), with a lattice set (b), and with a binary matrix (c)............. 10 1.10 Example of switching component and elementary switching. 12 1.11 Switching component graph. ................... 12 2.1 Different images with same horizontal and vertical projections............................... 17 2.2 Software phantom image classes.................. 22 2.3 Example of how the RME value changes by increasing the num- ber of projections........................... 26 2.4 Chessboard image (a) and its inversion (b). ........... 26 2.5 Sample SA results of the synthetic image classes. 30 2.6 Sample result of Ryser’s algorithm for Chessboard and Diago- nal image classes........................... 31 2.7 Frequency of occurrence of matrix M concerning increasing g weights for the Chessboard image class.............. 32 2.8 Frequency of occurrence of matrix M0 concerning increasing g weights for the Diagonal image class................ 32 2.9 Sample results of Fig. 2.2a...................... 33 2.10 Real image classes I. [18]....................... 34 2.11 Sample results of Fig. 2.10c. .................... 36 2.12 Real image classes II. [35]. ..................... 36 2.13 Sample results of Fig.2.12. ..................... 38 3.1 Instances of the BT (a,d,g), SCBT (b,e,h), and N ONOGRAM (c,f,i) problems. Padding zero elements of the matrices LH and LV are not indicated....................... 42 x 3.2 Sample for uniqueness (c,f) and non-uniqueness (a,d,b,e) of the SCBT problem.......................... 44 3.3 Steps of the CurveballSA algorithm................ 46 3.4 Sample for a new strip appearing (a), two strips merging (b), and no change (c andd)....................... 49 3.5 Images with 0%, 10%, . , 100% randomly selected object pixels.............................. 50 3.6 Mean pixel error (vertical axis) of the intlinprog (a) and the SA (b) methods for different image sizes (horizontal axis). 52 3.7 Mean running time in seconds (vertical axis) of the intlinprog (a) BasicSA (b), FixpixelSA (c), RyserSA (d) and CurveballSA (e) methods for different image sizes (horizontal axis). 54 3.8 Mean final objective value (vertical axis) of the BasicSA (a), FixpixelSA (b), RyserSA (c) and CurveballSA (d) methods for different image sizes (horizontal axis)............... 55 3.9 Mean strip difference (vertical axis) of the BasicSA (a) and Fix- pixelSA (b) methods for different image sizes (horizontal axis). 56 3.10 Mean running time in seconds RyserSA (a) and CurveballSA (b) methods for different image sizes (horizontal axis). 56 3.11 Mean final objective value (vertical axis) of the RyserSA (a) and CurveballSA (b) methods for different image sizes (hori- zontal axis). ............................. 57 3.12 Sample images from Web Paint-by-Number............ 57 3.13 TomoPhantom images taken from [94]............... 58 3.14 Objective function values during the millions of iterations for Fig. 3.13a................................ 60 4.1 Non-Q-convex image......................... 65 4.2 A Q-convex image (a) and a Q-concave image (b). 66 4.3 Sample images with enlacement values.............. 67 4.4 Enlacement landscapes of the last three images of Fig. 4.3. 68 4.5 Sample images from [30], where F
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