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Feature Tracking and Viewing for Time-Varying Data Sets FEATURE TRACKING AND VIEWING FOR TIME-VARYING DATA SETS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Guangfeng Ji, M.E. ***** The Ohio State University 2006 Dissertation Committee: Approved by Professor Han-Wei Shen, Adviser Professor Rephael Wenger Adviser Professor Raghu Machiraju Graduate Program in Computer Science and Engineering ABSTRACT Feature tracking plays an important role in understanding time-varying data sets since it allows scientists to focus on regions of interest and track their evolution and interaction over time. In this work, we first present an efficient algorithm to track time- varying isosurface and interval volume features using isosurfacing in higher dimensions. Instead of extracting these isosurface or interval volume features separately from mul- tiple time steps and computing the spatial correspondence between them, our algorithm extracts the correspondence directly from the higher dimensional geometry and allows more efficient feature tracking. We further show that the correspondence relationship for time-varying isosurfaces can only change at critical isovalues in R3 or R4. Based on the observation, we present a method to pre-compute the correspondence relationship at a preprocessing stage. At run time, isosurface tracking can be efficiently performed by simple table lookup operations with minimal overhead. For complex data sets, the previous feature tracking methods cannot guarantee the globally best matching because these methods use local matching criteria and track features independently in the local neighborhood. To amend the problem, we propose a novel global tracking technique to track features, which defines the globally best match as the one with a minimal overall matching cost. Noticing the deficiencies of previous tracking criteria, we use the Earth Mover’s Distance as a better metric to measure the matching cost. We also propose an efficient branch-and-bound algorithm to search the global minimal cost. ii In addition to tracking features, another important problem is how to view the time- varying features effectively. Due to the time-varying nature, animation remains the most general and common way to show how time-varying features evolve over time. A key issue of generating a good animation is to select ideal views through which the user can perceive the maximum information of the time-varying features. In this work, an algorithm is also presented to select dynamic views. We first propose an improved view selection method for static data, which measures the quality of a static view by analyz- ing the opacity, color and curvature distributions of the feature rendering images from the given view. A dynamic programming approach is used to select dynamic views. The process maximizes the information perceived from the time-varying features based on the constraint that the view should show smooth changes of direction and near-constant speed. Our feature tracking and viewing algorithms provide the user with a more effec- tive and efficient way to study the time-varying features, and allow the user to gain more insight into the time-varying data sets. iii Dedicated to my parents . iv ACKNOWLEDGMENTS First of all, I would like to express my sincere gratitude to my adviser, Dr. Han-Wei Shen, for his guidance, encouragement and support, during my years of Ph.D study at The Ohio State University. His insights, encouragement and solid professional knowl- edge have guided me through difficulties and challenges. I learned a lot from him and his valuable advices will accompany me throughout my career. I have been truly lucky to have the opportunity to work with him. Without his help and support, this dissertation would not be possible. I would also like to thank my dissertation committee members, Dr. Rephael Wenger and Dr. Raghu Machiraju for giving me valuable suggestions during my research and dissertation writing. Many fruitful hours were spent with them discussing research and the dissertation. They showed me new perspective of looking at problems, and broad- ened my thinking and knowledge scope. I also want to thank Dr. Roger Crawfis for his great help on my research. I want to thank my colleagues and friends for their great help. I really enjoyed the time I work with my team members: Jonathan Woodring, Chaoli Wang, Liya Li, Jinzhu Gao, Udeepta Bordoloi, and Antonio Garcia. We spent many hours discussing research and exchanging ideas. We shared code and helped on implementations. Yipeng Li and Yisheng Chen have spent their precious time helping me teaching. Caixia Zhang also v helped me a lot. I really enjoyed the time spending with all of my colleagues and friends and appreciate their great help. My family has always been there for me. Their unqualified love and support have been accompanying me throughout the journey. I am truly grateful to have such a happy and supportive family. vi VITA June 19, 1976 . Born - Shanxi, China 1993-1997 . B.S. Computer Science Peking University, China 1997-2000 . M.E. Computer Science Chinese Academy of Sciences, China 2000-2001 . Graduate Teaching Associate The Ohio State University 2001-2005 . Graduate Research Associate The Ohio State University 2005-present . Graduate Teaching Associate The Ohio State University PUBLICATIONS Research Publications G. Ji and H-W. Shen. Dynamic View Selection for Time-Varying Volumes. Technical report OSU-CISRC-5/06-TR50, The Ohio State University G. Ji and H-W. Shen. Feature Tracking Using Earth Mover’s Distance and Global Optimization. Technical report OSU-CISRC-5/06-TR49, The Ohio State University G. Ji and H-W. Shen. Time-Varying Isosurface Tracking by Global Optimization. Tech- nical report OSU-CISRC-2/05-TR12, The Ohio State University, 2005 G. Ji and H-W. Shen. Efficient Isosurface Tracking Using Precomputed Correspondence Table. In Joint Eurographics - IEEE TCVG Symposium on Visualization 2004, pages 283–292, 2004. vii G. Ji, H-W. Shen, and R. Wenger. Volume Tracking Using Higher Dimensional Isosur- facing. In Proceedings of IEEE Visualization 2003, pages 209–216, 2003. G. Ji, H-W. Shen and J. Gao. Interactive Exploration of Remote Isosurfaces with Point- Based Non-Photorealistic Rendering. Technical report OSU-CISRC-7/03-TR37, The Ohio State University FIELDS OF STUDY Major Field: Computer Science and Engineering viii TABLE OF CONTENTS Page Abstract . ii Dedication . iv Acknowledgments . v Vita . vii List of Tables . xii List of Figures . xiii Chapters: 1. Introduction . 1 1.1 Problem Statement . 1 1.2 Challenges . 3 1.3 Strategies and Contributions . 5 1.4 Organization . 10 2. Related Work . 12 2.1 Feature Tracking . 12 2.1.1 Aggregate Attribute Based Methods . 12 2.1.2 Volume Overlapping Based Methods . 14 2.2 View Selection . 17 2.2.1 Static View Selection . 17 2.2.2 Dynamic View Selection . 19 ix 3. Volume Tracking Using Higher Dimensional Isosurfacing . 21 3.1 Overview . 21 3.2 Isosurface Tracking . 21 3.2.1 Extracting Overlapping Time-varying Isosurfaces . 22 3.2.2 Verification . 27 3.3 Interval Volume Tracking . 29 3.3.1 Extracting Overlapping Time-Varying Interval Volumes . 29 3.3.2 Verification . 34 3.4 Results . 34 3.5 Summary . 37 4. Efficient Isosurface Tracking Using Precomputed Correspondence Table . 43 4.1 Overview . 43 4.2 Isosurface Tracking . 44 4.2.1 Tracking by Using Higher Dimensional Isosurfacing . 44 4.2.2 Generation of the Correspondence Lookup Table . 45 4.2.3 Optimization in Generation of the Correspondence Table . 54 4.2.4 Isosurface Tracking Using Correspondence Lookup Table . 55 4.3 Results . 56 4.4 Summary . 62 5. Feature Tracking Using Earth Mover’s Distance and Global Optimization . 65 5.1 Overview . 65 5.2 Using Earth Mover’s Distance as Matching Cost . 68 5.2.1 Earth Mover’s Distance . 71 5.2.2 Efficient EMD Computation . 73 5.3 Global Optimization Based on Branch-and-Bound . 75 5.3.1 The Search Tree . 75 5.3.2 Branch and Bound . 78 5.3.3 Further Speedup by a Good Estimation of the Minimal Cost . 80 5.3.4 Using EMD to Identify Compound Component Candidates . 81 5.4 Results . 83 5.5 Summary . 88 6. Dynamic View Selection for Time-Varying Volumes . 89 6.1 Overview . 89 6.2 Static View Selection . 90 x 6.2.1 Measurement of Opacity Distribution and Projection Size . 91 6.2.2 Measurement of Color Distribution . 93 6.2.3 Measurement of Curvature Information . 96 6.2.4 The Final Utility Function . 97 6.3 Dynamic View Selection . 98 6.3.1 Time-Varying View Selection . 99 6.3.2 Viewing Path Between any Two Views in a Given Timestep . 103 6.4 Results . 105 6.5 Summary . 109 7. Conclusions and Future Work . 117 Bibliography . 120 xi LIST OF TABLES Table Page 3.1 The time to track the isosurface component illustrated in Figure 3.5 (in seconds). 36 3.2 The time to track interval volume components illustrated in Figure 3.6 (in seconds). 37 4.1 The time to track the whole isosurface illustrated in figure 4.5 (in sec- onds). Timing from 5 time steps are shown due to space limitation. 58 4.2 The time to track two isosurface components illustrated in figure 4.6 (in seconds). Timing from time step 4, 9, 15 and 21 are shown due to space limitation. 59 4.3 The time to track two isosurface components illustrated in figure 4.7 (in seconds). Timing from time step 1, 2, 6, 7 and 14 are shown due to space limitation. 60 4.4 The comparison between two methods to generate the correspondence lookup table. 61 5.1 The timing (in seconds) for the case in figure 5.8. 86 3 6 11 5.2 The EMD values for F0 , F0 and F0 .
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