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Geometric Primitive Feature Extraction – Concepts, Algorithms, and Applications

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Geometric Primitive Feature Extraction – Concepts, Algorithms, and Applications GEOMETRIC PRIMITIVE FEATURE EXTRACTION – CONCEPTS, ALGORITHMS, AND APPLICATIONS DILIP KUMAR PRASAD School of Computer Engineering A Thesis submitted to the Nanyang Technological University in fulfillment of the requirement for the degree of Doctor of Philosophy 2012 Abstract This thesis presents important insights and concepts related to the topic of the extraction of geometric primitives from the edge contours of digital images. Three specific problems related to this topic have been studied, viz., polygonal approximation of digital curves, tangent estimation of digital curves, and ellipse fitting anddetection from digital curves. For the problem of polygonal approximation, two fundamental problems have been addressed. First, the nature of the performance evaluation metrics in relation to the local and global fitting characteristics has been studied. Second, an explicit error bound of the error introduced by digitizing a continuous line segment has been derived and used to propose a generic non-heuristic parameter independent framework which can be used in several dominant point detection methods. For the problem of tangent estimation for digital curves, a simple method of tangent estimation has been proposed. It is shown that the method has a definite upper bound of the error for conic digital curves. It has been shown that the method performs better than almost all (seventy two) existing tangent estimation methods for conic as well as several non-conic digital curves. For the problem of fitting ellipses on digital curves, a geometric distance minimization model has been considered. An unconstrained, linear, non- iterative, and numerically stable ellipse fitting method has been proposed and it has been shown that the proposed method has better selectivity for elliptic digital curves (high true positive and low false positive) as compared to several other ellipse fitting methods. For the problem of detecting ellipses in a set of digital curves, several innovative and fast pre- processing, grouping, and hypotheses evaluation concepts applicable for digital curves have been proposed and combined to form an ellipse detection method. Performance of the proposed ellipse detection method is better than several recent ellipse detection methods and close to the ideal case. All algorithms presented in this thesis have been developed using detailed mathematical analysis of the discrete geometry involved. The validity of these methods has been verified using rigorous mathematical analysis, numerical experiments in various difficult scenario, and extensive testing on large image datasets of practical importance. The utility of these algorithms has been shown using three practical applications related to image processing for robotics, medical image processing, and object and face detection. i Acknowledgements कमणयर् ेवािधकारते मा फलेष ु कदाचन। मा कमफलहर् ेतुभूमार् र् ते सङ्गोऽवकमिण।र् “Yours is the right to perform, not the right to expect (the fruits of your actions). Do not let the fruit be the purpose of your actions. By being driven by the fruits of your actions, do not lead yourself to inaction.” -Bhagvad Gita (Chapter 2.47) In this proud moment of my life, when I am writing the acknowledgement for my PhD dissertation, I pay my respects first to all the wise people in my life like my parents, my teachers, and the Bhagvad Gita for reiterating the above quote time and again in my life. I pay my humble respects to my teachers. Specifically, I recall the teachers who left indelible marks in my life: my parents, my elder sister Kaushalya, Master Ji, Ratan Maharaj (little monk) from Ramakrishna Ashram, Mrs. Gopa Gupta, Mrs. Tapati Das, Mrs. S. Mukherjee, Mr. Lal Bahadur Shastri, Dr. Subrata Bose, Mr. Arup Pal, Dr. Munindra Prakash, Dr. A Chattopadhayay, Dr. D.P Mukherjee, Dr. Maylor K.H. Leung, Dr. Janusz Starzyk, Dr. Wendy Torrance, and Dr. Chai Quek (in the chronological order of their first impact in my life). Life is a great teacher, and I salute to the provider of life and my little Ganesha. I especially thank Mrs. Gopa Gupta, Dr. Subrata Bose, Mr. Girish Mishra, Dr. Janusz Starzyk, Dr. Wendy Torrance, Dr. Maylor Leung, and Dr. Chai Quek, for mentoring a vagabond and stubborn person as me. I am very grateful to Dr. Maylor Leung for giving me the independence to pursue independent research on the topic of discrete geometry and for scrutinizing several lengthy derivations very patiently and persistently. I respect his philosophy of never compromising on the quality of work and this has motivated me to keep high expectation from myself in terms of the quality of work. I take this opportunity to thank Nanyang Technological University and Ministry of Education, Singapore for providing me with the necessary infrastructure and funding for my doctoral studies. I thank Dr. Jiang Xudong, Dr. Chai Quek, Dr. Wolfgang Mueller, Dr. Janusz Starzyk, Dr. Philip Fu, and Dr. Mao Kezhi for conducting exceptional graduate modules. I thank Centre of Life Sciences, National University of Singapore for allowing me to fulfill my ii desire to acquire more knowledge about the field of Neuroscience. I thank Dr. Dale Purves, Dr. George Augustine, Dr. Shih-Cheng Yen, Dr. Thorsten Wohland, Dr. Ji Hui,Dr. Soong Tuck Wah, Dr. Antonius VanDongen, Dr. Marc Fivaz, Dr. Hongyan Wang, Dr. Fengwei Yu, Dr. Eyleen Goh, and Dr. Suresh Jesuthasan for conducting the post graduate modules on Vision and Perception, Neuronal Signaling, Developmental Neurobiology and Neurological and Behavioural Disorder and making me an active participant of these modules. I thank Dr. Janusz Starzyk and Dr. Krishna Agarwal for being a constant source of inspiration for me. I thank Dr. Siu-Yeung Cho and Mrs. Christina Lee for providing me with a good and hassle- free laboratory environment. I had the privilege of having great friends in my life, who make the life a rich and happy experience. I begin with the friends who helped me directly or indirectly with my doctoral studies. I thank Dr. Krishna Agarwal for motivating and helping me to join the doctoral program. I thank Dr. Raj Gupta, Deepak Subramanian, Dr. Ashis Mallick, and Dr. Ranjan Das for being and remaining very good friends in odd and even times. Other friends in my research lab, who deserve special mention, are Dr. Tang Chaoying, Dr. Hengyi Zhang, Dr. Atiqur Rahman, Dr. Pravin Kakar, and Ha Thanh. My Ph.D. life would not have been as much fun without Melanie, Sulley Goh, Ngyuen Chi, Dr. Balaji Gokulan, Dr. Dwarikanath Mohapatra, Mimi, Kabita bhabhi, and fellow ISMites (Abhishek Seth, Dr. Amit Sachan, Dr. Amit Singh, Arpita Singh, Kushal Anand, Dr. A.V. Subramanyam, Dr. Alok Prakash, and Neha Tripathi) in Singapore. I also thank my friends and ex-colleagues, who are too many to count. In a non-exclusive list, I mention Vijay, Abhishek Awasthi, Srikanth, Pillai, Sridhar, Ramesh Babu, Atul Jha, Chandrashekar, Vineet Singh, Himanshu Pati, Kambli, Ashu, Dubi, and Kuseswar Prasad. I recall fondly Sanju, Sunita, Nupur, Loet, Erik, David Gernaat, Leila, and others. My start-up team Bharti, Prashant, Dishant, and Mohit Bansal understood my commitment towards my thesis and supported me throughout last 2 years. I am thankful to them too. I thank the 20 volunteers who participated in the generation of ground truth for section 6.1. They are Dr. A.V. Subramanyam, Dr. Alok Prakash, Dr. Amit Sachan, Dr. Amit Singh, Dr. Atiqur Rahman, Dr. Balaji Gokulan, Dr. Dwarikanath Mohapatra, Dr. Hengyi Zhang, Dr. Krishna Agarwal, Dr. Raj Kumar Gupta, Abhishek Seth, Deepak Subramanian, Kushal Anand, Neha Tripathi, Ngyuen Chi, K. Prasad Sir, Dr. Manish Narwaria, Bharti, Prashant, and Dishant. iii I acknowledge the support received from Dr. Alex Chia during my first month of Ph.D. and providing me with his insight about the problem of ellipse detection and sharing his source code for generating synthetic data for ellipse detection experiment. I acknowledge Dr. P. Kovesi, Dr. F. Mai, Dr. A. Opelt, Dr. R McLaughlin, Dr. Partha Bhowmick, and Dr. J.-O. Lachaud for sharing their insights or source code or executables for generating the results of their methods. I convey love and gratitude to my sisters, Kaushalya and Sangita for keeping me on track of my studies right from childhood. I would like to give special thanks to each and every person of my neighborhood during my childhood who indirectly took special care of me by protecting me from all the evil things and negative influences around me. I would like to thank my best friend Bhaskar and teenage friends Deepak, Narayan, Sulendra, Rajendra, Subodh, Mantu, Pintu, Bablu, Shankar da, Dadu, and others for protecting me from wrong and dark career paths. I like to thank Deepika for being indirect source of inspiration to study harder during senior school days. I thank Kaushalya Gupta and Sangita Gupta for taking care of my family in the difficult times and ensuring that my parents do not miss my presence. I fall short of words when trying to acknowledge my loving wife, Krishna. She has excelled and helped me in every possible way to pursue my study. I dedicate this important document of my life to my family and everyone related to me directly or indirectly in my life. My achievements are collective efforts of each and everyone in my life. I hope that this thesis will inspire a few future researchers to understand and tap the potential of discrete geometry in image processing applications. Dilip Prasad iv Table of contents Abstract ......................................................................................................................................
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