Prof. Tziritas for his numerous stimulating conversations, ideas, advising and financial/material supportance. Our excellent collaboration has started since June of 1999, supervising me during my diploma thesis (1999)(2000)(2001), my master thesis (2001)(2002)(2003) and my PhD thesis (2003)(2004)(2005)(2006)(2007). Throughout all my years (8 years) at the lab, Prof. Tziritas has always been a reference of dedication. Moreover, I am grateful to Prof. Tziritas for giving me the freedom to choose and explore different directions of research and for helping me to acquire my research style.I would like to express my gratitude to the members of my doctoral committee. Many thanks to Prof. Panos Trahanias and Assoc. Prof. Yannis Stylianou for useful remarks, advices and ideas during the thesis. Many thanks also to Assist. Prof. George Georgakopoulos for the numerous stimulating conversations and fruitful collaboration on the curve equipartition problem. I would like to thank Prof. Denis Pellerin for the excellent collaboration on human motion analysis, useful conversations and for the grateful hospitality during my visiting in Grenoble. Many thanks to thank Prof. Sergios Theodoridis for useful remarks and traveling to Heraklion to participate for my thesis defence. I 'd like to thank Prof. Lydia Kavraki for useful remarks and interesting ideas about possible applications and future work. In this paragraph, I would like to thank my real friend and excellent contributor, Emmanuel Ramasso (PhD, GIPSA-lab, Grenoble). Our PhDs have allowed a fruitful collaboration on human motion analysis during year 2004-2007 in SIMILAR framework. We have been involved in the SIMILAR PhD exchanges. I visited GIPSA-lab on January of 2006, while Emmanuel visited UOC on May of 2006. Special thanks go to Sylvie (wife of Emmanuel) for grateful hospitality. You are always invited to visit us in Crete. Moreover, I am grateful to Prof. Michele Rombaut, for the excellent iii hospitality, collaboration and useful discussions. Our work received the Sponsor Award for the most suitable work for commercialization on Intern. Conf. on Articulated Motion and Deformable Objects 2006 [1] and promises more results in the future, since we continue collaboration and research. Special thanks go to Ilias Grinias, to Assist. Prof. Anastasios Doulamis and to Prof. Paris Pamfilos for the many fruitful discussions and ideas. I would also like to thank my colleges (Antonis Papadogianakis, Nikos Komodakis, Panagiotis Koutsourakis, Giannis Augouleas and Giannis Polioudakis) at the Lab for the friendly atmosphere and the useful discussions that have greatly influenced this work.I also would like to thank, Assist. Prof. Eleni Kokkinou and Charis Papadakis for taking the time for proofreading, in spite of all other pressing activities.Last but not least, special thanks to my parents Manolis and Afroditi, my friends and especially my fiancee Maria for their constant support, encouragement and infinite patience.