Discrete Hidden Markov Models with Application to Isolated User- V T T P U B L I C a T I O N S Dependent Hand Gesture Recognition
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ISSN 1455–0849 (URL: http://www.inf.vtt.fi/pdf/) TECHNICAL RESEARCH CENTRE OF FINLAND ESPOO 2001 VTT PUBLICATIONS 449 Discrete hidden Markov models with application to isolated user-dependent hand gesture recognition Vesa-Matti Mäntylä VTT Electronics TECHNICAL RESEARCH CENTRE OF FINLAND ESPOO 2001 ISBN 951–38–5875–8 (soft back ed.) ISSN 1235–0621 (soft back ed.) ISBN 951–38–5876–6 (URL:http://www.inf.vtt.fi/pdf/) ISSN 1455–0849 (URL:http://www.inf.vtt.fi/pdf/ ) Copyright © Valtion teknillinen tutkimuskeskus (VTT) 2001 JULKAISIJA – UTGIVARE – PUBLISHER Valtion teknillinen tutkimuskeskus (VTT), Vuorimiehentie 5, PL 2000, 02044 VTT puh. vaihde (09) 4561, faksi (09) 456 4374 Statens tekniska forskningscentral (VTT), Bergsmansvägen 5, PB 2000, 02044 VTT tel. växel (09) 4561, fax (09) 456 4374 Technical Research Centre of Finland (VTT), Vuorimiehentie 5, P.O.Box 2000, FIN–02044 VTT, Finland phone internat. + 358 9 4561, fax + 358 9 456 4374 VTT Elektroniikka, Verkkoteknologiat, Kaitoväylä 1, PL 1100, 90571 OULU puh. vaihde (08) 551 2111, faksi (08) 551 2320 VTT Elektronik, Nätteknologier, Kaitoväylä 1, PB 1100, 90571 ULEÅBORG tel. växel (08) 551 2111, fax (08) 551 2320 VTT Electronics, Networking Research, Kaitoväylä 1, P.O.Box 1100, FIN–90571 OULU, Finland phone internat. + 358 8 551 2111, fax + 358 8 551 2320 Otamedia Oy, Espoo 2001 Mäntylä, Vesa-Matti. Discrete hidden Markov models with application to isolated user-dependent hand gesture recognition. Espoo 2001. Technical Research Centre of Finland, VTT Publications 449. 104 p. Keywords discrete hidden Markov models, hand gesture recognition, stochastic processes, discrete Markov chains, Bayes classification Abstract The development of computers and the theory of doubly stochastic processes, have led to a wide variety of applications of the hidden Markov models (HMMs). Due to their computational efficiency, discrete HMMs are often favoured. HMMs offer a flexible way of presenting events with temporal and dynamical variations. Both of these matters are present in hand gestures, which are of increasing interest in the research of human-computer interaction (HCI) technologies. The exploitation of human-to-human communication modalities has become actual in HCI applications. It is even expected, that the existing HCI techniques become a bottleneck in the effective utilization of the available information flow. In this work it is given mathematically uniform presentation of the theory of discrete hidden Markov models. Especially, three basic problems, scoring, decoding and estimation, are considered. To solve these problems it is presented forward and backward algorithms, Viterbi algorithm, and Baum-Welch algorithms, respectively. The second purpose of this work is to present an application of discrete HMMs to recognize a collection of hand gestures from measured acceleration signals. In pattern recognition terms, it is created an isolated user-dependent recognition system. In the light of recognition results, the effect of several matters to the optimality of the recognizer is analyzed. 3 Preface The main ideas for this thesis have been induced by the work done in the Networking Research area of VTT Electronics, during last two years. This work has been submitted to the University of Oulu, Faculty of Natural Sci- ences, as part of the qualiﬁcation for the degree of Licenciate of Philosophy. I want to express my gratitude to VTT Electronics for making possible the research and writing processes. Special thanks to Tapio Peltola, who has given valuable help concerning the theory of hidden Markov models and especially their practical implementa- tion. I would also like to thank Prof. Tapio Sepp¨anen, from the University of Oulu, for the valuable discussions about pattern recognition matters con- cerning the development of the recognition system. During the research and writing processes Esa Tuulari, Pekka Ruuska and Tapio Frantti have given encouraging comments, also. For this, special thanks to them. I would like to thank the supervisors of this thesis, PhD Erkki Laitinen from the Department of Mathematical Sciences of the University of Oulu and Prof. Petri M¨ah¨onen from VTT Electronics, for their valuable comments on writing this thesis. This work has been funded partially by Tekes, Technical Development Cen- tre Finland in the scope of the ITEA 99002 BEYOND project. In this con- nection, I want to express thanks to Mikko Kerttula. Oulu, August 2000 Vesa-Matti M¨antyl¨a 4 Contents Abstract 3 Preface 4 1 Introduction 7 1.1 Historical perspective . ................. 7 1.2 Motivation of hand gesture recognition . .......... 8 1.3 Pattern recognition concepts . .......... 9 1.4 Scopes of the research . ................. 11 2 Stochastic processes and discrete Markov chains 13 2.1 Probabilistic prerequisites . ................. 13 2.2 Markov chains ........................ 17 3 Discrete hidden Markov models 35 3.1 Formal deﬁnition and three basic problems . 35 3.2 Auxiliary properties of the conditional distributions . 39 3.3 Evaluation problem and forward-backward algorithm . 41 3.4 Decoding with smoothing and the Viterbi algorithm . 46 3.5 Parameter estimation and Baum-Welch algorithm . 54 3.6 Reestimates in forward and backward variables . 61 3.7 Implementation issues for HMMs . .......... 70 3.7.1 Scaling . ................. 70 3.7.2 Multiple observation sequences .......... 71 5 4 Bayes classiﬁcation and context-dependency 73 5 HMM recognition system 77 5.1 Measurements ........................ 77 5.2 Preprocessing ........................ 78 5.3 Feature extraction . ................. 78 5.4 Vector quantization . ................. 81 5.5 Choice of the model parameters . .......... 83 5.6 Implementation . ................. 84 6 Results 86 7 Conclusions 96 References 100 6 1 Introduction 1.1 Historical perspective The roots of the theory of the hidden Markov models (HMMs) can be traced to the 1950s, when statisticians were studying the problem of characteriz- ing random processes for which the incomplete observations were avail- able.