Stony Brook University The official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. ©©© AAAllllll RRRiiiggghhhtttsss RRReeessseeerrrvvveeeddd bbbyyy AAAuuuttthhhooorrr... Stony Brook University The official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. ©©© AAAllllll RRRiiiggghhhtttsss RRReeessseeerrrvvveeeddd bbbyyy AAAuuuttthhhooorrr... 3-D Shape Measurement Based on Fourier Transform and Phase Shifting Method A Dissertation Presented by Hong Guo to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mechanical Engineering Stony Brook University December 2009 Stony Brook University The Graduate School Hong Guo We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation. Dr. Peisen S. Huang – Dissertation Advisor Professor, Department of Mechanical Engineering Dr. Fu-pen Chiang – Chairperson of Defense Professor, Department of Mechanical Engineering Dr. Yu Zhou Assistant Professor, Department of Mechanical Engineering Dr. Hong Qin Professor of Computer Science, Department of Computer Science of Stony Brook University This dissertation is accepted by the Graduate School. Lawrence Martin Dean of the Graduate School ii Abstract of the Dissertation 3-D Shape Measurement Based on Fourier Transform and Phase Shifting Method by Hong Guo Doctor of Philosophy in Mechanical Engineering Stony Brook University 2009 Phase shifting method and the Fourier transform method are both fringe analysis methods. This dissertation research focuses on uti- lizing these two methods to extract 3-D shape information encoded in fringe patterns obtained from digital fringe projection tech- nique and shadow moir´e technique respectively. A modified Fourier transform method is developed for real-time 3-D shape measure- ment of dynamic objects based on the digital fringe projection technique. A phase shifting scheme is developed for the shadow moir´e technique in effort to improve its resolution and accuracy. A novel face recognition method is proposed, which employs phase shifting method and the Fourier transform method to obtain an efficient spectral representation of 3-D face. Digital fringe projection technique is a full-field, high-resolution, and high-speed 3-D shape measurement method. Real-time fringe pattern acquisition, processing, and 3-D display by use of 3-step phase shifting method has been previously achieved on a high- speed digital fringe projection system. However, measurement of iii fast moving or changing objects remains difficult in that at least three fringe patterns taken over time are required. Although the Fourier transform method only needs one frame of fringe pattern, the measurement quality is limited when objects with complex shapes are measured. In this research, a modified Fourier method is proposed, which aims at measuring dynamic objects with com- plex shapes. The basic idea is to acquire a flat image in addi- tion to a fringe image, which provides necessary information for overcoming the shortcomings of the conventional Fourier trans- form method. Two fringe projection schemes are proposed and compared. The experimental results demonstrated that the pro- posed method can be used for real-time 3-D shape measurement of complex shapes, and improved measurement quality over 3-step phase shifting method is achieved. Shadow moir´e is a traditional full-field optical 3-D shape measure- ment technique. By combining phase shifting method with shadow moir´e technique, the resolution of the measurement can be greatly improved. Various phase shifting schemes have been previously proposed. However, none of them provides exact close-form phase solution for the phase shifting shadow moir´e. In this research, we provide an elegant exact solution for phase shifting shadow moir´e. Four phase-shifted fringe patterns are obtained by translating the grating vertically in equal steps. The Carr´e algorithm is applied to the phase-shifted fringe patterns to obtain an exact close-form phase solution. Simulation and experimental results verified the proposed method. Face recognition is an intuitive and promising human biometrics method. 2-D and 3-D face recognition methods have been exten- sively studied. However, the performance of 2-D methods is greatly influenced by facial texture and illumination variations. 3-D meth- ods require reconstruction of the 3-D face geometry which results in high computation and storage expenses. In this research, a face recognition method is proposed, which employs a spectral represen- tation of 3-D face to perform face recognition without 3-D recon- struction. A high-speed digital fringe projection system captures three phase-shifted fringe patterns of a face. 3-step phase shifting method and the Fourier transform method are applied to face fringe patterns to remove facial texture and illumination variations and extract spectra related to the 3-D shape of the face. The eigenface algorithm is employed to analyze the face spectra database and iv recognize the identity of the unknown face. The experimental and simulation results demonstrated promising recognition rates with reduced computation and storage expenses. v Dedicated to My Family Contents List of Figures x List of Tables xiii Acknowledgements xiv 1 Introduction 1 1.1 Overview of 3-D Shape Measurement Technology . . . . . . . 2 1.1.1 Laser triangulation . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Time-of-flight . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.3 Stereo vision . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.4 Coded pattern projection . . . . . . . . . . . . . . . . . 3 1.1.5 Interferometry . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.6 Moir´e method . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.7 Digital fringe projection . . . . . . . . . . . . . . . . . 5 1.2 Motivation and Objective . . . . . . . . . . . . . . . . . . . . 7 1.2.1 3-D shape measurement of dynamic objects . . . . . . 7 1.2.2 Phase shifting shadow moir´e . . . . . . . . . . . . . . . 8 1.2.3 3-D human face recognition . . . . . . . . . . . . . . . 8 1.2.4 Research objectives . . . . . . . . . . . . . . . . . . . . 9 1.3 Dissertation Structure . . . . . . . . . . . . . . . . . . . . . . 10 2 Modified Fourier Transform Method for Real-time 3-D Shape Measurement 12 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.1 Principle of the Fourier transformed method . . . . . . 13 2.1.2 Related work . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Modified Fourier Transform Method . . . . . . . . . . . . . . . 18 2.2.1 Flat pattern + fringe pattern . . . . . . . . . . . . . . 19 2.2.2 Three phase-shifted fringe patterns . . . . . . . . . . . 19 2.2.3 Binary mask generation . . . . . . . . . . . . . . . . . 23 vii 2.2.4 Spectral leakage reduction . . . . . . . . . . . . . . . . 23 2.3 Phase Unwrapping . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.1 Quality index . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.2 Quality-guided path following . . . . . . . . . . . . . . 28 2.4 Absolute Phase Retrieval . . . . . . . . . . . . . . . . . . . . . 32 2.4.1 Marker detection . . . . . . . . . . . . . . . . . . . . . 32 2.4.2 Marker removal . . . . . . . . . . . . . . . . . . . . . . 34 2.5 3-D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 Software Implementation . . . . . . . . . . . . . . . . . . . . . 36 2.7 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 36 2.7.1 Projector grayscale calibration . . . . . . . . . . . . . . 37 2.7.2 Measurement of still object with complex shape . . . . 39 2.7.3 Measurement of moving object and changing face sequence 40 2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3 Phase Shifting Shadow Moir´e by use of Carr´e Algo- rithm 44 3.1 Introduction to Phase Shifting Shadow Moir´e Technique . . . 44 3.1.1 Principle of shadow moir´e technique . . . . . . . . . . . 44 3.1.2 Phase shifting algorithms for fringe analysis . . . . . . 47 3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.3 Grating Pattern Removal . . . . . . . . . . . . . . . . . . . . . 49 3.4 Phase Shifting Scheme and Carr´e Algorithm . . . . . . . . . . 52 3.4.1 Phase shifting scheme . . . . . . . . . . . . . . . . . . 52 3.4.2 Carr´e algorithm . . . . . . . . . . . . . . . . . . . . . . 53 3.4.3 Phase unwrapping . . . . . . . . . . . . . . . . . . . . 54 3.5 3-D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 54 3.6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 55 3.7 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 59 3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4 Face Recognition Based on Fringe Pattern Analysis 65 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2 Background and Related Work . . . . . . . . . . . . . . . . . . 66 4.3 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3.1 Digital fringe projection system . . . . . . . . . . . . . 68 4.3.2 Texture and illumination removal . . . . . . . . . . . . 68 4.3.3 Fourier spectra of fringe image . . . . . . . . . . . . . . 71 4.4 Face Image Normalization . . . . . . . . . . . . . . . . . . . . 73 4.5 Principal Component Analysis of the Fourier Spectra . . . . . 74 4.6 Experiments and Simulation . . . . . . . . . . . . . . . . . . . 74 viii