Spherical Mosaic Construction Using Physical Analogy for Consistent Image Alignment
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Spherical Mosaic Construction using Physical Analogy for Consistent Image Alignment by Manuel Guillén Gonzalez Thesis submitted to the University of Central Lancashire in partial fulfilment of the requirements for the degree of Doctor of Philosophy October 1999 The work presented in this thesis was carried out in the Department of Engineering and Product Design at the University of Central Lancashire, Preston, U.K. Declaration I declare that while registered with the University of Central Lancashire for the degree of Doctor of Philosophy I have not been a registered candidate or enrolled student for another award of the University of Central Lancashire or any other academic or professional institution during the research programme. No portion of the work referred to in this thesis has been submitted in support of any application for another degree or qualification of any other University or Institution of learning. Signed ........... To my parents and to Reyes Acknowledgements I would like to thank my director of studies Dr. Phil Holifield and my second supervisor Dr. Martin Varley for their encouragement and guidance through all stages of this project. I am grateful to Professor Trevor J. Terrell for his support and faith in me in the early stages of the project. I would like to thank Dr. Martyn Shaw for his help with VRML. The support of the University of Central Lancashire to this research project is gratefully acknowledged, and particularly that of the staff in the Department of Engineering and Product Design. I thank God for everything He does in my life, particularly for making this work possible. Abstract The research contained in this thesis is an investigation into mosaic construction. Mosaic techniques are used to obtain images with a large field of view by assembling a sequence of smaller individual overlapping images. In existing methods of mosaic construction only successive images are aligned. Accumulation of small alignment errors occur, and in the case of the image path returning to a previous position in the mosaic, a significant mismatch between non- consecutive images will result (looping path problem). A new method for consistently aligning all the images in a mosaic is proposed in this thesis. This is achieved by distribution of the small alignment errors. Each image is allowed to modify its position relative to its neighbour images in the mosaic by a small amount with respect to the computed registration. Two images recorded by a rotating ideal camera are related by the same transformation that relates the camera's sensor plane at the time the images were captured. When two images overlap, the intensity values in both images coincide through the intersection line of the sensor planes. This intersection line has the property that the images can be seamlessly joined through that line. An analogy between the images and the physical world is proposed to solve the looping path problem. The images correspond to rigid objects, and these are linked with forces which pull them towards the right positions with respect to their neighbours. That is, every pair of overlapping images are "hinged" through their corresponding intersection line. Aided by another constraint named the spherical constraint, this network of self- organising images has the ability of distributing itself on the surface of a sphere. As a direct result of the new concepts developed in this research work, spherical mosaics (i.e. mosaics with unlimited horizontal and vertical field of view) can be created. Contents Abstract I CHAPTER 1 INTRODUCTION 1 1.1 Background I 1.2 Aim of the Research 5 1.3 Overview of the Thesis 5 CHAPTER 2 IMAGE ACQUISITION 7 2.1 Introduction 7 2.2 Conventional Camera Technology 7 2.2.1 Image Sensor 7 2.2.2 Field of View and Focal Length 8 2.2.3 Lens Aperture 8 2.2.4 Depth of Field 9 2.2.5 Shutter Speed 10 2.2.6 Video Fields 10 2.2.7 Automatic Gain Control (AGC) 11 2.2.8 Lens Distortion 11 2.2.9 The Ideal Camera 12 2.2.10 The Human Eye 13 2.3 Special Devices for Panoramic Image Acquisition 13 2.3.1 Panoramic Cameras 13 2.3.2 Omnidirectional Cameras 14 2.3.3 Non-frontal Imaging Camera 15 2.4 Summary 16 CHAPTER 3 MOSAIC CONSTRUCFION 17 3.1 Introduction 17 3.2 Image Registration 17 3.2.1 Transformation Models 18 Ii 3.2.2 Camera Motion 20 3.2.3 Image Registration Techniques 23 3.2.3.1 Feature Space 23 3.2.3.2 Similarity Measure 23 3.2.3.3 Search Space 24 3.2.3.4 Search Strategy 24 3.2.4 Unwanted Elements 26 3.2.4.1 Motion Parallax 26 3.2.4.2 Lens Distortion 26 3.2.4.3 Moving Objects 27 3.2.4.4 Motion Blur 28 3.3 Image Integration 28 3.3.1 Image Blending 28 3.4 Voronoi Diagrams and Delaunay Triangulation 30 3.5 Summary 34 CHAPTER 4 THE LOOPING PATH PROBLEM AND PROPOSED SOLUTION 35 4.1 Introduction 35 4.2 Previous Approaches 36 4.2.1 Registering New Image with Current Mosaic 37 4.2.2 Registering Sub-mosaics 37 4.2.3 Distribution of the Error 37 4.2.4 Simultaneous Registration of All Images 38 4.3 Proposed Solution to the Looping Path Problem 39 4.4 Minimisation using Physical Simulation 42 4.4.1 Why Physical Simulation? 43 4.4.2 Physical Simulation 44 4.4.2.1 The Rigid Body 44 4.4.2.2 Coordinate Systems 44 4.4.2.3 Linear Equations of Motion 46 4.4.2.4 Angular Equations of Motion 47 4.4.2.5 Simulation Engine 48 4.4.2.6 Forces 49 4.4.2.7 Euler's Integration Method 49 U' 4.4.2.8 Midpoint and Runge-Kutta Integration Methods 52 4.4.3 Physical Model for the Images 54 4.4.4 The Hinge Constraint 55 4.4.5 Stability and Convergence of Image System 58 4.4.5.1 Spring-Mass System 58 4.4.5.2 Damped Spring-Mass System 60 4.4.5.3 Image System - 65 4.4.5.4 Example 68 4.5 Summary 70 CHAPTER 5 PLANAR SCENE MOSAIC 71 5.1 Introduction 71 5.2 Image Acquisition 71 5.3 Implementation of Image Registration 73 5.3.1 Transformation Model 73 5.3.2 Feature Space 74 5.3.3 Similarity Measure 75 5.3.4 Search Space 77 5.3.5 Search Strategy 77 5.3.5.1 Hierarchical Pyramids 78 5.3.5.2 Rotation 80 5.3.5.3 Image Registration with Progressive Complexity Models 81 5.3.5.4 Subpixel Accuracy 84 5.4 Physical Model for the Planar Mosaic 85 5.5 Image Integration 86 5.6 Experimental Results on Document Mosaic 86 5.7 Summary 93 CHAPTER 6 SPHERICAL MOSAIC 94 6.1 Introduction 94 6.2 Image Registration Considerations 94 6.3 Partial Spherical Mosaic Mapped to a Plane 95 6.3.1 Image Acquisition 95 6.3.2 Physical Model for Image Alignment 96 iv 6.3.3 Image Integration 97 6.3.4 Results 97 6.3.5 Summary 99 6.4 Double Band Panoramic Mosaic 99 6.4.1 Image Acquisition 100 6.4.2 Physical Model for Image Alignment 101 6.4.2.1 The Spherical Constraint 103 6.4.2.2 The Same Plane Constraint 107 6.4.2.3 Hinge Parameters 108 6.4.2.4 Effects of Damping on Convergence 109 6.4.2.5 Voronoi Tessellation and Delaunay Diagram on the Sphere 110 6.4.3 Image Integration 110 6.4.4 Results 111 6.5 Full Spherical Mosaic 114 6.5.1 Image Acquisition 114 6.5.2 Physical Model for Image Alignment 115 6.5.3 Image Integration and Display 120 6.5.4 Displaying Results 121 6.6 Summary 122 CHAPTER 7 CONCLUSIONS & FURTHER WORK . 127 7.1 Contributions 127 7.2 Further Work 129 7.3 Summary 131 REFERENCES 132 APPENDIX A CD-ROM 139 APPENDIX B PUBLICATIONS 141 v Chapter 1 Chapter 1 INTRODUCTION 1.1 Background Mosaics are images with a large field of view obtained by assembling two or more individual overlapping images. Historically, the most significant application for image mosaicing is in the development of aerial images [Wolf, 1974] and satellite images [Horii, Oshima and Hirao, 1995], [Milgram, 19751. These mosaics are commonly used as substitutes for maps and also for remote sensing applications. With the arrival of digital photography, new applications for mosaicing were created [Milgram, 1975] [Milgram, 1977] [Peleg, 19811 [Burt and Adelson, 1983a]. The list of applications using mosaic techniques is extensive today, a typical application being the creation of panoramas (images with a 360° horizontal field of view). Mosaics can be useful where the image sensor does not have sufficient pixel resolution to provide a single image with the level of detail needed. The attainable resolution in a mosaic is essentially unlimited [Szeliski, 1994a]. Since the images can be acquired using any optical technology (from microscopy, through hand-held video cameras, to satellite photography), the range or scale of the scene being reconstructed is not an issue. Analogously, the field of view is not a limiting factor in a mosaic. Panoramas have a 3600 horizontal field of view, and full spherical mosaics with an unlimited vertical field of view are also possible. The use of video as a source of images for constructing mosaics has been recently investigated by many researchers [Giaccone, Greenhill and Jones, 1998], [Burt, Hansen and Anandan, 1996], [Irani, Anandan and Hsu, 19951, [Mann and Picard, 1995], [Peleg and Herman, 1997b], [Rousso, Peleg and Finci, 1997b], [Bender, 1993], [Szeliski, I 994b], etc.