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Computer Vision: Algorithms and Applications Richard Szeliski September 3, 2010 draft ©c 2010 Springer This electronic draft is for non-commercial personal use only, and may not be posted or re-distributed in any form. Please refer interested readers to the book’s Web site at http://szeliski.org/Book/.
1 Introduction 1 What is computer vision? • A brief history • Book overview • Sample syllabus • Notation 2 Image formation 29 n^ Geometric primitives and transformations • Photometric image formation • The digital camera 3 Image processing 99 Point operators • Linear filtering • More neighborhood operators • Fourier transforms • Pyramids and wavelets • Geometric transformations • Global optimization 4 Feature detection and matching 205 Points and patches • Edges • Lines 5 Segmentation 267 Active contours • Split and merge • Mean shift and mode finding • Normalized cuts • Graph cuts and energy-based methods 6 Feature-based alignment 309 2D and 3D feature-based alignment • Pose estimation • Geometric intrinsic calibration 7 Structure from motion 343 Triangulation • Two-frame structure from motion • Factorization • Bundle adjustment • Constrained structure and motion
8 Dense motion estimation 381 Translational alignment • Parametric motion • Spline-based motion • Optical flow • Layered motion 9 Image stitching 427 Motion models • Global alignment • Compositing 10 Computational photography 467 Photometric calibration • High dynamic range imaging • Super-resolution and blur removal • Image matting and compositing • Texture analysis and synthesis 11 Stereo correspondence 533 Epipolar geometry • Sparse correspondence • Dense correspondence • Local methods • Global optimization • Multi-view stereo 12 3D reconstruction 577 Shape from X • Active rangefinding • Surface representations • Point-based representations • Volumetric representations • Model-based reconstruction • Recovering texture maps and albedos 13 Image-based rendering 619 View interpolation • Layered depth images • Light fields and Lumigraphs • Environment mattes • Video-based rendering 14 Recognition 655 Object detection • Face recognition • Instance recognition • Category recognition • Context and scene understanding • Recognition databases and test sets
Preface The seeds for this book were first planted in 2001 when Steve Seitz at the University of Wash- ington invited me to co-teach a course called “Computer Vision for Computer Graphics”. At that time, computer vision techniques were increasingly being used in computer graphics to create image-based models of real-world objects, to create visual effects, and to merge real- world imagery using computational photography techniques. Our decision to focus on the applications of computer vision to fun problems such as image stitching and photo-based 3D modeling from personal photos seemed to resonate well with our students. Since that time, a similar syllabus and project-oriented course structure has been used to teach general computer vision courses both at the University of Washington and at Stanford. (The latter was a course I co-taught with David Fleet in 2003.) Similar curricula have been adopted at a number of other universities and also incorporated into more specialized courses on computational photography. (For ideas on how to use this book in your own course, please see Table 1.1 in Section 1.4.) This book also reflects my 20 years’ experience doing computer vision research in corpo- rate research labs, mostly at Digital Equipment Corporation’s Cambridge Research Lab and at Microsoft Research. In pursuing my work, I have mostly focused on problems and solu- tion techniques (algorithms) that have practical real-world applications and that work well in practice. Thus, this book has more emphasis on basic techniques that work under real-world conditions and less on more esoteric mathematics that has intrinsic elegance but less practical applicability. This book is suitable for teaching a senior-level undergraduate course in computer vision to students in both computer science and electrical engineering. I prefer students to have either an image processing or a computer graphics course as a prerequisite so that they can spend less time learning general background mathematics and more time studying computer vision techniques. The book is also suitable for teaching graduate-level courses in computer vision (by delving into the more demanding application and algorithmic areas) and as a gen- eral reference to fundamental techniques and the recent research literature. To this end, I have attempted wherever possible to at least cite the newest research in each sub-field, even if the
viii Computer Vision: Algorithms and Applications (September 3, 2010 draft) technical details are too complex to cover in the book itself. In teaching our courses, we have found it useful for the students to attempt a number of small implementation projects, which often build on one another, in order to get them used to working with real-world images and the challenges that these present. The students are then asked to choose an individual topic for each of their small-group, final projects. (Sometimes these projects even turn into conference papers!) The exercises at the end of each chapter contain numerous suggestions for smaller mid-term projects, as well as more open-ended problems whose solutions are still active research topics. Wherever possible, I encourage students to try their algorithms on their own personal photographs, since this better motivates them, often leads to creative variants on the problems, and better acquaints them with the variety and complexity of real-world imagery. In formulating and solving computer vision problems, I have often found it useful to draw inspiration from three high-level approaches: • Scientific: build detailed models of the image formation process and develop mathe- matical techniques to invert these in order to recover the quantities of interest (where necessary, making simplifying assumption to make the mathematics more tractable). • Statistical: use probabilistic models to quantify the prior likelihood of your unknowns and the noisy measurement processes that produce the input images, then infer the best possible estimates of your desired quantities and analyze their resulting uncertainties. The inference algorithms used are often closely related to the optimization techniques used to invert the (scientific) image formation processes. • Engineering: develop techniques that are simple to describe and implement but that are also known to work well in practice. Test these techniques to understand their limitation and failure modes, as well as their expected computational costs (run-time performance). These three approaches build on each other and are used throughout the book. My personal research and development philosophy (and hence the exercises in the book) have a strong emphasis on testing algorithms. It’s too easy in computer vision to develop an algorithm that does something plausible on a few images rather than something correct. The best way to validate your algorithms is to use a three-part strategy. First, test your algorithm on clean synthetic data, for which the exact results are known. Second, add noise to the data and evaluate how the performance degrades as a function of noise level. Finally, test the algorithm on real-world data, preferably drawn from a wide variety of sources, such as photos found on the Web. Only then can you truly know if your algorithm can deal with real-world complexity, i.e., images that do not fit some simplified model or assumptions.
Preface ix In order to help students in this process, this books comes with a large amount of supple- mentary material, which can be found on the book’s Web site http://szeliski.org/Book. This material, which is described in Appendix C, includes: • pointers to commonly used data sets for the problems, which can be found on the Web • pointers to software libraries, which can help students get started with basic tasks such as reading/writing images or creating and manipulating images • slide sets corresponding to the material covered in this book • a BibTeX bibliography of the papers cited in this book. The latter two resources may be of more interest to instructors and researchers publishing new papers in this field, but they will probably come in handy even with regular students. Some of the software libraries contain implementations of a wide variety of computer vision algorithms, which can enable you to tackle more ambitious projects (with your instructor’s consent). Acknowledgements I would like to gratefully acknowledge all of the people whose passion for research and inquiry as well as encouragement have helped me write this book. Steve Zucker at McGill University first introduced me to computer vision, taught all of his students to question and debate research results and techniques, and encouraged me to pursue a graduate career in this area. Takeo Kanade and Geoff Hinton, my Ph. D. thesis advisors at Carnegie Mellon University, taught me the fundamentals of good research, writing, and presentation. They fired up my interest in visual processing, 3D modeling, and statistical methods, while Larry Matthies introduced me to Kalman filtering and stereo matching. Demetri Terzopoulos was my mentor at my first industrial research job and taught me the ropes of successful publishing. Yvan Leclerc and Pascal Fua, colleagues from my brief in- terlude at SRI International, gave me new perspectives on alternative approaches to computer vision. During my six years of research at Digital Equipment Corporation’s Cambridge Research Lab, I was fortunate to work with a great set of colleagues, including Ingrid Carlbom, Gudrun Klinker, Keith Waters, Richard Weiss, St´ephane Lavall´ee, and Sing Bing Kang, as well as to supervise the first of a long string of outstanding summer interns, including David Tonnesen, Sing Bing Kang, James Coughlan, and Harry Shum. This is also where I began my long-term collaboration with Daniel Scharstein, now at Middlebury College.
x Computer Vision: Algorithms and Applications (September 3, 2010 draft) At Microsoft Research, I’ve had the outstanding fortune to work with some of the world’s best researchers in computer vision and computer graphics, including Michael Cohen, Hugues Hoppe, Stephen Gortler, Steve Shafer, Matthew Turk, Harry Shum, Anandan, Phil Torr, An- tonio Criminisi, Georg Petschnigg, Kentaro Toyama, Ramin Zabih, Shai Avidan, Sing Bing Kang, Matt Uyttendaele, Patrice Simard, Larry Zitnick, Richard Hartley, Simon Winder, Drew Steedly, Chris Pal, Nebojsa Jojic, Patrick Baudisch, Dani Lischinski, Matthew Brown, Simon Baker, Michael Goesele, Eric Stollnitz, David Nist´er, Blaise Aguera y Arcas, Sudipta Sinha, Johannes Kopf, Neel Joshi, and Krishnan Ramnath. I was also lucky to have as in- terns such great students as Polina Golland, Simon Baker, Mei Han, Arno Sch¨odl, Ron Dror, Ashley Eden, Jinxiang Chai, Rahul Swaminathan, Yanghai Tsin, Sam Hasinoff, Anat Levin, Matthew Brown, Eric Bennett, Vaibhav Vaish, Jan-Michael Frahm, James Diebel, Ce Liu, Josef Sivic, Grant Schindler, Colin Zheng, Neel Joshi, Sudipta Sinha, Zeev Farbman, Rahul Garg, Tim Cho, Yekeun Jeong, Richard Roberts, Varsha Hedau, and Dilip Krishnan. While working at Microsoft, I’ve also had the opportunity to collaborate with wonderful colleagues at the University of Washington, where I hold an Affiliate Professor appointment. I’m indebted to Tony DeRose and David Salesin, who first encouraged me to get involved with the research going on at UW, my long-time collaborators Brian Curless, Steve Seitz, Maneesh Agrawala, Sameer Agarwal, and Yasu Furukawa, as well as the students I have had the privilege to supervise and interact with, including Fr´ederic Pighin, Yung-Yu Chuang, Doug Zongker, Colin Zheng, Aseem Agarwala, Dan Goldman, Noah Snavely, Rahul Garg, and Ryan Kaminsky. As I mentioned at the beginning of this preface, this book owes its inception to the vision course that Steve Seitz invited me to co-teach, as well as to Steve’s encouragement, course notes, and editorial input. I’m also grateful to the many other computer vision researchers who have given me so many constructive suggestions about the book, including Sing Bing Kang, who was my infor- mal book editor, Vladimir Kolmogorov, who contributed Appendix B.5.5 on linear program- ming techniques for MRF inference, Daniel Scharstein, Richard Hartley, Simon Baker, Noah Snavely, Bill Freeman, Svetlana Lazebnik, Matthew Turk, Jitendra Malik, Alyosha Efros, Michael Black, Brian Curless, Sameer Agarwal, Li Zhang, Deva Ramanan, Olga Veksler, Yuri Boykov, Carsten Rother, Phil Torr, Bill Triggs, Bruce Maxwell, Jana Koˇseck´a, Eero Si- moncelli, Aaron Hertzmann, Antonio Torralba, Tomaso Poggio, Theo Pavlidis, Baba Vemuri, Nando de Freitas, Chuck Dyer, Song Yi, Falk Schubert, Roman Pflugfelder, Marshall Tap- pen, James Coughlan, Sammy Rogmans, Klaus Strobel, Shanmuganathan, Andreas Siebert, Yongjun Wu, Fred Pighin, Juan Cockburn, Ronald Mallet, Tim Soper, Georgios Evangelidis, Dwight Fowler, Itzik Bayaz, Daniel O’Connor, and Srikrishna Bhat. Shena Deuchers did a fantastic job copy-editing the book and suggesting many useful improvements and Wayne Wheeler and Simon Rees at Springer were most helpful throughout the whole book pub- lishing process. Keith Price’s Annotated Computer Vision Bibliography was invaluable in
Preface xi tracking down references and finding related work. If you have any suggestions for improving the book, please send me an e-mail, as I would like to keep the book as accurate, informative, and timely as possible. Lastly, this book would not have been possible or worthwhile without the incredible sup- port and encouragement of my family. I dedicate this book to my parents, Zdzisław and Jadwiga, whose love, generosity, and accomplishments have always inspired me; to my sis- ter Basia for her lifelong friendship; and especially to Lyn, Anne, and Stephen, whose daily encouragement in all matters (including this book project) makes it all worthwhile. Lake Wenatchee August, 2010
Contents Preface vii Contents xiii 1 Introduction 1 1.1 What is computer vision? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 A brief history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Book overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.4 Sample syllabus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5 A note on notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2 Image formation 29 2.1 Geometric primitives and transformations . . . . . . . . . . . . . . . . . . . 31 2.1.1 Geometric primitives . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.1.2 2D transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.1.3 3D transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.1.4 3D rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.1.5 3D to 2D projections . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.1.6 Lens distortions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.2 Photometric image formation . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.2.1 Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.2.2 Reflectance and shading . . . . . . . . . . . . . . . . . . . . . . . . 62 2.2.3 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.3 The digital camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.3.1 Sampling and aliasing . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.3.2 Color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.3.3 Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
xiv Computer Vision: Algorithms and Applications (September 3, 2010 draft) 2.4 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3 Image processing 99 3.1 Point operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.1.1 Pixel transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.1.2 Color transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.1.3 Compositing and matting . . . . . . . . . . . . . . . . . . . . . . . . 105 3.1.4 Histogram equalization . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.1.5 Application: Tonal adjustment . . . . . . . . . . . . . . . . . . . . . 111 3.2 Linear filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.2.1 Separable filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.2.2 Examples of linear filtering . . . . . . . . . . . . . . . . . . . . . . . 117 3.2.3 Band-pass and steerable filters . . . . . . . . . . . . . . . . . . . . . 118 3.3 More neighborhood operators . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.3.1 Non-linear filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.3.2 Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 3.3.3 Distance transforms . . . . . . . . . . . . . . . . . . . . . . . . . . 129 3.3.4 Connected components . . . . . . . . . . . . . . . . . . . . . . . . . 131 3.4 Fourier transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 3.4.1 Fourier transform pairs . . . . . . . . . . . . . . . . . . . . . . . . . 136 3.4.2 Two-dimensional Fourier transforms . . . . . . . . . . . . . . . . . . 140 3.4.3 Wiener filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 3.4.4 Application: Sharpening, blur, and noise removal . . . . . . . . . . . 144 3.5 Pyramids and wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 3.5.1 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 3.5.2 Decimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 3.5.3 Multi-resolution representations . . . . . . . . . . . . . . . . . . . . 150 3.5.4 Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 3.5.5 Application: Image blending . . . . . . . . . . . . . . . . . . . . . . 160 3.6 Geometric transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 3.6.1 Parametric transformations . . . . . . . . . . . . . . . . . . . . . . . 163 3.6.2 Mesh-based warping . . . . . . . . . . . . . . . . . . . . . . . . . . 170 3.6.3 Application: Feature-based morphing . . . . . . . . . . . . . . . . . 173 3.7 Global optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 3.7.1 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 3.7.2 Markov random fields . . . . . . . . . . . . . . . . . . . . . . . . . 180 3.7.3 Application: Image restoration . . . . . . . . . . . . . . . . . . . . . 192
Contents xv 3.8 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 3.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 4 Feature detection and matching 205 4.1 Points and patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 4.1.1 Feature detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 4.1.2 Feature descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 4.1.3 Feature matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 4.1.4 Feature tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 4.1.5 Application: Performance-driven animation . . . . . . . . . . . . . . 237 4.2 Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 4.2.1 Edge detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 4.2.2 Edge linking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 4.2.3 Application: Edge editing and enhancement . . . . . . . . . . . . . . 249 4.3 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 4.3.1 Successive approximation . . . . . . . . . . . . . . . . . . . . . . . 250 4.3.2 Hough transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 4.3.3 Vanishing points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 4.3.4 Application: Rectangle detection . . . . . . . . . . . . . . . . . . . . 257 4.4 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 5 Segmentation 267 5.1 Active contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 5.1.1 Snakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 5.1.2 Dynamic snakes and CONDENSATION . . . . . . . . . . . . . . . . 276 5.1.3 Scissors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 5.1.4 Level Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 5.1.5 Application: Contour tracking and rotoscoping . . . . . . . . . . . . 282 5.2 Split and merge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 5.2.1 Watershed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 5.2.2 Region splitting (divisive clustering) . . . . . . . . . . . . . . . . . . 286 5.2.3 Region merging (agglomerative clustering) . . . . . . . . . . . . . . 286 5.2.4 Graph-based segmentation . . . . . . . . . . . . . . . . . . . . . . . 286 5.2.5 Probabilistic aggregation . . . . . . . . . . . . . . . . . . . . . . . . 288 5.3 Mean shift and mode finding . . . . . . . . . . . . . . . . . . . . . . . . . . 289 5.3.1 K-means and mixtures of Gaussians . . . . . . . . . . . . . . . . . . 289 5.3.2 Mean shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
xvi Computer Vision: Algorithms and Applications (September 3, 2010 draft) 5.4 Normalized cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 5.5 Graph cuts and energy-based methods . . . . . . . . . . . . . . . . . . . . . 300 5.5.1 Application: Medical image segmentation . . . . . . . . . . . . . . . 304 5.6 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 5.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 6 Feature-based alignment 309 6.1 2D and 3D feature-based alignment . . . . . . . . . . . . . . . . . . . . . . 311 6.1.1 2D alignment using least squares . . . . . . . . . . . . . . . . . . . . 312 6.1.2 Application: Panography . . . . . . . . . . . . . . . . . . . . . . . . 314 6.1.3 Iterative algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 6.1.4 Robust least squares and RANSAC . . . . . . . . . . . . . . . . . . 318 6.1.5 3D alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 6.2 Pose estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 6.2.1 Linear algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 6.2.2 Iterative algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 6.2.3 Application: Augmented reality . . . . . . . . . . . . . . . . . . . . 326 6.3 Geometric intrinsic calibration . . . . . . . . . . . . . . . . . . . . . . . . . 327 6.3.1 Calibration patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 6.3.2 Vanishing points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 6.3.3 Application: Single view metrology . . . . . . . . . . . . . . . . . . 331 6.3.4 Rotational motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 6.3.5 Radial distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 6.4 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 6.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 7 Structure from motion 343 7.1 Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 7.2 Two-frame structure from motion . . . . . . . . . . . . . . . . . . . . . . . . 347 7.2.1 Projective (uncalibrated) reconstruction . . . . . . . . . . . . . . . . 353 7.2.2 Self-calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 7.2.3 Application: View morphing . . . . . . . . . . . . . . . . . . . . . . 357 7.3 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 7.3.1 Perspective and projective factorization . . . . . . . . . . . . . . . . 360 7.3.2 Application: Sparse 3D model extraction . . . . . . . . . . . . . . . 362 7.4 Bundle adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 7.4.1 Exploiting sparsity . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 7.4.2 Application: Match move and augmented reality . . . . . . . . . . . 368
Contents xvii 7.4.3 Uncertainty and ambiguities . . . . . . . . . . . . . . . . . . . . . . 370 7.4.4 Application: Reconstruction from Internet photos . . . . . . . . . . . 371 7.5 Constrained structure and motion . . . . . . . . . . . . . . . . . . . . . . . . 374 7.5.1 Line-based techniques . . . . . . . . . . . . . . . . . . . . . . . . . 374 7.5.2 Plane-based techniques . . . . . . . . . . . . . . . . . . . . . . . . . 376 7.6 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 8 Dense motion estimation 381 8.1 Translational alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 8.1.1 Hierarchical motion estimation . . . . . . . . . . . . . . . . . . . . . 387 8.1.2 Fourier-based alignment . . . . . . . . . . . . . . . . . . . . . . . . 388 8.1.3 Incremental refinement . . . . . . . . . . . . . . . . . . . . . . . . . 392 8.2 Parametric motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 8.2.1 Application: Video stabilization . . . . . . . . . . . . . . . . . . . . 401 8.2.2 Learned motion models . . . . . . . . . . . . . . . . . . . . . . . . . 403 8.3 Spline-based motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 8.3.1 Application: Medical image registration . . . . . . . . . . . . . . . . 408 8.4 Optical flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 8.4.1 Multi-frame motion estimation . . . . . . . . . . . . . . . . . . . . . 413 8.4.2 Application: Video denoising . . . . . . . . . . . . . . . . . . . . . 414 8.4.3 Application: De-interlacing . . . . . . . . . . . . . . . . . . . . . . 415 8.5 Layered motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 8.5.1 Application: Frame interpolation . . . . . . . . . . . . . . . . . . . . 418 8.5.2 Transparent layers and reflections . . . . . . . . . . . . . . . . . . . 419 8.6 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 8.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 9 Image stitching 427 9.1 Motion models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 9.1.1 Planar perspective motion . . . . . . . . . . . . . . . . . . . . . . . 431 9.1.2 Application: Whiteboard and document scanning . . . . . . . . . . . 432 9.1.3 Rotational panoramas . . . . . . . . . . . . . . . . . . . . . . . . . . 433 9.1.4 Gap closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 9.1.5 Application: Video summarization and compression . . . . . . . . . 436 9.1.6 Cylindrical and spherical coordinates . . . . . . . . . . . . . . . . . 438 9.2 Global alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 9.2.1 Bundle adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
xviii Computer Vision: Algorithms and Applications (September 3, 2010 draft) 9.2.2 Parallax removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 9.2.3 Recognizing panoramas . . . . . . . . . . . . . . . . . . . . . . . . 446 9.2.4 Direct vs. feature-based alignment . . . . . . . . . . . . . . . . . . . 450 9.3 Compositing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 9.3.1 Choosing a compositing surface . . . . . . . . . . . . . . . . . . . . 451 9.3.2 Pixel selection and weighting (de-ghosting) . . . . . . . . . . . . . . 453 9.3.3 Application: Photomontage . . . . . . . . . . . . . . . . . . . . . . 459 9.3.4 Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 9.4 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 9.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 10 Computational photography 467 10.1 Photometric calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 10.1.1 Radiometric response function . . . . . . . . . . . . . . . . . . . . . 470 10.1.2 Noise level estimation . . . . . . . . . . . . . . . . . . . . . . . . . 473 10.1.3 Vignetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 10.1.4 Optical blur (spatial response) estimation . . . . . . . . . . . . . . . 476 10.2 High dynamic range imaging . . . . . . . . . . . . . . . . . . . . . . . . . . 479 10.2.1 Tone mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 10.2.2 Application: Flash photography . . . . . . . . . . . . . . . . . . . . 494 10.3 Super-resolution and blur removal . . . . . . . . . . . . . . . . . . . . . . . 497 10.3.1 Color image demosaicing . . . . . . . . . . . . . . . . . . . . . . . 502 10.3.2 Application: Colorization . . . . . . . . . . . . . . . . . . . . . . . 504 10.4 Image matting and compositing . . . . . . . . . . . . . . . . . . . . . . . . . 505 10.4.1 Blue screen matting . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 10.4.2 Natural image matting . . . . . . . . . . . . . . . . . . . . . . . . . 509 10.4.3 Optimization-based matting . . . . . . . . . . . . . . . . . . . . . . 513 10.4.4 Smoke, shadow, and flash matting . . . . . . . . . . . . . . . . . . . 516 10.4.5 Video matting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 10.5 Texture analysis and synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 518 10.5.1 Application: Hole filling and inpainting . . . . . . . . . . . . . . . . 521 10.5.2 Application: Non-photorealistic rendering . . . . . . . . . . . . . . . 522 10.6 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524 10.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 11 Stereo correspondence 533 11.1 Epipolar geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 11.1.1 Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
Contents xix 11.1.2 Plane sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540 11.2 Sparse correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 11.2.1 3D curves and profiles . . . . . . . . . . . . . . . . . . . . . . . . . 543 11.3 Dense correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 11.3.1 Similarity measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 11.4 Local methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548 11.4.1 Sub-pixel estimation and uncertainty . . . . . . . . . . . . . . . . . . 550 11.4.2 Application: Stereo-based head tracking . . . . . . . . . . . . . . . . 551 11.5 Global optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 11.5.1 Dynamic programming . . . . . . . . . . . . . . . . . . . . . . . . . 554 11.5.2 Segmentation-based techniques . . . . . . . . . . . . . . . . . . . . 556 11.5.3 Application: Z-keying and background replacement . . . . . . . . . . 558 11.6 Multi-view stereo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 11.6.1 Volumetric and 3D surface reconstruction . . . . . . . . . . . . . . . 562 11.6.2 Shape from silhouettes . . . . . . . . . . . . . . . . . . . . . . . . . 567 11.7 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 11.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 12 3D reconstruction 577 12.1 Shape from X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 12.1.1 Shape from shading and photometric stereo . . . . . . . . . . . . . . 580 12.1.2 Shape from texture . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 12.1.3 Shape from focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 12.2 Active rangefinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 12.2.1 Range data merging . . . . . . . . . . . . . . . . . . . . . . . . . . 588 12.2.2 Application: Digital heritage . . . . . . . . . . . . . . . . . . . . . . 590 12.3 Surface representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 12.3.1 Surface interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . 592 12.3.2 Surface simplification . . . . . . . . . . . . . . . . . . . . . . . . . 594 12.3.3 Geometry images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 12.4 Point-based representations . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 12.5 Volumetric representations . . . . . . . . . . . . . . . . . . . . . . . . . . . 596 12.5.1 Implicit surfaces and level sets . . . . . . . . . . . . . . . . . . . . . 596 12.6 Model-based reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 12.6.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 12.6.2 Heads and faces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601 12.6.3 Application: Facial animation . . . . . . . . . . . . . . . . . . . . . 603 12.6.4 Whole body modeling and tracking . . . . . . . . . . . . . . . . . . 605
xx Computer Vision: Algorithms and Applications (September 3, 2010 draft) 12.7 Recovering texture maps and albedos . . . . . . . . . . . . . . . . . . . . . 610 12.7.1 Estimating BRDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . 612 12.7.2 Application: 3D photography . . . . . . . . . . . . . . . . . . . . . 613 12.8 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 12.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 13 Image-based rendering 619 13.1 View interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 13.1.1 View-dependent texture maps . . . . . . . . . . . . . . . . . . . . . 623 13.1.2 Application: Photo Tourism . . . . . . . . . . . . . . . . . . . . . . 624 13.2 Layered depth images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626 13.2.1 Impostors, sprites, and layers . . . . . . . . . . . . . . . . . . . . . . 626 13.3 Light fields and Lumigraphs . . . . . . . . . . . . . . . . . . . . . . . . . . 628 13.3.1 Unstructured Lumigraph . . . . . . . . . . . . . . . . . . . . . . . . 632 13.3.2 Surface light fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 632 13.3.3 Application: Concentric mosaics . . . . . . . . . . . . . . . . . . . . 634 13.4 Environment mattes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 13.4.1 Higher-dimensional light fields . . . . . . . . . . . . . . . . . . . . . 636 13.4.2 The modeling to rendering continuum . . . . . . . . . . . . . . . . . 637 13.5 Video-based rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638 13.5.1 Video-based animation . . . . . . . . . . . . . . . . . . . . . . . . . 639 13.5.2 Video textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640 13.5.3 Application: Animating pictures . . . . . . . . . . . . . . . . . . . . 643 13.5.4 3D Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 13.5.5 Application: Video-based walkthroughs . . . . . . . . . . . . . . . . 645 13.6 Additional reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648 13.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650 14 Recognition 655 14.1 Object detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658 14.1.1 Face detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658 14.1.2 Pedestrian detection . . . . . . . . . . . . . . . . . . . . . . . . . . 666 14.2 Face recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 14.2.1 Eigenfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671 14.2.2 Active appearance and 3D shape models . . . . . . . . . . . . . . . . 679 14.2.3 Application: Personal photo collections . . . . . . . . . . . . . . . . 684 14.3 Instance recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685 14.3.1 Geometric alignment . . . . . . . . . . . . . . . . . . . . . . . . . . 686
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