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xvi Contents

7 Structure from motion 303
7.1 Triangulation .................................. 305
7.2 Two-frame structure from motion ........................ 307
7.2.1 Projective (uncalibrated) reconstruction ................ 312
7.2.2 Self-calibration ............................. 313
7.2.3 Application: View morphing ...................... 315
7.3 Factorization .................................. 315
7.3.1 Perspective and projective factorization ................ 318
7.3.2 Application: Sparse 3D model extraction ............... 319
7.4 Bundle adjustment ............................... 320
7.4.1 Exploiting sparsity ........................... 322
7.4.2 Application: Match move and augmented reality ........... 324
7.4.3 Uncertainty and ambiguities ...................... 326
7.4.4 Application: Reconstruction from Internet photos ........... 327
7.5 Constrained structure and motion ........................ 329
7.5.1 Line-based techniques ......................... 330
7.5.2 Plane-based techniques ......................... 331
7.6 Additional reading ............................... 332
7.7 Exercises .................................... 332

8 Dense motion estimation 335
8.1 Translational alignment ............................. 337
8.1.1 Hierarchical motion estimation ..................... 341
8.1.2 Fourier-based alignment ........................ 341
8.1.3 Incremental refinement ......................... 345
8.2 Parametric motion ................................ 350
8.2.1 Application: Video stabilization .................... 354
8.2.2 Learned motion models ......................... 354
8.3 Spline-based motion .............................. 355
8.3.1 Application: Medical image registration ................ 358
8.4 Optical flow ................................... 360
8.4.1 Multi-frame motion estimation ..................... 363
8.4.2 Application: Video denoising ..................... 364
8.4.3 Application: De-interlacing ...................... 364
8.5 Layered motion ................................. 365
8.5.1 Application: Frame interpolation .................... 368
8.5.2 Transparent layers and reflections ................... 368
8.6 Additional reading ............................... 370
8.7 Exercises .................................... 371
9 Image stitching 375
9.1 Motion models ................................. 378
9.1.1 Planar perspective motion ....................... 379
9.1.2 Application: Whiteboard and document scanning ........... 379
9.1.3 Rotational panoramas .......................... 380
9.1.4 Gap closing ............................... 382