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10.6 Motion Segmentation by Parameter Estimation . . . . . . . . . . . . 313
10.6.1 Optical Flow and Motion . . . . ... .. ... .. .. ... . 315
10.6.2 Flow Models . . . . . .. .. .. ... .. ... .. .. ... . 316
10.6.3 Motion Segmentation with Layers . . . . . . . . . . . . . . . 317
10.7 Model Selection: Which Model Is the Best Fit? . ... .. .. ... . 319
10.7.1 Model Selection Using Cross-Validation . . . . . . . . . . . . 322
10.8 Notes . . . . . . .. .. .. ... .. .. ... .. ... .. .. ... . 322

11 Tracking 326
11.1 Simple Tracking Strategies . ... .. .. ... .. ... .. .. ... . 327
11.1.1 Tracking by Detection . . . . . . ... .. ... .. .. ... . 327
11.1.2 Tracking Translations by Matching . . . . . . . . . . . . . . . 330
11.1.3 Using Affine Transformations to Confirm a Match . . . . . . 332
11.2 Tracking Using Matching . . . . . . . . . . . . . . . . . . . . . . . . 334
11.2.1 Matching Summary Representations . . . . . . . . . . . . . . 335
11.2.2 Tracking Using Flow ... .. .. ... .. ... .. .. ... . 337
11.3 Tracking Linear Dynamical Models with Kalman Filters . . . . . . . 339
11.3.1 Linear Measurements and Linear Dynamics . . . . . . . . . . 340
11.3.2 The Kalman Filter . ... .. .. ... .. ... .. .. ... . 344
11.3.3 Forward-backward Smoothing . . . . . . . . . . . . . . . . . . 345
11.4 Data Association . . . . . . ... .. .. ... .. ... .. .. ... . 349
11.4.1 Linking Kalman Filters with Detection Methods . . . . . . . 349
11.4.2 Key Methods of Data Association . . . . . . . . . . . . . . . 350
11.5 Particle Filtering .. .. .. ... .. .. ... .. ... .. .. ... . 350
11.5.1 Sampled Representations of Probability Distributions . . . . 351
11.5.2 The Simplest Particle Filter . . . . . . . . . . . . . . . . . . . 355
11.5.3 The Tracking Algorithm . . . . . . . . . . . . . . . . . . . . . 356
11.5.4 A Workable Particle Filter .. .. ... .. ... .. .. ... . 358
11.5.5 Practical Issues in Particle Filters . . . . ... .. .. ... . 360
11.6 Notes . . . . . . .. .. .. ... .. .. ... .. ... .. .. ... . 362

V HIGH-LEVEL VISION 365

12 Registration 367
12.1 Registering Rigid Objects . ... .. .. ... .. ... .. .. ... . 368
12.1.1 Iterated Closest Points . . . . . . ... .. ... .. .. ... . 368
12.1.2 Searching for Transformations via Correspondences . . . . . . 369
12.1.3 Application: Building Image Mosaics . . . . . . . . . . . . . . 370
12.2 Model-based Vision: Registering Rigid Objects with Projection . . . 375