i image formation 1 
1 geometric camera models 3 
1.1 image formation 4 
1.1.1 pinhole perspective 4 
1.1.2 weak perspective 6 
1.1.3 cameras with lenses 8 
1.1.4 the human eye 12 
1.2 intrinsic and extrinsic parameters 14 
1.2.1 rigid transformations and homogeneous coordinates 14 
1.2.2 intrinsic parameters 16 
1.2.3 extrinsic parameters 18 
1.2.4 perspective projection matrices 19 
1.2.5 weak-perspective projection matrices 20 
1.3 geometric camera calibration 22 
1.3.1 alinear approach to camera calibration 23 
1.3.2 anonlinear approach to camera calibration 27 
1.4 notes 29 
2 light and shading 32 
2.1 modelling pixel brightness 32 
2.1.1 reflection at surfaces 33 
2.1.2 sources and their effects 34 
2.1.3 the lambertian+specular model 36 
2.1.4 area sources 36 
2.2 inference from shading 37 
2.2.1 radiometric calibration and high dynamic range images 38 
2.2.2 the shape of specularities 40 
2.2.3 inferring lightness and illumination 43 
2.2.4 photometric stereo: shape from multiple shaded images 46 
2.3 modelling interreflection 52 
2.3.1 the illumination at a patch due to an area source 52 
2.3.2 radiosity and exitance 54 
2.3.3 an interreflection model 55 
2.3.4 qualitative properties of interreflections 56 
2.4 shape from one shaded image 59 
2.5 notes 61 
3 color 68 
3.1 human color perception 68 
3.1.1 color matching 68 
3.1.2 color receptors 71 
3.2 the physics of color 73 
3.2.1 the color of light sources 73 
3.2.2 the color of surfaces 76 
3.3 representing color 77 
3.3.1 linear color spaces 77 
3.3.2 non-linear color spaces 83 
3.4 amodel of image color 86 
3.4.1 the diffuse term 88 
3.4.2 the specular term 90 
3.5 inference from color 90 
3.5.1 finding specularities using color 90 
3.5.2 shadow removal using color 92 
3.5.3 color constancy: surface color from image color 95 
3.6 notes 99 
ii early vision: just one image 105 
4 linear filters 107 
4.1 linear filters and convolution 107 
4.1.1 convolution 107 
4.2 shift invariant linear systems 112 
4.2.1 discrete convolution 113 
4.2.2 continuous convolution 115 
4.2.3 edge effects in discrete convolutions 118 
4.3 spatial frequency and fourier transforms 118 
4.3.1 fourier transforms 119 
4.4 sampling and aliasing 121 
4.4.1 sampling 122 
4.4.2 aliasing 125 
4.4.3 smoothing and resampling 126 
4.5 filters as templates 131 
4.5.1 convolution as a dot product 131 
4.5.2 changing basis 132 
4.6 technique: normalized correlation and finding patterns 132 
4.6.1 controlling the television by finding hands by normalized 
correlation 133 
4.7 technique: scale and image pyramids 134 
4.7.1 the gaussian pyramid 135 
4.7.2 applications of scaled representations 136 
4.8 notes 137 
5 local image features 141 
5.1 computing the image gradient 141 
5.1.1 derivative of gaussian filters 142 
5.2 representing the image gradient 144 
5.2.1 gradient-based edge detectors 145 
5.2.2 orientations 147 
5.3 finding corners and building neighborhoods 148 
5.3.1 finding corners 149 
5.3.2 using scale and orientation to build a neighborhood 151 
5.4 describing neighborhoods with sift and hog features 155 
5.4.1 sift features 157 
5.4.2 hog features 159 
5.5 computing local features in practice 160 
5.6 notes 160 
6 texture 164 
6.1 local texture representations using filters 166 
6.1.1 spots and bars 167 
6.1.2 from filter outputs to texture representation 168 
6.1.3 local texture representations in practice 170 
6.2 pooled texture representations by discovering textons 171 
6.2.1 vector quantization and textons 172 
6.2.2 k-means clustering for vector quantization 172 
6.3 synthesizing textures and filling holes in images 176 
6.3.1 synthesis by sampling local models 176 
6.3.2 filling in holes in images 179 
6.4 image denoising 182 
6.4.1 non-local means 183 
6.4.2 block matching 3d (bm3d) 183 
6.4.3 learned sparse coding 184 
6.4.4 results 186 
6.5 shape from texture 187 
6.5.1 shape from texture for planes 187 
6.5.2 shape from texture for curved surfaces 190 
6.6 notes 191 
iii early vision: multiple images 195 
7 stereopsis 197 
7.1 binocular camera geometry and the epipolar constraint 198 
7.1.1 epipolar geometry 198 
7.1.2 the essential matrix 200 
7.1.3 the fundamental matrix 201 
7.2 binocular reconstruction 201 
7.2.1 image rectification 202 
7.3 human stereopsis 203 
7.4 local methods for binocular fusion 205 
7.4.1 correlation 205 
7.4.2 multi-scale edge matching 207 
7.5 global methods for binocular fusion 210 
7.5.1 ordering constraints and dynamic programming 210 
7.5.2 smoothness and graphs 211 
7.6 using more cameras 214 
7.7 application: robot navigation 215 
7.8 notes 216 
8 structure from motion 221 
8.1 internally calibrated perspective cameras 221 
8.1.1 natural ambiguity of the problem 223 
8.1.2 euclidean structure and motion from two images 224 
8.1.3 euclidean structure and motion from multiple images 228 
8.2 uncalibrated weak-perspective cameras 230 
8.2.1 natural ambiguity of the problem 231 
8.2.2 affine structure and motion from two images 233 
8.2.3 affine structure and motion from multiple images 237 
8.2.4 from affine to euclidean shape 238 
8.3 uncalibrated perspective cameras 240 
8.3.1 natural ambiguity of the problem 241 
8.3.2 projective structure and motion from two images 242 
8.3.3 projective structure and motion from multiple images 244 
8.3.4 from projective to euclidean shape 246 
8.4 notes 248 
iv mid-level vision 253 
9 segmentation by clustering 255 
9.1 human vision: grouping and gestalt 256 
9.2 important applications 261 
9.2.1 background subtraction 261 
9.2.2 shot boundary detection 264 
9.2.3 interactive segmentation 265 
9.2.4 forming image regions 266 
9.3 image segmentation by clustering pixels 268 
9.3.1 basic clustering methods 269 
9.3.2 the watershed algorithm 271 
9.3.3 segmentation using k-means 272 
9.3.4 mean shift: finding local modes in data 273 
9.3.5 clustering and segmentation with mean shift 275 
9.4 segmentation, clustering, and graphs 277 
9.4.1 terminology and facts for graphs 277 
9.4.2 agglomerative clustering with a graph 279 
9.4.3 divisive clustering with a graph 281 
9.4.4 normalized cuts 284 
9.5 image segmentation in practice 285 
9.5.1 evaluating segmenters 286 
9.6 notes 287 
10 grouping and model fitting 290 
10.1 the hough transform 290 
10.1.1 fitting lines with the hough transform 290 
10.1.2 using the hough transform 292 
10.2 fitting lines and planes 293 
10.2.1 fitting a single line 294 
10.2.2 fitting planes 295 
10.2.3 fitting multiple lines 296 
10.3 fitting curved structures 297 
10.4 robustness 299 
10.4.1 m-estimators 300 
10.4.2 ransac: searching for good points 302 
10.5 fitting using probabilistic models 306 
10.5.1 missing data problems 307 
10.5.2 mixture models and hidden variables 309 
10.5.3 the em algorithm for mixture models 310 
10.5.4 difficulties with the em algorithm 312 
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 
12.2.1 verification: comparing transformed and rendered source 
to target 377 
12.3 registering deformable objects 378 
12.3.1 deforming texture with active appearance models 378 
12.3.2 active appearance models in practice 381 
12.3.3 application: registration in medical imaging systems 383 
12.4 notes 388 
13 smooth surfaces and their outlines 391 
13.1 elements of differential geometry 393 
13.1.1 curves 393 
13.1.2 surfaces 397 
13.2 contour geometry 402 
13.2.1 the occluding contour and the image contour 402 
13.2.2 the cusps and inflections of the image contour 403 
13.2.3 koenderink’s theorem 404 
13.3 visual events: more differential geometry 407 
13.3.1 the geometry of the gauss map 407 
13.3.2 asymptotic curves 409 
13.3.3 the asymptotic spherical map 410 
13.3.4 local visual events 412 
13.3.5 the bitangent ray manifold 413 
13.3.6 multilocal visual events 414 
13.3.7 the aspect graph 416 
13.4 notes 417 
14 range data 422 
14.1 active range sensors 422 
14.2 range data segmentation 424 
14.2.1 elements of analytical differential geometry 424 
14.2.2 finding step and roof edges in range images 426 
14.2.3 segmenting range images into planar regions 431 
14.3 range image registration and model acquisition 432 
14.3.1 quaternions 433 
14.3.2 registering range images 434 
14.3.3 fusing multiple range images 436 
14.4 object recognition 438 
14.4.1 matching using interpretation trees 438 
14.4.2 matching free-form surfaces using spin images 441 
14.5 kinect 446 
14.5.1 features 447 
14.5.2 technique: decision trees and random forests 448 
14.5.3 labeling pixels 450 
14.5.4 computing joint positions 453 
14.6 notes 453 
15 learning to classify 457 
15.1 classification, error, and loss 457 
15.1.1 using loss to determine decisions 457 
15.1.2 training error, test error, and overfitting 459 
15.1.3 regularization 460 
15.1.4 error rate and cross-validation 463 
15.1.5 receiver operating curves 465 
15.2 major classification strategies 467 
15.2.1 example: mahalanobis distance 467 
15.2.2 example: class-conditional histograms and naive bayes 468 
15.2.3 example: classification using nearest neighbors 469 
15.2.4 example: the linear support vector machine 470 
15.2.5 example: kernel machines 473 
15.2.6 example: boosting and adaboost 475 
15.3 practical methods for building classifiers 475 
15.3.1 manipulating training data to improve performance 477 
15.3.2 building multi-class classifiers out of binary classifiers 479 
15.3.3 solving for svms and kernel machines 480 
15.4 notes 481 
16 classifying images 482 
16.1 building good image features 482 
16.1.1 example applications 482 
16.1.2 encoding layout with gist features 485 
16.1.3 summarizing images with visual words 487 
16.1.4 the spatial pyramid kernel 489 
16.1.5 dimension reduction with principal components 493 
16.1.6 dimension reduction with canonical variates 494 
16.1.7 example application: identifying explicit images 498 
16.1.8 example application: classifying materials 502 
16.1.9 example application: classifying scenes 502 
16.2 classifying images of single objects 504 
16.2.1 image classification strategies 505 
16.2.2 evaluating image classification systems 505 
16.2.3 fixed sets of classes 508 
16.2.4 large numbers of classes 509 
16.2.5 flowers, leaves, and birds: some specialized problems 511 
16.3 image classification in practice 512 
16.3.1 codes for image features 513 
16.3.2 image classification datasets 513 
16.3.3 dataset bias 515 
16.3.4 crowdsourcing dataset collection 515 
16.4 notes 517 
17 detecting objects in images 519 
17.1 the sliding window method 519 
17.1.1 face detection 520 
17.1.2 detecting humans 525 
17.1.3 detecting boundaries 527 
17.2 detecting deformable objects 530 
17.3 the state of the art of object detection 535 
17.3.1 datasets and resources 538 
17.4 notes 539 
18 topics in object recognition 540 
18.1 what should object recognition do? 540 
18.1.1 what should an object recognition system do? 540 
18.1.2 current strategies for object recognition 542 
18.1.3 what is categorization? 542 
18.1.4 selection: what should be described? 544 
18.2 feature questions 544 
18.2.1 improving current image features 544 
18.2.2 other kinds of image feature 546 
18.3 geometric questions 547 
18.4 semantic questions 549 
18.4.1 attributes and the unfamiliar 550 
18.4.2 parts, poselets and consistency 551 
18.4.3 chunks of meaning 554 
vi applications and topics 557 
19 image-based modeling and rendering 559 
19.1 visual hulls 559 
19.1.1 main elements of the visual hull model 561 
19.1.2 tracing intersection curves 563 
19.1.3 clipping intersection curves 566 
19.1.4 triangulating cone strips 567 
19.1.5 results 568 
19.1.6 going further: carved visual hulls 572 
19.2 patch-based multi-view stereopsis 573 
19.2.1 main elements of the pmvs model 575 
19.2.2 initial feature matching 578 
19.2.3 expansion 579 
19.2.4 filtering 580 
19.2.5 results 581 
19.3 the light field 584 
19.4 notes 587 
20 looking at people 590 
20.1 hmm’s, dynamic programming, and tree-structured models 590 
20.1.1 hidden markov models 590 
20.1.2 inference for an hmm 592 
20.1.3 fitting an hmm with em 597 
20.1.4 tree-structured energy models 600 
20.2 parsing people in images 602 
20.2.1 parsing with pictorial structure models 602 
20.2.2 estimating the appearance of clothing 604 
20.3 tracking people 606 
20.3.1 why human tracking is hard 606 
20.3.2 kinematic tracking by appearance 608 
20.3.3 kinematic human tracking using templates 609 
20.4 3d from 2d: lifting 611 
20.4.1 reconstruction in an orthographic view 611 
20.4.2 exploiting appearance for unambiguous reconstructions 613 
20.4.3 exploiting motion for unambiguous reconstructions 615 
20.5 activity recognition 617 
20.5.1 background: human motion data 617 
20.5.2 body configuration and activity recognition 621 
20.5.3 recognizing human activities with appearance features 622 
20.5.4 recognizing human activities with compositional models 624 
20.6 resources 624 
20.7 notes 626 
21 image search and retrieval 627 
21.1 the application context 627 
21.1.1 applications 628 
21.1.2 user needs 629 
21.1.3 types of image query 630 
21.1.4 what users do with image collections 631 
21.2 basic technologies from information retrieval 632 
21.2.1 word counts 632 
21.2.2 smoothing word counts 633 
21.2.3 approximate nearest neighbors and hashing 634 
21.2.4 ranking documents 638 
21.3 images as documents 639 
21.3.1 matching without quantization 640 
21.3.2 ranking image search results 641 
21.3.3 browsing and layout 643 
21.3.4 laying out images for browsing 644 
21.4 predicting annotations for pictures 645 
21.4.1 annotations from nearby words 646 
21.4.2 annotations from the whole image 646 
21.4.3 predicting correlated words with classifiers 648 
21.4.4 names and faces 649 
21.4.5 generating tags with segments 651 
21.5 the state of the art of word prediction 654 
21.5.1 resources 655 
21.5.2 comparing methods 655 
21.5.3 open problems 656 
21.6 notes 659 
vii background material 661 
22 optimization techniques 663 
22.1 linear least-squares methods 663 
22.1.1 normal equations and the pseudoinverse 664 
22.1.2 homogeneous systems and eigenvalue problems 665 
22.1.3 generalized eigenvalues problems 666 
22.1.4 an example: fitting a line to points in a plane 666 
22.1.5 singular value decomposition 667 
22.2 nonlinear least-squares methods 669 
22.2.1 newton’s method: square systems of nonlinear equations670 
22.2.2 newton’s method for overconstrained systems 670 
22.2.3 the gauss—newton and levenberg—marquardt algorithms 671 
22.3 sparse coding and dictionary learning 672 
22.3.1 sparse coding 672 
22.3.2 dictionary learning 673 
22.3.3 supervised dictionary learning 675 
22.4 min-cut/max-flow problems and combinatorial optimization 675 
22.4.1 min-cut problems 676 
22.4.2 quadratic pseudo-boolean functions 677 
22.4.3 generalization to integer variables 679 
22.5 notes 682 

index  684
list of algorithms 707