Chapter 14: Image-based rendering

• As with other areas of computer vision, most recently published image-based rendering and neural rendering papers now come with open source implementations.

Appendix A: Linear algebra and numerical techniques

• The first edition of this book (Szeliski 2010, Appendix C.2) lists a number of widely used linear algebra and non-linear least squares packages such as BLAS, LAPACK, ATLAS, MKL, MINPACK, PARADISO, TAUCS, HSL, and ITSOL. Most of these are now integrated into larger packages such as Python's NumPy and GPU machine learning frameworks such as PyTorch and TensorFlow.

• If you are interested in sparse linear least squares solvers, it is worth looking at SuiteSparse (https://people.engr.tamu.edu/davis/suitesparse.html), since it contains a wide range of algorithms and associated publications (Davis 2006, 2011).

Appendix B: Bayesian modeling and inference

• The Middlebury benchmark for MRF minimization, https://vision.middlebury.edu/MRF/code, contains implementations of basic MRF inference algorithms (Szeliski, Zabih et al. 2008).

• The OpenGM2 library and benchmarks for discrete factor graph models, http://hciweb2.iwr.uni-heidelberg.de/opengm, contains a more extensive and up-to-date set of algorithms. (Kappes, Andres et al. 2015).

C.3 Slides and lectures

While there are no official slide sets to go with this book, its content largely parallels that of the courses I have co-taught at the University of Washington, https://www.cs.washington.edu/education/courses/cse576.

Related computer vision and deep learning classes include:

Noah Snavely's Introduction to Computer Vision class at Cornell Tech, https://www.cs.cornell.edu/courses/cs5670/2021sp/

• Alyosha Efros' Intro to Computer Vision and Computational Photography class at Berkeley https://inst.eecs.berkeley.edu/~cs194-26/fa20.

• David Fouhey's and Justin Johnson's Computer Vision class at the University of Michigan, https://web.eecs.umich.edu/~justincj/teaching/eecs442.

• Bill Freeman, Antonio Torralba, and Phillip Isola's Advances in Computer Vision class at MIT http://6.869.csail.mit.edu/sp21.

• Justin Johnson’s Deep Learning for Computer Vision class at the University of Michigan, https://web.eecs.umich.edu/~justincj/teaching/eecs498.

• Yann LeCun and Alfredo Canziani's Deep Learning class at NYU, https://atcold.github.io/NYU-DLSP21.

• UC Berkeley’s class on Deep Unsupervised Learning, https://sites.google.com/view/berkeley-cs294-158-sp20.

You can find a more comprehensive list of such courses on the book's web site, https://szeliski.org/

Book/default.htm#Slides.

There are also some great online lectures series, including:

• The 2004 UW-MSR Course on Vision Algorithms, http://www.cs.washington.edu/education/courses/cse577/04sp/index.htm.

• The 2020-2021 TUM AI Guest Lecture Series, https://niessner.github.io/TUM-AI-Lecture-Series.

• The 2020-2021 3DGV virtual seminar series on Geometry Processing and 3D Computer Vision, https://3dgv.github.io.

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Index

3D Rotations, see Rotations

3D alignment, 410

absolute orientation, 410, 651

orthogonal Procrustes, 411

3D convolutional neural networks, 252

3D model capture, 676

3D photography, 676, 690

3D scanning, 647

3D video, 706

Absolute orientation, 410, 651

Activation functions, 217

rectified linear unit (ReLU), 217

sigmoid, 217

Active appearance model (AAM), 291

Active contours, 373

Active illumination, 647

Active rangefinding, 647

Active shape model (ASM), 291, 376

Active stereo, 649

Activity recognition, 673

Adadelta, 230

AdaGrad, 230

Adam optimization algorithm, 231

Adaptive smoothing, 108

Adversarial examples, 248, 321

Affine transforms, 33, 36

Affinities (segmentation), 391

AlexNet neural network, 238

Algebraic multigrid, 388

Algorithms

testing, viii

Aliasing, 67, 491

Alignment, see Image alignment

Alpha

opacity, 91

pre-multiplied, 91

Alpha matte, 91

Ambient illumination, 57

Analog to digital conversion (ADC), 66

Anisotropic diffusion, 108

Anisotropic filtering, 140

Anti-aliasing filter, 68, 491

Aperture, 60

Aperture problem, 453

Applications, 3

3D model capture, 676

3D model reconstruction, 576

3D photography, 676, 690

augmented reality, 555, 587

automotive safety, 6

background replacement, 617

biometrics, 289

colorization, 169

digit classification, 237

digital heritage, 654

document scanning, 414

edge editing, 372

facial animation, 665

flash photography, 506

frame interpolation, 473

gaze correction, 612

head tracking, 611

hole filling, 531

image search, 287

industrial, 6

intelligent photo editing, 314

Internet photos, 576

location recognition, 555

machine inspection, 6

match move, 574

medical imaging, 6, 310, 461

morphing, 142

mosaic-based video compression, 417

non-photorealistic rendering, 532

Optical character recognition (OCR), 3

panography, 405

performance-driven animation, 363

© Springer Nature Switzerland AG 2022

R. Szeliski, Computer Vision, Texts in Computer Science, https://doi.org/10.1007/978-3-030-34372-9

photo pop-up, 314

Photo Tourism, 686

Photomontage, 435

planar pattern tracking, 555

rolling shutter wobble removal, 468

rotoscoping, 380

scene completion, 314

scratch removal, 531

segmentation, 181

self-driving vehicles, 6

single view reconstruction, 548

style transfer, 534

synthetic re-focusing, 698

tonal adjustment, 95

video denoising, 469

video stabilization, 457

video summarization, 417

video-based walkthroughs, 708

view morphing, 568

visual effects, 6

whiteboard scanning, 414

z-keying, 617

Arc length parameterization of a curve, 370

Architectural reconstruction, 660

Area statistics, 113

mean (centroid), 113

perimeter, 113

second moment (inertia), 113

Aspect ratio, 46, 47

Atrous convolution, 234

Attention, 257

Augmented reality, 439, 555, 587

Auto-calibration, 566

Autoencoder, 235, 261

Automatic gain control (AGC), 66

Average pooling, 234

Axis/angle representation of rotations, 37

B-snake, 375

B-spline, 141, 375, 377, 381, 461

cubic, 120

multilevel, 655

octree, 659

Backbone network, 237

Background plate, 528

Background subtraction (maintenance), 668

Backpropagation, 214, 226

gradient checkpointing, 228

guided, 245

Backside illumination (back-illuminated) sensor

Backward convolution, 235

Bag of words (keypoints), 279

distance metrics, 281

Band-pass filter, 101

Bartlett filter, see Bilinear kernel

Barycentric coordinates, 156

Batch channel normalization, 222

Batch normalization, see Deep neural networks

Bayer pattern (RGB sensor mosaic), 74

demosaicing, 74, 515

Bayes' rule, 171, 750

MAP (maximum a posteriori) estimate, 750

posterior distribution, 750

Bayesian classification, 194

Bayesian modeling, 170, 750

MAP estimate, 171, 750

matting, 522

posterior distribution, 171, 750

prior distribution, 171, 750

uncertainty, 171

Belief propagation (BP), 175

Benchmarks, 756

Bias, 89, 447

Bias-variance tradeoff, 162

Bidirectional Reflectance Distribution Function, see BRDF

Bilateral filter, 107, 147

joint, 506

range kernel, 107

tone mapping, 502

Bilateral solver, 168

Bilinear blending, 94

Bilinear kernel, 100

Biometrics, 289

Bipartite problem, 572

Blind image deconvolution, 508

Block-based motion estimation (block matching), 448

Blocks world, 10

Blue screen matting, 91, 145, 519

Blur kernel, 60

estimation, 491, 540

Blur removal, 118, 147

Body color, 56

Boltzmann distribution, 171, 751

Boosting, 297

decision stump, 298

weak learner, 298

Border (boundary) effects, 98, 146

Boundary detection, 368

Box filter, 100

Boxlet, 104

BRDF, 54

anisotropic, 55

isotropic, 55

recovery, 675

spatially varying (SVBRDF), 675

Brightness, 89

Brightness constancy, 3, 446

constraint, 446, 452, 462

Bundle adjustment, 570

C3D network, 253

Calibration, see Camera calibration

Calibration matrix, 45

Camera calibration, 44, 83

accuracy, 590

aliasing, 491

extrinsic, 45, 552

intrinsic, 44, 545

optical blur, 491, 540

patterns, 546

photometric, 486

plumb-line method, 551, 591

point spread function, 491, 540

radial distortion, 550

radiometric, 486, 494, 538

rotational motion, 549, 590

slant edge, 491

vanishing points, 547

vignetting, 489

Camera matrix, 45, 48

Catadioptic optics, 62

Category-level recognition, 278

bag of words, 279

part-based, 282

surveys, 326

CCD, 63

blooming, 63

Central difference, 101

Chain rule

as used in backpropagation, 226

Chained transformations, 554, 571

Chamfer matching, 111

Channel-separated convolution, 234

Characteristic function, 113, 379, 653, 65

Characteristic polynomial, 731

cheirality, 559, 563

Cholesky factorization, 732

algorithm, 732

incomplete, 740

sparse, 738

Chromatic aberration, 61, 592

Chromaticity coordinates, 71

CIE L $ *a*b $*, see Color

CIE L $ *u*b $*, see Color

CIE XYZ, see Color

Circle of confusion, 60

CLAHE, see Histogram equalization

Classification, 190, 191

Bayesian, 194

CLIP, 251, 321

Closing, 111

Clustering, 205

agglomerative, 205, 387

cluster analysis, 386, 394

divisive, 205, 387

CMOS, 64

CNN stereo matching costs, 619

Co-vector, 34

Coefficient matrix, 167

Collineation, 36

Color, 69

balance, 75, 82, 144, 145

camera, 73

demosaicing, 74, 515

fringing, 516

hue, saturation, value (HSV), 77

L*a*b*, 72

L*u*v*, 72, 205, 389

primaries, 70

profile, 488

ratios, 77

RGB, 70

transform, 90

twist, 75, 90

XYZ, 70

YIQ, 76

YUV, 76

Color filter array (CFA), 74, 515

Color line model, 524

ColorChecker chart, 488

Colorization, 169

Compositing, 91, 143, 145

image stitching, 426

opacity, 91

over operator, 91

surface, 426

transparency, 91

Compression, 78

Computational photography, 483

active illumination, 507

flash and non-flash, 506

high dynamic range, 494

references, 485, 537

tone mapping, 499

Concentric mosaic, 418, 698

CONDENSATION, 377

Condition number, 739

Conditional batch normalization, 223

Conditional generative adversarial network, 264

Conditional random field (CRF), 177, 308, 613

dense, 179

fully connected, 179

Confidence calibration, 224

Confusion matrix (table), 353

Conic section, 30

Conjugate gradient descent (CG), 739

algorithm, 739

non-linear, 740

preconditioned, 740

Connected components, 113

Constellation model, 283

Content-based image retrieval (CBIR), 287, 358

Content-preserving warps, 425, 458

Continuation method, 168

Contour

arc length parameterization, 370

chain code, 370

detection, 368

matching, 371, 397

smoothing, 371

Contrast, 89

Contrastive (metric) learning, 251

Contrastive loss, 224, 225

Controlled-continuity spline, 165

Convolution, 96

kernel, 96

mask, 96

superposition, 96

Convolutional neural networks

1 × 1 convolutions, 233

Convolutional neural networks (CNNs), 231

Correlation, 96, 448

windowed, 450

Correspondence map, 455

Cramer–Rao lower bound, 410, 454, 752

Cross-entropy loss, 198, 223

multi-class, 198

Cross-validation, 162

Cube map

Hough transform, 383

image stitching, 429

Curve

arc length parameterization, 370

evolution, 371

matching, 371

smoothing, 371

Cylindrical coordinates, 418

DALL-E, 263

Data energy (term), 171, 751

Data fitting

robust, 162

Data interpolation, 155

Dataset augmentation, see Deep neural networks

Dataset bias, 249

Datasets and test databases, 756

Decimation, 122

Decimation kernels

bicubic, 123

binomial, 122, 123

QMF, 123

windowed sinc, 122

Decision theory, 191

Decision trees and random forests, 202

Deconvolution network, 245

Deep learning, 189, 214

courses, 267

history, 267

layers, 215

surveys, 267

textbooks, 267

Deep neural networks, 214

3D, 252

3D point clouds and meshes, 254

activation functions, 217

adversarial examples, 248

AlexNet, 238

architectures, 238

attention, 256

backbone, 237

backbone (trunk), 249

backpropagation, 226

batch normalization, 220

bottleneck, 235

channels, 232

convolutional neural networks, 231

dataset augmentation, 219

deconvolution, 245

dropout, 220

efficient (mobile) networks, 241

feature maps, 232

fine-tuning, 249

fully convolutional, 237

generative adversarial networks (GANs), 263

GoogLeNet, 238

group normalization, 222

He initialization, 226

head (branches), 249

instance normalization, 222

layer normalization, 222

learning rate, 229, 269

loss functions, 223

LSTMs, 255

minibatch stochastic gradient descent, 229

model zoo, 242

momentum, 230

neural architecture search (NAS), 243

optimization, 228

pre-training, 249

recurrent networks (RNNs), 255

regularization, 219

ResNet, 239

sequence modeling, 255

size and efficiency, 243

solvers, 228

spatio-temporal, 255

stereo matching, 618

stochastic gradient descent (SGD), 229

training, 228

transformer, 256

U-Net, 237

VGG, 238

visualization, 244

weight initialization, 225

weight sharing, 233

weights, 215

Delaunay triangulation, 156

Demosaicing (Bayer), 74, 515

Denoising image, 513

video, 469

Dense captioning, 322

Dense conditional random field (CRF), 179

Depth estimation monocular, 632

Depth from defocus, 646

Depth map, see Disparity map

Depth of field, 60, 81

Depth recovery, see Stereo deep networks, 618

multi-view, 620

Depthwise convolution, 234

DETR, 260

Di-chromatic reflection model, 58

Difference matting (keying), 91, 145, 520, 668

Difference of Gaussians (DoG), 125

Difference of low-pass (DOLP), 127

Diffuse reflection, 56

Diffusion anisotropic, 108

Digital camera, 63

color filter array (CFA), 74

compression, 78

Dilation, 111

Dimensionality reduction

non-linear embeddings, 211

Direct current (DC), 79

Direct linear transform (DLT), 552

Direct sparse matrix techniques, 737

Directional derivative, 102

selectivity, 103

Discrete cosine transform (DCT), 79, 117

Discrete Fourier transform (DFT), 115

Discriminant analysis

Fisher, 197

linear, 197

quadratic, 197

Discriminative models

decision trees and random forests, 202

deep neural networks, 214

feedforward networks, 214, 219

logistic regression, 198

support vector machines, 199

Discriminative random field (DRF), 178

Disparity, 44, 601

Disparity map, 601

geometric consistency, 623

multiple, 622

Disparity space image (DSI), 601

generalized, 603

Displaced frame difference (DFD), 446

Displacement field, 141

Distance from face space (DFFS), 210

Distance in face space (DIFS), 210

Distance map, see Distance transform

Distance transform, 111

Euclidean, 112

image stitching, 430

Manhattan (city block), 111

signed, 112

Domain (of a function), 89

Domain adaptation, 249

Domain scaling law, 138

Downsampling, see Decimation

Downstream task, 249

Dropout, see Deep neural networks

DSAC, see RANSAC

Dynamic programming (DP), 614

monotonicity, 615

ordering constraint, 615

scanline optimization, 615

Dynamic snake, 376

Dynamic texture, 705

Edge detection, 364, 396

boundary detection, 368

Canny, 365

chain code, 370

color, 367

Difference of Gaussian, 366

edgel (edge element), 366

hysteresis, 368

Laplacian of Gaussian, 366

linking, 368, 397

marching cubes, 366

scale selection, 366

steerable filter, 366

zero crossing, 366

Eigenface, 209

Eigenvalue decomposition, 209, 375, 729

Eigenvector, 729

Elastic deformations, 461

image registration, 461

Elastic nets, 374

Elliptical weighted average (EWA), 139

Empirical risk minimization, 191

Energy functions

regular, 173

sub-modular, 173

Energy-based models, 153, 163

Environment map, 53, 696

Environment matte, 699

Epipolar constraint, 560

Epipolar geometry, 560, 599

pure rotation, 564

pure translation, 564

Epipolar line, 599

Epipolar plane, 600, 605

image (EPI), 621, 694

Epipolar volume, 694

Epipole, 561, 599

Erosion, 111

Error rates

accuracy (ACC), 354

false negative (FN), 353

false positive (FP), 353

positive predictive value (PPV), 354

precision, 354

recall, 354

ROC curve, 354

true negative (TN), 353

true positive (TP), 353

Errors-in-variable model, 422, 734

heteroscedastic, 735

ESAC, see RANSAC

Essential matrix, 561

5-point algorithm, 562

eight-point algorithm, 561

re-normalization, 562

seven-point algorithm, 562

twisted pair, 563

Estimation theory, 745

Euclidean transformation, 33, 35

Euler angles, 37

Expectation maximization (EM), 207

Exponential twist, 38

Exposure bracketing, 494

Exposure value (EV), 61, 486

F-number (stop), 60, 82

F-score, 303, 354

F-theta lens, 52

Face detection, 295

boosting, 297

cascade of classifiers, 299

clustering and PCA, 297

neural networks, 297

support vector machines, 297

Face modeling, 663

Face recognition, 289

active appearance model, 291

eigenface, 209

elastic bunch graph matching, 290

local binary patterns (LBP), 327

local feature analysis, 290

Face transfer, 702

Facial expression recognition, 290

Facial motion capture, 663, 668, 702

Factor graph, 171, 172, 584, 751

Factorization, 14, 568

missing data, 569

projective, 570

Fast Fourier transform (FFT), 115

Fast marching method (FMM), 379

Feature descriptor, 347, 396

bias and gain normalization, 348

GLOH, 349

patch, 348

PCA-SIFT, 349

performance (evaluation), 350

quantization, 281, 358

RootSIFT, 349

SIFT, 348

steerable filter, 349

Feature detection, 335, 337, 395

Adaptive non-maximal suppression, 346

affine invariance, 346

Förstner, 340

Harris, 340

Laplacian of Gaussian, 343

MSER, 346

region, 347

repeatability, 342

rotation invariance, 344

scale invariance, 343

Feature maps in deep neural networks, 232

Feature matching, 335, 352, 396

densification, 358

efficiency, 356

error rates, 353

hashing, 356

indexing structure, 356

k-d trees, 357

locality sensitive hashing, 356

nearest neighbor, 355

strategy, 353

verification, 358

Feature tracking, 361, 396

affine, 361

learning, 362

Feature tracks, 568, 576

Feature-based alignment, 403

2D, 403

3D, 410

iterative, 406

Jacobian, 404

least squares, 403

match verification, 277

RANSAC, 409

robust, 408

Field of Experts (FoE), 175

Fill factor, 65

Fill-in, 572, 737

Filter

adaptive, 108

band-pass, 101

bilateral, 107, 147

directional derivative, 102

edge-preserving, 106, 108

guided, 109, 147

Laplacian of Gaussian, 102

median, 105

moving average, 100

non-linear, 105

separable, 99, 146

steerable, 102, 147

Filter coefficients, 96

Filter kernel, see Kernel

Finding faces, see Face detection

Fine-grained category recognition, 285

Fine-tuning deep neural networks, 249

Finite element analysis, 166

stiffness matrix, 167

Finite impulse response (FIR) filter, 95, 104

Fisher discriminant analysis, 197

Fisher information matrix, 405, 410, 746, 752

Fisheye lens, 52

Flash and non-flash merging, 506

Flash matting, 528

Flip-book animation, 438

Flying spot scanner, 648

Focal length, 46, 47, 60

Focus, 60

shape-from, 646, 679

Focus of expansion (FOE), 564

Form factor, 59

Forward mapping, see Forward warping

Forward warping, 135, 150

Fourier transform, 113, 147

discrete, 115

magnitude (gain), 114

phase (shift), 114

power spectrum, 117

two-dimensional, 115

Fourier-based motion estimation, 449

Frame interpolation, 473

Free-viewpoint video, 706, 708

Fully connected (FC) layer, 216

Fully connected conditional random field (CRF), 179

Fully convolutional network, 237

Fundamental matrix, 565

estimation, see Essential matrix

Fundamental radiometric relation, 63

Gain, 89, 447

Gamma, 90

Gamma correction, 75, 82

Gap closing (image stitching), 416

Garbage matte, 528

Gated convolution, 234

Gaussian kernel, 100

Gaussian Markov random field (GMRF), 174, 179, 510

Gaussian mixture model, 374, 377

color model, 522

expectation maximization (EM), 207

mixing coefficient, 207

Gaussian mixture models, 206

Gaussian pyramid, 123

Gaussian scale mixtures (GSM), 175

Gaussians mixture model

soft assignment, 207

Gaze correction, 612

Geman–McClure function, 446

Generalized cylinders, 10, 650, 655

Generalized mean pooling (GeM), 235

Generative adversarial networks (GANs), 263

conditional, 264

discriminator, 263

generator, 263

Generative models, 155, 170, 194, 261, 750

probabilistic generative classification, 194

Geodesic active contour, 379

Geodesic distance (segmentation), 183

Geometric image formation, 29

Geometric lens aberrations, 61

Geometric primitives, 29

homogeneous coordinates, 29

lines, 30, 31

normal vectors, 30, 31

planes, 31

points, 29, 31

Geometric transformations

2D, 32, 135

3D, 35

3D perspective, 36

3D rotations, 36

affine, 33, 36

bilinear, 35

calibration matrix, 45

collineation, 36

Euclidean, 33, 35

forward warping, 135, 150

hierarchy, 34

homography, 33, 36, 49, 413

inverse warping, 136

perspective, 33

projections, 41

projective, 33

rigid body, 33, 35

scaled rotation, 33, 36

similarity, 33, 36

translation, 32, 35

Geometry image, 656

Gesture recognition, 668

Gibbs distribution, 171, 751

Gimbal lock, 37

Gist (of a scene), 285, 314

Global illumination, 58

GooLeNet neural network, 238

Gradient checkpointing, 228

Gradient location-orientation histogram (GLOH), 349

Graduated non-convexity (GNC), 168

Graph cuts

MRF inference, 173

normalized cuts, 391

Graph-based segmentation, 388

Graphical models, 170, 171, 283

Grassfire transform, 112, 371, 430

Ground control points, 411, 562

Group normalization, 222

Guided image filter, 109, 147

Hammersley–Clifford theorem, 171, 751

Hand tracking, 670

Harris corner detector, see Feature detection

HDR imaging, see High dynamic range (HDR) imaging

He initialization rule for neural network weights, 226

Head tracking, 611

active appearance model (AAM), 291

Helmholtz reciprocity, 55

Hessian, 167, 341, 405, 406, 410, 453, 456, 733

eigenvalues, 454

image, 453, 463

inverse, 410, 454

local, 462, 463

patch-based, 456

rank-deficient, 575

reduced motion, 572

sparse, 572, 593, 737

Heteroscedastic, 405, 735

Hidden Markov model (HMM), 703

Hierarchical motion estimation, 448

High dynamic range (HDR) imaging, 494

formats, 499

tone mapping, 499

video, 499

Highest confidence first (HCF), 173

Hilbert transform pair, 103

Hinge loss, 201

Hinton diagrams, 244

Histogram equalization, 92, 145

locally adaptive, 94, 146

Histogram intersection, 281

Histogram of oriented gradients (HOG), 300

History of computer vision, 9

Hole filling, 531

Holistic 3D reconstruction, 662

Homogeneous coordinates, 29, 559

Homography, 33, 49, 413

Hough transform, 381

cascaded, 383

cube map, 383

generalized, 381

Human activity recognition, 316

Human body shape modeling, 671

Index

Human motion tracking, 668

activity recognition, 673

adaptive shape modeling, 671

background subtraction, 668

flow-based, 669

initialization, 669

kinematic models, 669

particle filtering, 671

probabilistic models, 671

Hyper-Laplacian, 168, 174, 175

Hyperlapse videos, 711

Hyperparameters, 162, 231

Ideal points, 30

Ill-conditioned problems, 157

Ill-posed (ill-conditioned) problems, 163

Illusions, 3

Image alignment

feature-based, 403, 604

intensity-based, 445

Image analogies, 532

Image blending

feathering, 432

GIST, 437

gradient domain, 435

image stitching, 430

Poisson, 435

pyramid, 132, 435

Image center, 46

Image classification, 278

Image compositing, see Compositing

Image compression, 78

Image decimation, 122

Image deconvolution, see Blur removal

Image denoising, 147, 513

Image filtering, see Filter

Image formation

geometric, 29

photometric, 53

Image gradient, 102, 109, 452

constraint, 166

Image interpolation, 119

Image matting, 518, 541

Image processing, 87

textbooks, 87, 143, 184

Image pyramid, 119, 148

Image quality assessment, 119

Image resampling, 135, 147

test images, 148

Image restoration, 118

blur removal, 118, 147

deblocking, 186

denoising, 118, 147

noise removal, 151

Image sensing, see Sensing

Image statistics, 113

Image stitching, 411

automatic, 425

bundle adjustment, 421

compositing, 426

coordinate transformations, 429

cube map, 429

cylindrical, 418, 440

deghosting, 425, 433, 441

exposure compensation, 437

feathering, 432

gap closing, 416

global alignment, 421

homography, 413

motion models, 412

panography, 405

parallax removal, 424

photogrammetry, 411

pixel selection, 430

planar perspective motion, 413

recognizing panoramas, 425

rotational motion, 414

seam selection, 432

spherical, 419

up vector selection, 423

Image Transformer, 259

Image warping, 135, 149, 449

Image-based modeling, 685

Image-based rendering, 475, 681

concentric mosaic, 698

environment matte, 699

impostors, 688

layered depth image, 688

layers, 688

light field, 693

Lumigraph, 693

modeling vs. rendering continuum, 701

multiplane image (MPI), 689

reflections, 690

sprites, 688

surface light field, 696

unstructured Lumigraph, 696

view interpolation, 683

view-dependent texture maps, 685

Image-based visual hull, 631

Image-to-image translation, 264

Implicit surface, 658

Impostors, see Sprites

Impulse response, 96

Inception module, 239

Incremental refinement

motion estimation, 449, 451

Incremental rotation, 40

Indexing structure, 356

Indicator function, 658

Inductive spatial locality bias, 257

Industrial applications, 6

Infinite impulse response (IIR) filter, 104

Influence function, 168, 408, 749

Information criteria (BIC, AIC), 162

Information matrix, 405, 410, 575, 746, 752

Inpainting, 531

Instance normalization, 222

Instance recognition, 276

geometric alignment, 277

inverted index, 358

large-scale, 358

match verification, 277

query expansion, 359

stop list, 359

visual words, 359

Integrability constraint, 643

Integral image, 103

Integrating sphere, 488

Intelligent scissors, 378

Interaction potential, 171, 172, 751

Interactive computer vision, 677

Interactive segmentation, 181

International Color Consortium (ICC), 488

Internet photos, 576

Interpolation, 119

scattered data, 155

Interpolation kernels

bicubic, 121

bilinear, 120

binomial, 120

sinc, 121

spline, 121

Intrinsic camera calibration, 545

Intrinsic images, 10

Inverse kinematics (IK), 669

Inverse mapping, see Inverse warping

Inverse problems, 3, 163

Inverse warping, 136

ISO setting, 66

Isomap, 211

Iterated conditional modes (ICM), 173

Iterative back projection (IBP), 509

Iterative closest point (ICP), 374, 411, 651

Iterative feature-based alignment, 406

Iterative sparse matrix techniques, 738

conjugate gradient, 739

Iteratively reweighted least squares, 199

(IRLS), 408, 455, 554, 749

Iteratively reweighted least squares (IRLS), 162

Jacobian, 404, 452, 554, 571, 736

image, 453

motion, 456

sparse, 572, 593, 737

Joint bilateral filter, 506

Joint domain (feature space), 389

K-d trees, 357

K-means, 206

K-nearest neighbors (kNN), 192

Kalman snakes, 376

Kanade–Lucas–Tomasi (KLT) tracker, 362

Karhunen–Loève transform, 117, 209

Kernel, 100

bilinear, 100

Gaussian, 100

low-pass, 101

Sobel operator, 101

unsharp mask, 101

Kernel basis function, 166

Kernel density estimation, 158

Kernel functions, 157

Kernel methods, 157

Kernel regression, 157, 158, 201

Keypoint detection, see Feature detection

KinectFusion, 653

Kinematic model (chain), 669

Kruppa equations, 567

L*a*b*, see Color

L*u*v*, see Color

L₁ norm, 168, 446, 463, 659

L∞ norm, 574

Lambertian reflection, 56

Laplacian Eigenmaps, 211

Laplacian matting, 525

Laplacian of Gaussian (LoG) filter, 102

Laplacian pyramid, 125

blending, 132, 148, 435

perfect reconstruction, 125

Lasso (least absolute shrinkage and selection operator), 158

Latent Dirichlet process (LDP), 284

Layered depth image (LDI), 688

Layered depth panorama, 698

Layered motion estimation, 470

reflections, 474

transparent, 474

Layout consistent random field, 308

Learning, 189

classification, 191

nearest neighbors, 192

contrastive (metric), 251

deep neural networks, 214

regression, 191

self-supervised, 249

semi-supervised, 212, 250

student-teacher, 252

supervised, 190, 191

test phase, 191

training phase, 191

unsupervised, 190, 205

weak, 250

weakly supervised, 214

Learning rate, see Deep neural networks

Least median of squares (LMS), 409

Least squares

iterative solvers, 554, 738

linear, 81, 403, 410, 445, 729, 733, 744, 747

non-linear, 406, 554, 559, 736, 748

robust, see Robust least squares

sparse, 571, 737

total, 734

weighted, 170, 405, 506, 508

LeNet-5, 231

Lens

compound, 61

nodal point, 61

thin, 60

Lens distortions, 51

calibration, 550

decentering, 52

radial, 51

spline-based, 52

tangential, 52

Lens law, 60

Level of detail (LOD), 656

Level sets, 379, 380

fast marching method, 379

geodesic active contour, 379

Levenberg-Marquardt, 407, 576, 593, 736, 765

Lidar (Light Detection and Ranging), 647

Lifting, see Wavelets

Light field

higher dimensional, 700

light slab, 694

ray space, 694

rendering, 693

surface, 696

Lightness, 72

Line at infinity, 30

Line detection, 381

Hough transform, 381

RANSAC, 383

simplification, 381, 398

successive approximation, 381, 398

Line equation, 30, 31

Line fitting, 81

uncertainty, 398

Line hull, see Visual hull

Line labeling, 10

Line process, 184, 613, 751

Line segment detector (LSD), 384

Line spread function (LSF), 491

Line support regions, 384

Line-based structure from motion, 581

Linear algebra, 727

least squares, 733

matrix decompositions, 728

references, 728

Linear blend, 89

Linear discriminant analysis (LDA), 197

Linear filtering, 95

Linear operator, 89

superposition, 89

Linear shift invariant (LSI) filter, 96

Live-wire, 378

Local distance functions, 211

Local Laplacian, 127, 149

Local Linear Embedding (LLE), 211

Local operator, 95

Locality sensitive hashing (LSH), 356

Localization, 555

Locally adaptive histogram equalization, 94

Location recognition, 555

Log likelihood, 194

Log odds, 195

Logistic regression, 196, 198

Logistic sigmoid function (curve), 195

Logit, 195

Long short-term memory (LSTM), 255

Loopy belief propagation (LBP), 175

Loss function, 223

ArcFace, 225

contrastive, 224

cross-entropy, 223

perceptual, 224

triplet, 224

Low-pass filter, 101

sinc, 101

Lumigran, 693

unstructured, 696

Luminance, 71

Lumisphere, 696

M-estimator, 162, 408, 446, 748

Machine learning, see Learning

textbooks, 267

Machine learning models

discriminative vs. generative, 198

MAGSAC, see RANSAC

Mahalanobis distance, 207, 211, 746

Manhattan world, 582

Manifold learning, 211

Manifold mosaic, 432, 718

Markov chain Monte Carlo (MCMC), 747

Markov random field, 170, 751

cliques, 172, 751

directed edges, 182

flux, 182

inference, see MRF inference

layout consistent, 308

learning parameters, 170

line process, 184, 613, 751

neighborhood, 172, 751

order, 172, 751

random walker, 183

stereo matching, 613

Marr's framework, 10

computational theory, 11

hardware implementation, 11

representations and algorithms, 11

Masked convolution, 234

Match move, 574

Matrix decompositions, 728

Cholesky, 732

eigenvalue (ED), 729

QR, 731

singular value (SVD), 728

square root, 732

Matte reflection, 56

Matting, 91, 518, 541

alpha matte, 91

Bayesian, 522

blue screen, 91, 145, 519

difference, 91, 145, 520, 668

flash, 528

GrabCut, 524

Laplacian, 525

natural, 521

optimization-based, 524

Poisson, 524

shadow, 528

smoke, 527

triangulation, 519, 528

trimap, 521

two screen, 519

video, 528

Max pooling, 234

Maximally stable extremal region (MSER), 346

Maximum a posteriori (MAP) estimate, 171, 750

Maximum margin classifier, 199

Mean absolute difference (MAD), 607

Mean average precision, 354

Mean shift, 389

Mean square error (MSE), 79, 607

Measurement equation (model), 558, 745

Measurement model, see Bayesian model

Medial axis transform (MAT), 112

Median absolute deviation (MAD), 446

Median filter, 105

Medical image registration, 461

Medical image segmentation, 310

Membrane, 165

Mesh-based warping, 140, 149

Metamer, 71

Metric learning, 211

Metric tree, 358

Minibatch stochastic gradient descent), 229

MIP-mapping, 138

trilinear, 139

Mixture of Gaussians, see Gaussian mixture model

MLESAC, see RANSAC

Model selection, 162, 413, 750

Model zoo, see Deep neural networks

Model-based reconstruction, 660

architecture, 660

heads and faces, 663

human body, 668

Model-based stereo, 661, 685

Models

Bayesian, 170, 750

forward, 3

physically based, 12

physics-based, 3

probabilistic, 3

Modulation transfer function (MTF), 69, 491

Momentum, see Deep neural networks

Monocular depth estimation, 632

Morphable model

body, 671

face, 665, 702

multidimensional, 702

Morphing, 142, 150, 683, 684

3D body, 671

3D face, 665

automated, 481

facial feature, 702

feature-based, 142, 150

flow-based, 481

video textures, 703

view morphing, 684, 719

Morphological operator, 110

Morphology, 110

Mosaic, see Image stitching

Mosaics

motion models, 412

video compression, 417

whiteboard and document scanning, 414

Motion compensated video compression, 448, 478

Motion compensation, 79

Motion estimation, 445

affine, 455

aperture problem, 453

compositional, 457

Fourier-based, 449

frame interpolation, 473

hierarchical, 448

incremental refinement, 451

layered, 470

learning, 457, 463

linear appearance variation, 454

optical flow, 461

parametric, 455

patch-based, 445, 456

phase correlation, 451

quadtree spline-based, 460

reflections, 474

rolling shutter, 468

spline-based, 459

translational, 445

transparent, 474

uncertainty modeling, 454

Motion field, 455

Motion models

learned, 457

Motion segmentation, 482

Motion stereo, 622

Moving least squares (MLS), 657

MRF inference, 173, 751

alpha expansion, 175

belief propagation, 175

expansion move, 175

graph cuts, 173

highest confidence first, 173

iterated conditional modes, 173

loopy belief propagation, 175

simulated annealing, 173

stochastic gradient descent, 173

swap move (alpha-beta), 175

Multi-frame motion estimation, 468

Multi-layer perceptron (MLP), 216

Multi-pass transforms, 140

Multi-perspective panoramas, 418, 698

Multi-perspective plane sweep (MPPS), 424

Multi-view stereo, 620

epipolar plane image, 621

evaluation, 630

initialization requirements, 630

point clouds, 625

reconstruction algorithm, 629

scene representation, 625

shape priors, 629

silhouettes, 630

space carving, 629

spatio-temporally shiftable window, 622

taxonomy, 624

visibility, 628

volumetric, 624, 626

voxel coloring, 629

Multidimensional scaling (MDS), 211

Multigrid, 741

algebraic (AMG), 388, 741

Multinomial logistic regression objective, 198

Multiplane image (MPI), 689

Multiple hypothesis tracking, 377

Multiple object tracking, 478

Multiple-center-of-projection images, 418, 698, 718

Multiresolution representation, 123

Mutual information, 448, 461

Naïve Bayes, 195

Natural image matting, 521

Nearest neighbor, 192

distance ratio (NNDR), 355

matching, see Feature matching

Negative posterior log likelihood, 171, 746, 750

Neighborhood operator, 95, 105

Neural architecture search (NAS), 243

Neural network

backbone, 242

backpropagation, 214

branches, 242

confidence calibration, 224

fine tuning, 242

for face detection, 297

head(s), 242

pre-trained, 242

trunk, 242

Neural network pooling

average, 234

generalized mean (GeM), 235

max, 234

unpooling, 235

Neural rendering, 711

depth images and layers, 713

implicit functions using MLPs, 715

texture mapped meshes and models, 713

voxel grids, 714

Neural textures, 713

Nodal point, 61, 414

Noise (sensor), 66, 488

Noise level function (NLF), 66, 82, 488, 539

Noise removal, see (enoising)118, 151

Non-linear filter, 105, 143

Non-linear least squares

seeLeast squares, 406

Non-maximal suppression, see Feature detection

Non-parametric density modeling, 389

Non-photorealistic rendering (NPR), 532

Normal equations, 404, 452, 733, 736

Normal map (geometry image), 656

Normal vector, 31

Normalized cross-correlation (NCC), 448, 479, 607

Normalized cuts, 391

intervening contour, 392

Normalized device coordinates (NDC), 43, 47

Normalized exponential, 194

Normalized sum of squared differences (NSSD), 448

Norms

$ L_{1} $, 168, 446, 463, 659

$ L_{\infty} $, 574

Novel view synthesis (NVS), 683

Nyquist rate/frequency, 68

Object detection, 295

car, 299, 327

face, 295

part-based, 300

pedestrian, 294, 299

Object tracking, 477

Object-centered projection, 50

Obstruction-free photography, 475

Occluding contours, 604

Octree reconstruction, 631

Octree spline, 461

Omnidirectional vision systeghyms, 708

One-hot encoding, 198

Opacity, 91

OpenGV, 565, 765

Opening, 111

Operator linearity, 89

Optic flow, see Optical flow

Optical flow, 461

anisotropic smoothness, 463

benchmarks and datasets, 465

coarse-to-fine, 465

combinatorial optimization, 465

constraint equation, 452

deep learning, 466

evaluation, 465

fusion move, 465

global and local, 463

Large displacement, 465

Markov random field, 465

multi-frame, 468

neural networks, 466

normal flow, 453

patch-based, 462

region-based, 472

regularization, 462

robust regularization, 463

smoothness, 462

task-oriented, 468

total variation, 463

variational, 463

Optical illusions, 3

Optical transfer function (OTF), 69, 491

Optical triangulation, 647

Optics, 59

chromatic aberration, 61

Seidel aberrations, 61

vignetting, 62, 539

Optimal motion estimation, 570

Oriented particles (points), 657

Orthogonal Procrustes, 411

Orthographic projection, 41

Osculating circle, 605

Over operator, 91

Overfitting, 159, 193

Overview, 18

Padding, 98, 146

Pairwise alignment, 403

Panography, 405, 439

Panorama, see Image stitching

Panorama with depth, 418, 603, 698

Para-perspective projection, 43

Parallel tracking and mapping (PTAM), 58

Parameter sensitive hashing, 356

Parametric motion estimation, 455

Parametric surface, 655

Parametric transformation, 135, 149

Part-based recognition, 282

constellation model, 283

Partial convolution, 234

Particle filtering, 377, 671, 747

Partition function, 198

Parzen window, 158

Patch-based motion estimation, 445

PatchMatch, 530

PatchMatch Stereo, 614

Peak signal-to-noise Ratio (PSNR), 79, 118

Pedestrian detection, 299

Penumbra, 53

Perceptual loss, 119, 224, 535

Perceptual similarity metrics, 118, 119, 224

Performance-driven animation, 363, 667, 702

Perspective n-point problem (PnP), 553

Perspective projection, 43

Perspective transform (2D), 33

Phase correlation, 451, 479

Phong shading, 57

Photo pop-up, 314

Photo Tourism, 686

Photo-mosaic, 411

Photoconsistency, 602, 628

Photometric image formation, 53

calibration, 486

global illumination, 58

lighting, 53

optics, 59

radiosity, 58

reflectance, 54

shading, 57

Photometric stereo, 643

Photometry, 53

Photomontage, 435

Physically based models, 12

Physics-based vision, 14

Pictorial structures, 10, 16, 282

Pixel transform, 89

Plücker coordinates, 32

Planar pattern tracking, 555

Plane at infinity, 31

Plane equation, 31

Plane plus parallax, 48, 459, 471, 602, 688

Plane sweep, 602, 636

Plane-based structure from motion, 582

Plenoptic function, 693

Plenoptic modeling, 684

Plumb-line calibration method, 551, 591

Point distribution model, 375

Point operator, 87

Point process, 8/

Point spread function (PSF), 68

estimation, 491, 540

Point-based representations, 657

Points at infinity, 30

Poisson

blending, 435

equations, 659

matting, 524

noise, 66

surface reconstruction, 659

Polar coordinates, 30

Polar projection, 52, 420

Polyphase filter, 120

Pop-out effect, 4

Pose estimation, 552

iterative, 554

RGB-D data, 652

Power spectrum, 117

Pre-training deep neural networks, 249

Precision, see Error rates

mean average, 354

Preconditioning, 740

Pretext task, 249

Principal component analysis (PCA), 209, 297, 375, 730, 746

face modeling, 663

generalized, 731

missing data, 569, 731

Principal point, see Image center

Prior energy (term), 171, 751

Prior model, see Bayesian model

Probabilistic generative classification, 194

Profile curves, 604

Progressive mesh (PM), 656

Projections

object-centered, 50

orthographic, 41

para-perspective, 43

perspective, 43

Projective (uncalibrated) reconstruction, 565

Projective depth, 49, 602

Projective disparity, 49, 602

Projective space, 30

PROSAC (PROgressive SAmple Consensus), 409

PSNR, see Peak signal-to-noise ratio

Pull-push algorithm, 157

Pyramid, 119, 148

blending, 132, 148

Gaussian, 123

half-octave, 127

Laplacian, 125

motion estimation, 449

octave, 123

radial frequency implementation, 132

steerable, 132

amid match kernel, 281

QR factorization, 731

Quadratic discriminant analysis, 197

Quadratic form, 166

Quadrature mirror filter (QMF), 123

Quadric equation, 30, 32

Quadtree spline

motion estimation, 460

restricted, 460

Quaternions, 39

antipodal, 39

multiplication, 40

Query by image content (QBIC), 287

Query expansion, 359

Quincunx sampling, 127

Radial basis function, 141, 157, 166, 655

Radial distortion, 51

barrel, 51

calibration, 550

parameters, 51

pincushion, 51

Radiance map, 497

Radiometric image formation, 53

Radiometric response function, 486

Radiometry, 53

Radiosity, 59

Random forests, 202

Random walker, 183

Range (of a function), 89

Range data, see Range scan

Range image, see Range scan

Range scan alignment, 651, 679

large scenes, 654

merging, 652

registration, 651, 679

segmentation, 651

volumetric, 653

Range sensing (rangefinding), 647

coded pattern, 648

light stripe, 647

shadow stripe, 648, 679

spacetime stereo, 650

stereo, 649

texture pattern (checkerboard), 648

time of flight, 649

Ranking loss, 224, 251

INLIERS, 409

preemptive, 409

progressive (PROSAC), 409

RANSAC (RANdom SAmple Consensus), 38

RAW image format, 66

Ray space (light field), 694

Ray tracing, 58

Rayleigh quotient, 392

Recall, see Error rates

Receiver Operating Characteristic

area under the curve (AUC), 354

mean average precision, 354

ROC curve, 354, 396

Recognition, 273

category (class), 278

color similarity, 287

context, 284

contour-based, 327

face, 289

instance, 276

part-based, 282

scene understanding, 284

semantic segmentation, 307

shape context, 327

Rectangle detection, 386

Rectification, 600, 635

standard rectified geometry, 601

Rectified linear unit (ReLU), 217

Recurrent neural networks (RNNs), 255

Recursive filter, 104

Reference plane, 49

Reflectance, 54

Reflectance map, 642

Reflectance modeling, 674

Reflection

di-chromatic, 58

diffuse, 56

specular, 56

Reflection layers, 474, 690

Region merging and splitting, 205, 387

Registration, see Image Alignment feature-based, 403

intensity-based, 445

medical image, 461

Regression, 155, 190, 191

Regularization, 158, 163, 460

neural network, 219

robust, 168

weight decay, 219

Regularization parameter, 165

Index

Residual error, 162, 403, 408, 409, 446, 452, 456, 463, 558, 571, 733, 739

Residual network (ResNet), 239

RGB (red green blue), see Color

Ridge regression, 158

Rigid body transformation, 33, 35

Risk minimization, 191

RMSProp, 230

Robust data fitting, 162

Robust error metric, see Robust penalty function

Robust least squares, 385, 408, 446, 748

iteratively reweighted, 408, 455, 554, 749

Robust loss function, 162

Robust penalty function, 168, 446, 454, 509, 603, 607, 608, 613, 749

Robust regularization, 168

Robust statistics, 446, 748

inliers, 409

loss function, 162

M-estimator, 162, 408, 446, 748

Rodrigues' formula, 38

Rolling shutter wobble removal, 468

Root mean square error (RMS), 79, 447

Rotations, 36

Euler angles, 37

axis/angle, 37

exponential twist, 38

incremental, 40

interpolation, 40

quaternions, 39

Rodrigues' formula, 38

Sampling, 67

Scale invariant feature transform (SIFT), 348

Scale-space, 12, 102, 126, 380

Scatter matrix, 209

Scattered data approximation, 155

overfitting, 159

underfitting, 159

Scattered data interpolation, 141, 155

Scene completion, 314

Scene flow, 624, 706

Scene understanding, 284

gist, 285, 314

Schur complement, 572, 737

Scratch removal, 531

Seam selection in image stitching, 432

Second-order cone programming (SOCP), 574

Seed and grow

stereo, 604

structure from motion, 577

Segmentation

active contours, 373

affinities, 391

binary MRF, 172, 181

CONDENSATION, 377

connected components, 113

energy-based, 181

Gaussian mixture model, 206

geodesic active contour, 379

geodesic distance, 183

GrabCut, 182, 524

graph cuts, 181

graph-based, 388

hierarchical, 388

intelligent scissors, 378

joint feature space, 389

k-means, 206

level sets, 379

mean shift, 389

medical image, 310

merging, 205, 387

minimum description length (MDL), 181

Mumford–Shah, 181

non-parametric, 389

normalized cuts, 391

probabilistic aggregation, 388

random walker, 183

snakes, 373

splitting, 205, 387

stereo matching, 616

thresholding, 110

tobogganing, 378, 388

watershed, 387

weighted aggregation (SWA), 392

Seidel aberrations, 61

Self-attention, 258

Self-calibration, 566

bundle adjustment, 568

Kruppa equations, 567

Self-supervised learning, 249

Semantic image synthesis, 264

Semantic segmentation, 307

Semi-global matching (SGM), 616, 619

Semi-supervised learning, 212, 250

transductive vs. inductive, 212

Sensing, 63

aliasing, 67, 491

color, 69

color balance, 75

gamma, 75

pipeline, 64, 487

sampling, 67

sampling pitch, 65

Sensor noise, 66, 488

amplifier, 66

dark current, 66

fixed pattern, 66

shot noise, 66

Separable filtering, 99, 146

Sequential minimal optimization (SMO), 202

Shading, 57

equation, 56

shape-from, 642

Shadow matting, 528

Shape context, 327, 372

Shape from

focus, 646, 679

photometric stereo, 643

profiles, 604

shading, 642

silhouettes, 630

specularities, 646

stereo, 595

texture, 645

Shape parameters, 291, 375

Shape-from-X, 12

focus, 12

photometric stereo, 12

shading, 12

texture, 12

Shift invariance, 96

Shiftable multi-scale transform, 132

Shutter speed, 64

Siamese network, 224

Sigmoid activation function, 217

Sigmoid function, 195

Signed distance function, 379, 651, 652, 657, 658

Silhouette-based reconstruction, 630

octree, 631

visual hull, 630

Similarity metrics

perceptual, 119

Similarity metrics (perceptual), 118

Similarity transform, 33, 36

Simulated annealing, 173

Simultaneous localization and mapping (SLAM), 583

Sinc filter

interpolation, 121

low-pass, 101

windowed, 121

Single image depth estimation, 632

Single view metrology, 548, 591

Singular value decomposition (SVD), 728

Skeletal set, 574, 577

Skeleton, 112, 371

Skew, 43, 40

Slant edge calibration, 491

Slippery spring, 374

SlowFast neural network architecture, 253

Smoke matting, 527

Smoothness constraint, 165

Smoothness penalty, 165

Snakes, 373

ballooning, 373

dynamic, 376

internal energy, 373

Kalman, 376

shape priors, 375

slippery spring, 374

Soft assignment, 207

Softmax function, 194, 198

Software, 761

Space carving

multi-view stereo, 629

Spacetime stereo, 650

Sparse flexible model, 283

Sparse matrices, 737

compressed sparse row (CSR), 737

skyline storage, 737

Sparse methods

direct, 737

iterative, 738

Spatial pyramid matching, 281

Spatially varying bidirectional reflectance distribution function (SVBRDF), 676

Spectral (weight) normalization, 223

Spectral response function, 73

Spectral sensitivity, 73

Specular flow, 646

Specular reflection, 56

Spherical coordinates, 31, 383, 419

Spherical linear interpolation, 40

Spin image, 651

Splatting, see Forward warping, 157

volumetric, 657

Spline, 156

controlled continuity, 165

octree, 461

quadtree, 460

tensor product, 156

thin plate, 165

Spline-based motion estimation, 459

Splining images, see Laplacian pyramid blending

Sprites

image-based rendering, 688

motion estimation, 470

video, 705

video compression, 417

with depth, 688

Statistical decision theory, 745, 747

Statistical models: discriminative vs. generative, 198

Steerable filter, 102, 147

Steerable pyramid, 132

Steerable random field, 174

Stereo, 595

aggregation methods, 609, 636

coarse-to-fine, 614

cooperative algorithms, 613

correspondence, 597

curve-based, 604

deep networks, 618

dense correspondence, 606

depth map, 597

dynamic programming, 614

edge-based, 604

epipolar geometry, 599

feature-based, 604

global optimization, 612, 637

graph cut, 613

layers, 617

local methods, 609

model-based, 661, 685

multi-view, 620

non-parametric similarity measures, 607

photoconsistency, 602

plane sweep, 602, 636

rectification, 600, 635

region-based, 609

scanline optimization, 615

seed and grow, 604

segmentation-based, 609, 616

semi-global matching (SGM), 616, 619

shiftable window, 622

similarity measure, 607

spacetime, 650

sparse correspondence, 604

sub-pixel refinement, 610

support region, 609

taxonomy, 597, 606

uncertainty, 611

window-based, 609, 636

winner-take-all (WTA), 610

Stereo-based head tracking, 611

Stiffness matrix, 167

Stitching, see Image stitching

Stochastic gradient descent (SGD), 173, 229

Strided convolution, 234

Structural Similarity (SSIM) index, 119

Structure from motion, 545

bas-relief ambiguity, 575

bundle adjustment, 570

constrained, 580

factorization, 568

feature tracks, 576

iterative factorization, 570

line-based, 581

multi-frame, 568

orthographic, 569

plane-based, 570, 582

projective factorization, 570

seed and grow, 577

self-calibration, 566

skeletal set, 574, 577

two-frame, 560

uncertainty, 575

Student-teacher learning, 252

Style transfer, 534

Sub-modular energy functions, 173

Subdivision surface, 655

subdivision connectivity, 656

Subspace learning, 211

Sum of absolute differences (SAD), 446, 479, 607

Sum of squared differences (SSD), 445, 479, 607

bias and gain, 447

Fourier-based computation, 450

normalized, 448

surface, 338

weighted, 447

windowed, 447

Sum of sum of squared differences (SSSD), 621

Summed area table, 103

Super-resolution, 508, 540

example-based, 510

faces, 510

hallucination, 510

prior, 510

video, 513

Superposition principle, 89

Superquadric, 658

Supervised learning, 190, 191

SuperVision neural network, 238

Support vector machine (SVM), 199, 297, 300

Support vectors, 200

Surface element (surf), 657

Surface interpolation, 655

Surface light field, 696

Surface representations, 654

non-parametric, 655

parametric, 655

point-based, 657

simplification, 656

splines, 655

subdivision surface, 655

symmetry-seeking, 655

triangle mesh, 655

surface simplification, 656

t-distributed Stochastic Neighbor Embedding (t-

Telecentric lens, 41, 646

Temporal derivative, 452, 463

Temporal texture, 705

Testing algorithms, viii

TextonBoost, 307

Texture addressing mode, 98

Texture map

recovery, 674

view-dependent, 674, 685

Texture mapping

anisotropic filtering, 140

MIP-mapping, 138

multi-pass, 140

trilinear interpolation, 139

Texture synthesis, 529, 542

by numbers, 533

hole filling, 531

image quilting, 530

non-parametric, 529

transfer, 532

Texture, shape-from, 645

Thin lens, 60

Thin-plate spline, 165

Thresholding, 110

Through-the-lens camera control, 555, 575

Tobogganing, 378, 388

Tonal adjustment, 95, 145, 146

Tone mapping, 499

adaptive, 500

bilateral filter, 502

global, 499

gradient domain, 502

halos, 500

interactive, 503

local, 500

scale selection, 503

Total least squares (TLS), 455, 734

Total variation, 168, 463, 659

Tracking

feature, 361

head, 611

human motion, 668

multiple hypothesis, 377

multiple object, 478

object, 477

planar pattern, 555

PTAM, 587

Training error, 162

Transfer learning, 243, 249

Transformers, 257

Translational motion estimation, 445

bias and gain, 447

Transparency, 91

Transposed convolution, 235

Travelling salesman problem (TSP), 374

Tri-chromatic sensing, 70

Tri-stimulus values, 70, 74

Triangular irregular network (TIN), 156

Triangulation, 558

planar, 156

Trilinear interpolation, see MIP-mapping

Trimap (matting), 521

Triplet loss, 224

Truncated signed distance function (TSDF), 652, 657

Trust region method, 736

Two-dimensional Fourier transform, 115

U-Net, 237

Uncertainty

correspondence, 405

modeling, 410, 752

weighting, 405

Underfitting, 159, 193

Unpooling, 235

Unsharp mask, 101

Unsupervised learning, 190, 205

clustering, 205

principal component analysis, 209

Upsampling, see Interpolation

Validation error, 162

Validation set, 159

Vanishing point detection, 384, 399

Hough, 385

modeling, 661

uncertainty, 399

Variable reordering, 737

minimum degree, 737

multi-frontal, 737

nested dissection, 737

Variable state dimension filter (VSDF), 573

Variational autoencoder (VAE), 262

Variational method, 164

Variational methods, 163

VGG neural network, 238

Video compression

motion compensated, 448

Video compression (coding), 478

Video denoising, 469

Video matting, 528

Video object segmentation, 476

Video objects (coding), 470

Video segmentation, 476

Video sprites, 705

Video stabilization, 457, 480

Video super-resolution, 513

Video texture, 703

Video understanding, 316

Video-based animation, 702

Video-based rendering, 701

3D video, 706

animating pictures, 705

sprites, 705

video texture, 703

virtual viewpoint video, 706

walkthroughs, 708

View correlation, 575

View interpolation, 568, 683, 719

View morphing, 568, 684, 703

View-dependent texture maps, 685

Vignetting, 62, 447, 489, 539

mechanical, 63

natural, 62

Virtual viewpoint video, 706

Vision Transformer, 259

Visual hull, 630

image-based, 631

Visual illusions, 3

Visual localization, 555

Visual object tracking, 477

Visual odometry, 583

Visual place recognition, 555

Visual search, 287

Visual similarity (search), 287

Visual words, 279, 358, 359

Visual-inertial odometry, 585

Vocabulary tree, 358

Volumetric 3D reconstruction, 624

Volumetric performance capture, 708

Volumetric range image processing (VRIP), 65

Volumetric representations, 658

Voronoi diagram, 432

Voxel coloring multi-view stereo, 629

VQ-VAE, 262

Watershed, 387, 389

basins, 387, 389

oriented, 388

Wavelets, 128, 149

compression, 149

lifting, 129

overcomplete, 128, 132

second generation, 131

self-inverting, 132

tight frame, 128

weighted, 131

Weak learning, 250

Weakly supervised learning, 214

Weaving wall, 605

Weight decay, 158, 219

Weight initialization, see Deep neural networks

Weight sharing, 233

Weight standardization, 222

Weighted least squares (WLS), 170, 503

Weighted prediction (bias and gain), 447

White balance, 75, 82

Wiener filter, 117

Wire removal, 531

Wrapping mode, 98

XYZ, see Color

Zippering, 652