1 2 2 HANDBOOK OF COMPUTER VISION AND APPLICATIONS Volume Signal Processing and Pattern Recognition Bernd Jähne Horst Haußecker Peter Geißler ACADEMIC PRESS Handbook of Computer Vision and Applications Volume Signal Processing and Pattern Recognition Handbook of Computer Vision and Applications Volume Signal Processing and Pattern Recognition Editors Bernd Jähne Interdisciplinary Center for Scientific Computing University of Heidelberg, Heidelberg, Germany and Scripps Institution of Oceanography University of California, San Diego Horst Haußecker Peter Geißler Interdisciplinary Center for Scientific Computing University of Heidelberg, Heidelberg, Germany ACADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto This book is printed on acid-free paper Copyright © 1999 by Academic Press All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher The appearance of code at the bottom of the first page of a chapter in this book indicates the Publisher’s consent that copies of the chapter may be made for personal or internal use of specific clients This consent is given on the condition, however, that the copier pay the stated per-copy fee through the Copyright Clearance Center, Inc (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U.S Copyright Law This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale Copy fees for pre-1999 chapters are as shown on the title pages; if no fee code appears on the title page, the copy fee is the same as for current chapters ISBN 0-12-379770-5/$30.00 ACADEMIC PRESS A Division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, CA 92101-4495 http://www.apnet.com ACADEMIC PRESS 24-28 Oval Road, London NW1 7DX, UK http://www.hbuk.co.uk/ap/ Library of Congress Cataloging-In-Publication Data Handbook of computer vision and applications / edited by Bernd Jähne, Horst Haussecker, Peter Geissler p cm Includes bibliographical references and indexes Contents: v Sensors and imaging — v Signal processing and pattern recognition — v Systems and applications ISBN 0–12–379770–5 (set) — ISBN 0–12–379771-3 (v 1) ISBN 0–12–379772–1 (v 2) — ISBN 0–12–379773-X (v 3) Computer vision — Handbooks, manuals etc I Jähne, Bernd 1953– II Haussecker, Horst, 1968– III Geissler, Peter, 1966– TA1634.H36 1999 006.3 — dc21 98–42541 CIP Printed in the United States of America 99 00 01 02 03 DS Contents Preface xi Contributors xiii Introduction B Jähne 1.1 Signal processing for computer vision 1.2 Pattern recognition for computer vision 1.3 Computational complexity and fast algorithms 1.4 Performance evaluation of algorithms 1.5 References I Signal Representation Continuous and Digital Signals B Jähne 2.1 Introduction 2.2 Continuous signals 2.3 Discrete signals 2.4 Relation between continuous and discrete signals 2.5 Quantization 2.6 References Spatial and Fourier Domain B Jähne 3.1 Vector spaces and unitary transforms 3.2 Continuous Fourier transform (FT) 3.3 The discrete Fourier transform (DFT) 3.4 Fast Fourier transform algorithms (FFT) 3.5 References Multiresolutional Signal Representation B Jähne 4.1 Scale in signal processing 4.2 Scale filters 4.3 Scale space and diffusion 4.4 Multigrid representations 4.5 References v 10 10 13 23 30 34 35 35 41 51 57 66 67 67 70 76 84 90 vi Contents II Elementary Spatial Processing Neighborhood Operators B Jähne 5.1 Introduction 5.2 Basics 5.3 Linear shift-invariant filters 5.4 Recursive filters 5.5 Classes of nonlinear filters 5.6 Efficient neighborhood operations 5.7 References 93 Principles of Filter Design B Jähne, H Scharr, and S Körkel 6.1 Introduction 6.2 Filter design criteria 6.3 Windowing techniques 6.4 Filter cascading 6.5 Filter design as an optimization problem 6.6 Design of steerable filters and filter families 6.7 References Local Averaging B Jähne 7.1 Introduction 7.2 Basic features 7.3 Box filters 7.4 Binomial filters 7.5 Cascaded averaging 7.6 Weighted averaging 7.7 References 94 94 98 106 113 116 124 125 125 126 128 132 133 143 151 153 Interpolation B Jähne 8.1 Introduction 8.2 Basics 8.3 Interpolation in Fourier space 8.4 Polynomial interpolation 8.5 Spline-based interpolation 8.6 Optimized interpolation 8.7 References 153 154 158 163 167 173 174 175 Image Warping B Jähne 9.1 Introduction 9.2 Forward and inverse mapping 9.3 Basic geometric transforms 9.4 Fast algorithms for geometric transforms 9.5 References 175 176 180 182 187 190 192 193 193 194 195 199 206 vii Contents III Feature Estimation 10 Local Structure B Jähne 10.1 Introduction 10.2 Properties of simple neighborhoods 10.3 Edge detection by first-order derivatives 10.4 Edge detection by zero crossings 10.5 Edges in multichannel images 10.6 First-order tensor representation 10.7 References 209 11 Principles for Automatic Scale Selection T Lindeberg 11.1 Introduction 11.2 Multiscale differential image geometry 11.3 A general scale-selection principle 11.4 Feature detection with automatic scale selection 11.5 Feature localization with automatic scale selection 11.6 Stereo matching with automatic scale selection 11.7 Summary and conclusions 11.8 References 12 Texture Analysis T Wagner 12.1 Importance of texture 12.2 Feature sets for texture analysis 12.3 Assessment of textural features 12.4 Automatic design of texture analysis systems 12.5 References 13 Motion H Haußecker and H Spies 13.1 Introduction 13.2 Basics: flow and correspondence 13.3 Optical flow-based motion estimation 13.4 Quadrature filter techniques 13.5 Correlation and matching 13.6 Modeling of flow fields 13.7 Confidence measures and error propagation 13.8 Comparative analysis 13.9 References 14 Bayesian Multiscale Differential E P Simoncelli 14.1 Introduction 14.2 Differential formulation 14.3 Uncertainty model 14.4 Coarse-to-fine estimation 14.5 Implementation issues 14.6 Examples 14.7 Conclusion 14.8 References 239 240 240 247 251 262 265 269 270 275 276 278 299 306 307 309 Optical Flow 210 210 213 223 226 227 238 310 312 321 345 353 356 369 373 392 397 397 398 400 404 410 414 419 420 viii Contents 15 Nonlinear Diffusion Filtering J Weickert 15.1 Introduction 15.2 Filter design 15.3 Continuous theory 15.4 Algorithmic details 15.5 Discrete theory 15.6 Parameter selection 15.7 Generalizations 15.8 Summary 15.9 References 423 16 Variational Methods C Schnörr 16.1 Introduction 16.2 Processing of two- and three-dimensional 16.3 Processing of vector-valued images 16.4 Processing of image sequences 16.5 References 17 Stereopsis - Geometrical H A Mallot 17.1 Introduction 17.2 Stereo geometry 17.3 Global stereopsis 17.4 References 451 images and Global Aspects 451 455 471 476 481 485 18 Stereo Terrain Reconstruction by Dynamic Programming G Gimel’farb 18.1 Introduction 18.2 Statistical decisions in terrain reconstruction 18.3 Probability models of epipolar profiles 18.4 Dynamic programming reconstruction 18.5 Experimental results 18.6 References 19 Reflectance-Based Shape Recovery R Klette, R Kozera, and K Schlüns 19.1 Introduction 19.2 Reflection and gradients 19.3 Three light sources 19.4 Two light sources 19.5 Theoretical framework for shape from 19.6 Shape from shading 19.7 Concluding remarks 19.8 References 424 425 433 436 439 441 444 446 446 485 487 499 502 505 505 509 514 520 524 528 531 shading 532 539 552 559 571 574 586 587 20 Depth-from-Focus P Geißler and T Dierig 20.1 Introduction 20.2 Basic concepts 20.3 Principles of depth-from-focus algorithms 591 592 593 595 ix Contents 20.4 20.5 20.6 20.7 IV Multiple-view depth-from-focus Dual-view depth-from-focus Single-view depth-from-focus References 596 601 608 622 Object Analysis, Classification, Modeling, Visualization 21 Morphological Operators P Soille 21.1 Introduction 21.2 Basics 21.3 Morphological operators 21.4 Efficient computation of morphological operators 21.5 Morphological image processing 21.6 References 627 22 Fuzzy Image Processing H Haußecker and H R Tizhoosh 22.1 Introduction 22.2 Why fuzzy image processing? 22.3 Fuzzy image understanding 22.4 Fuzzy image processing systems 22.5 Theoretical components of fuzzy image processing 22.6 Selected application examples 22.7 Conclusions 22.8 References 23 Neural Net Computing for Image Processing A Meyer-Bäse 23.1 Introduction 23.2 Multilayer perceptron (MLP) 23.3 Self-organizing neural networks 23.4 Radial-basis neural networks (RBNN) 23.5 Transformation radial-basis networks (TRBNN) 23.6 Hopfield neural networks 23.7 References 628 629 637 659 664 678 683 684 691 692 699 702 714 721 722 729 24 Graph Theoretical Concepts for Computer Vision D Willersinn et al 24.1 Introduction 24.2 Basic definitions 24.3 Graph representation of two-dimensional digital images 24.4 Voronoi diagrams and Delaunay graphs 24.5 Matching 24.6 Graph grammars 24.7 References 729 730 736 740 743 747 751 753 754 754 760 762 775 780 786 25 Shape Reconstruction from Volumetric Data R Eils and K Sätzler 25.1 Introduction 25.2 Incremental approach 791 791 794 928 autoregressive texture features 295 autoregressive-moving average process 106 auxiliary variables 467 average gray-level invariance 434, 440 averaging mask 437 B B-splines 187 backpropagation 732 backward difference approach 573 backward diffusion 429 backward-backward FDS 573 backward-forward FDS 573 bandwidth-duration product 48 bandlimited signal 27 bandpass decomposition 82, 87 bandpass filter 70, 126 bandstop filter 126 base characteristics 577 basis image 36 Bayesian classifier 819, 823, 824, 844, 852 Beckmann-Spizzichino model 545 benchmark 276 bias variance trade-off 851 bidirectional reflectance-distribution function 539 bifurcation 566 binomial operator 119 BioImage database 910, 921 bit reversal 59 bitwise operator 661 black level 538 blank wall problem 399 blob detection 257 blob separation 677 blooming 537 body reflection 545 body reflection color 546 Boolean logic 689 Boolean operator 689 box filter 158 box function 50 Index brightness change constraint equation 313 brightness constancy constraint equation 398 Brillouin zone 27 butterfly operation 60 C canonical coordinates 362 catchment basin 674 Cauchy problem 572 causal filter 106, 127 CCC 912 center morphological 672 center of area 690, 702 central moment 435 charge coupled device 536 Chen’s texture features 285 chessboard distance 18 circuit 757 city block distance 18 classification 730, 821–823, 825, 828, 835, 850, 892, 899, 902 clipping 536, 898 clique 756 closing 643 by reconstruction 655 intersection of 669 top-hat by 646 cluster 708 CNN 734 co-occurrence histogram 295 co-occurrence matrix 279, 295 coarse-to-fine estimation 406 coarse-to-fine matching 265 code Freeman 661 codebook 739 codewords 739 coding interval 662 coffee beans 677 coherence 432 coherence direction 432 coherence-enhancing diffusion vector-valued 445 coherency measure 237 Index color histograms 548 color image segmentation 475 combination of MM filters parallel 668 sequential 669 Compact Confocal Camera 912 complementation 631 complex exponential 107 complex polynomial 107 component of a graph 757 component velocity 352 computation time 299 computational binocular stereo 506 computational complexity computer generated image computer graphics computer vision concept 860 modified 862 primitive 859, 863 conditional dilation 650 confidence map 523 confidence measures 321, 369 connected 632 connected region 19 connectedness 696, 697 consistency measure for corner detection 264 for stereo matching 266 constraint line 313 continuity equation 425 continuous dependence 440 continuous least squares 322 contrast local 666 morphological 673 contrast adaptation 714 contrast parameter 429 control module 858, 865, 868 control surface 707 convergence 435, 441 convex (concave) 584 convex skirt 585 convex/concave surfaces 562 convolution 24, 38, 234, 635 convolution mask 46 convolution neural network 734 convolution theorem 46, 56 929 Cooley-Tukey algorithm 61 corner 231 corner detection 259 corner localization 262 corner measure 337 correlation 499, 706 correlation method 320 correspondence 320 correspondence problem 320 covariance 665 covariance matrices 370 covariance matrix 370 critical assumptions 534 cross correlation 354 cross section 630 cross-correlation function 354 cubic B-spline interpolation 187 cut 757 cutset 757 cycle of a face 759 cyclic 212 cyclic convolution 123 D Dapeng texture features 295 dark current 538 data set 300 data snooping 369 database 908 BioImage 910, 921 Microsoft Access 917 ORDBMS 923 query 910 relational 908 size 918 structure 912 system requirements 917 Daubechies wavelet 286 DaVinci stereopsis 487 decimation-in-frequency FFT 62 decomposition logarithmic 661 threshold 630 defuzzification 690, 706 degree of a vertex 755 Delaunay graph 791 shape from contours 791, 797 applications 802 930 classification of tetrahedra 799 hierachical contours 797 hierarchical contours 801 multiple sections 801 topological prerequisites 798 shape representation 791 skeleton 801 tetrahedral object representation 797 weighted 807 computation of components 809 DEM 506 depth 550 depth from focus 592 depth map 535, 550 derivative filter 128, 234, 410 detection 817 deterministic annealing 455 dichromatic plane, color-signal plane 547 dichromatic reflection model 546 DICOM 911 difference histogram 282 difference of Gaussian 224, 225, 228 difference of Gaussian filter 228 difference operator 223 differential invariant 242 for quasi quadrature 261 homogeneous 250 scaling property 250 differential scale space 82, 86 differential stereo matching 265 diffuse 545 diffuse reflecting surface 541 diffuse step edge 252, 259 diffusion coherence-enhancing 432 color images 444 discrete theory 439 edge-enhancing 431 forward-backward 428 homogeneous 425 in higher dimensions 444 inhomogeneous 425 Index linear 425 nonlinear 423, 424 physics 425 tensor 434 diffusion coefficient 78 diffusion equation 240, 425 diffusion filter stopping time 444 diffusion model nonlinear isotropic vector-valued 445 diffusion tensor 425 diffusivity 425, 428 digital elevation model 506 digital image 760 size of a 760 digital image restoration 749 digital object 19 digital parallax map 506 digital surface model 506 digital terrain model 506 dilation 358, 638 conditional 650 fast algorithm 660 geodesic 649 dimension 10 direct linear relation 536 directio-pyramidal decomposition 88 direction 212 direction analysis 666 direction of illumination 533 directional derivative 228, 241 in preferred coordinate system 243 discrete scale space 83 discrete-space Fourier transform 106 discretization 459 disk digital approximation 636 disparate shading 487 disparity 485, 491 disparity map 487 dispersion 341 displacement vector field 198 distance 633 chamfer 663 chess board 633 Index city-block 633 Euclidean 633 function 633, 677 and erosion 640 geodesic 656 transform 633 distance measure 354 distance minimization 354 distance transform fast algorithm 659 divergence 358 DoG 224, 225, 228 double subgraph isomorphism 777 DPM 506, 509–511, 516, 523, 525 DSM 506, 509, 510, 523 DTM 506 dual base 26 dual graph combinatorial 758 geometrical 759 dual line 544 duality 635 DVF 198 dynamic programming stereo 509 dynamic programming terrain reconstruction 520, 528 dynamic range 536 E 231, 754 end vertex of 755 independent 777 of a graph 632 pendant 755 edge detection 251, 426, 428, 612, 716 edge enhancement 429 edge enhancing 430 edge measure 337 edge strength measure 252, 261 edge surface 252 eigenvalue 37, 331 eigenvalue analysis 334, 351 eigenvalue problem 230, 331 eigenvector 37, 331 edge 931 eikonal equation 574 elongatedness 704 ELS 334 EM algorithm 845, 846 emittance angle 542 end vertex of an edge 755 energy 346 energy function 840 energy functionals 444 entropy 435, 705 epipolar line 492, 510, 512 epipolar profile 510, 512, 514 epipolar transformation 493 equal-height contour 581 erosion 637 and distance function 640 fast algorithm 660 geodesic 650 error-correction learning 743 Euclidean distance 18 Euclidean norm 138 even symmetry 155 expansion operator 87 expectation maximization algorithm 845, 847 extended least squares technique 334 extensivity 635 extrapolating extension 123 extremum 652 extremum principle 434, 440 F 759 finite 759 infinite 759 fast algorithm fast Fourier transform 57 fast marching level set method 582 feature feature detection 251 feature extraction 468 feature map 736 feature relevance 745 feature sets for texture analysis 278 feature-based matching 354 face 932 feature-localization 262 FEM 458 FFT 57 FFT, decimation-in-frequency 62 FFT, multidimensional 63 Fick system 495 Fick’s law 425 field-of-view 507 field-programmable gate array 118 Filippov 574 filter alternating sequential 670 close-open 669 design 667 median 114 open-close 669 rank-value 114 filter design 425 filter operation 46 filter, an infinite-duration impulse response 108 filter, finite-duration impulse response 108 fingerprint enhancement 432 finite difference method 436 finite difference scheme 572 finite element method 458, 459 finite-duration impulse response 108 FIR 108 first-order derivative filter 134 fit-and-miss 656 flooding simulation 675 flow estimation 265 flux function 429 focus series 595 forward difference approach 572 forward diffusion 429 forward mapping 194, 195 forward-backward diffusion 429 forward-backward FDS 573 forward-forward FDS 573 four-point mapping 196 Fourier domain 316 Fourier ring 52 Fourier texture features 292 Fourier transform 37, 41, 43 Fourier transform pair 41, 49 Index FOV 507 FPGA 118 fractal texture feature 289 Frankot-Chellappa algorithm 551 frequency estimation 260 function Gaussian 741 radially-symmetric 741 functions 549 fuzzification 706 fuzzy 684 fuzzy clustering 708 fuzzy compactness 703 fuzzy correlation 706 fuzzy dilation 709 fuzzy entropy 705 fuzzy erosion 709 fuzzy grammar 714 fuzzy Hough transform 721 fuzzy inference 706 fuzzy integral 710 fuzzy logic 686, 689 fuzzy measure 710 fuzzy morphology 709 fuzzy sets 685, 686 fuzzy singleton 687 G Gabor filter 71, 294, 346 Gabor wavelet 294 Galloway’s texture features 284 gamma correction 537 gamma value 33, 537 Gauss-Markov conditions 369 Gauss-Seidel iteration 327, 328 Gauss-Seidel method 368 Gaussian function 741 Gaussian kernel 240 Gaussian potential function unit 744 Gaussian pyramid 84, 85, 298 Gaussian sphere 535 general Lambertian surface 542 generalized aperture problem 314, 356 generalized coordinates 362 generalized gradient 363 generalized initial curve 578 Index 933 generalized least-squares 369 genuine Lambertian surface 534 geodesic dilation 649 distance 656 erosion 650 skeleton by influence zones 656 geodesic transform fast algorithm 663 geodesics 633 geometric distortions 507 geometric texture features 284 geometry of binocular space 487 geometry pipeline 882 Gibbs distribution 454 Gibbs field 840 global integration method 551 global smoothness 326 global stereopsis 499 GPFU 744 gradient 398 external 641 internal 641 morphological 641 gradient histogram 298 gradient map 550 gradient space 543 gradient vector 213 gradient-descent procedure 743 granulometry 646 computation of 662 graph 754 acyclic 760 combinatorial dual of a 758 connected 756 definition 632 embeddable 758 geometrical dual of a 759 planar 759 planar embedding of a 759 plane 759 graph isomorphism 776 Green’s function 101 grid 632 H Haralick’s texture features Hardley transform 65 281 heat equation 425 heat transfer 425 Heidelberg raytracer approach 889 height 535 height map 550 Helmholtz system 495 Hering coordinates 488 Hessian 325, 373 hexagonal lattice 162 hidden layer 730 hidden Markov model 820 hidden variable 848 hierarchical contours 801 high-pass filter 126 Hilbert filter 128, 135, 345 Hilbert space 37 Hilbert transform 72 histogram 818 moving 661 hit-or-miss 656 holes removal binary 652 homogeneous diffusion 425 homogeneous system 24 Hopfield neural network 747 horizontal disparity 486, 490, 506 horopter 492, 496 hybridly reflecting surfaces 545 hyperbolas of Hillebrand 489 hyperbolic point 563 hyperbolic tangent 50 hyperellipsoid 373 hyperpixel 17 hyperspectral 11 hyperspectral imaging I idempotence 634 IIR 108 ill-conditioned 373 ill-posedness 430 illumination direction 538 image 2-D 760 and PDE 455 noisy-blurred 749 image analysis 743 934 image border 652 image coding 743 image content 923 image enhancement 424 image format DICOM 911 TIFF 908 image grid 550 image irradiance 536 image irradiance equation 534, 539, 548 image partitioning 453 image restoration 424, 469 image segmentation 453, 468 image sequence image structure representation by dual graphs 761 imperfection 690 impulse response 101, 108 incident angle 542 increasingness 635 index of area coverage 704 index of fuzziness 705 index theory 585 inertia tensor 233 inference 820, 825 inference engine 707 infinite-duration impulse response 108 influence function 367 influence zone 633 geodesic 656 inhomogeneous diffusion 425 inner product 36, 234 innovation 324 input layer 730 instance 860 instantiation path 866 integrability condition 549 integration of vector field 550 integration path 550 integration scale 432, 443 integration scale parameter 244 intensity-based model 818 interest operator 432 interface reflection 545 interface reflection color 546 interpolation 29, 175 Index cubic B-spline 187 in Fourier space 180 linear 182 optimized 190 polynomial 184 spline-based 187 interpolation condition 179 interpolation filter 128 intersection 631 invariance 242 invariant function 362 inverse 3S PSM 539 inverse Fourier transform 41, 43 inverse mapping 194, 195 inverse perspective mapping 500 irradiance 1, 533 irregular grids 903 isoirradiance curves 544 isomorphism double subgraph 777 subgraph 776 double 777 isoradiance curves 544 isotropic 425 isotropic diffusion regularized 436 isotropic nonlinear diffusion 427 isotropy 18 J Jacobi method 334 Jacobian matrix 226, 371 K Kaˇanov method 466 c kernel 51 kernel of weights 734 kernel, separable 53 Kirsch operator 289 knowledge declarative 862 procedural 862 Kohonen map 736 Kullback-Leibler statistics 846 L laboratory information management system 908 Index Lagrange multiplier 330 Lagrange parameter 330 Lambert’s cosine law 534, 541 Lambertian reflectance map 544 Lambertian reflector 541 Lambertian surfaces 535, 542 Laplace of Gaussian 224, 612 Laplace operator 224 Laplacian operator 82, 240, 257 Laplacian pyramid 84, 86 lattice of neurons 736 lattice vector 14, 17 lattice vectors 100 Laws’ texture features 291 layered texture 231 learning 849 error-correction 743 learning-rate parameter 738 least squares approach 332 least squares technique extended 334 level-crossing 435 Lie algebra 360 Lie group 360 Lie group of transformations 361 lighting factor 895 LIMS 908 line periodic 636 linear 537 linear diffusion 425 linear image irradiance equation 572 linear interpolation 182 linear orthogonal l2 approximation 332 linear reflectance map 543 linear SFS 571 linear shift-invariant filter 214 linear shift-invariant operator 38, 99 linear symmetry 210, 232, 325 linear system theory linear time-invariant operator 99 linearization 466 linguistic variables 688 Listing system 495 LMS algorithm 743 935 local amplitude 73 local integration techniques 550 local orientation 210, 232, 373 local phase 73 local scale parameter 244 local texture features 287 local wave number 69, 76 LoG 224, 612 log-polar coordinate system 40 logarithmic decomposition 661 logarithmic scale space 81 lognormal 76 lognormal function 350 look-up table solution to 3S PSM 554 Lorentzian function 50 loss function 822 low level motion 319 low-pass filter 126 LS 332 LSI 99 LTI 99 Lyapunov functional 434, 442 Lyapunov sequence 440 M M-estimator 367 machine vision 276 MAP 402 marching cubes 884 marker function 676 marker image choice of 651 Markov chain 514, 517, 518 Markov random field 294, 454, 818, 837 mask 94 mask image choice of 651 matching 777 in a graph 777 maximal 777 maximum 777 perfect 777 mathematical morphology 628 maximal matching 777 maximizing 354 maximum a posteriori estimate 402 936 maximum filter 114 maximum intensity projection 897 maximum matching 777 maximum norm 139 mean of maxima 690 mean of maximum 702 measurement 665 medial filter 661 median filter 114 medical diagnosis 732 membership function 686 mesh 759 method of characteristic strips 577 metric 633 microscope 908 compact confocal camera 912 confocal 909, 917 LSM410 912 LSM510 912 user interface 918, 919 minima imposition 653, 676 regional 675 algorithm 663 minimal motion 318 minimization algorithm 466 minimum regional 653 minimum filter 114 minimum-maximum principle 77 missing information principle 845 mixture density 832 MLP 730 MM 628 model 859, 862 model density 825 model generation automatic 819 models vector-valued 444 Moiré effect 28 monocular occlusion 487 monotonicity preserving 430 Monte Carlo 877 morphological filter 114, 667 Index morphological gradient 677 morphology 628 motion motion boundary 476 motion constraint equation 265, 313 motion field 310, 397, 476 MRF 837 MRT 897 multichannel image 444 multichannel signal 12 multilayer perceptron 730 multiresolution representation 68, 84 multiresolutional image processing 87 multiresolutionaldata structure multiscale 406, 412 multiuser system 911 N N-jet representation 241 naive Bayes 850 neighborhood 19, 674, 838 neighborhood function 737, 738 neighborhood operation neighborhood, 4- 19 neighborhood, 8- 19 neural connection 730 neural network 729 neuron 730 winning 737 neuron allocation automatic 746 neuron state 747 neurons 730 neutral interface reflection model 547 noise 904 homogeneous 12 zero-mean 12 noise scale 431, 443 noise suppression 469 noisy-blurred images 749 noncharacteristic condition 578 nonenhancement property of local extrema 247 nonlinear 537 Index nonlinear classification 731 nonlinear diffusion 424, 455 nonlinear diffusion filter 425 nonlinear relaxation 466 nonlinear signal processing nonmaximum suppression 251 normal flow 313, 402 normal optical flow 318 normal velocity 352 normalized convolution 115, 173, 340, 370 normalized derivative 248, 260 scaling property 250 normalized residual 263, 266 null space 230 Nyquist 154 O object recognition 277, 828 object relational database 923 object segmentation 277 object surface geometry 534 obstacle avoidance 500 OpenGL 881 opening 642, 667 algebraic 645 by reconstruction 654 fast algorithm 662 function 662 top-hat by 646 union of 669 operations on fuzzy sets 686 operator notation 96 optical character recognition 732 optical flow 310, 398, 476 optical transfer function 24 optimization method 740 optimized interpolation 190 ordering relationships between images 631 for image transformations 631 orientation 212 orientation analysis 315 orientation disparity 487 orientation vector 212, 236 oriented smoothness 327 oriented texture 231 orthonormal base 36, 51 937 orthonormality relation outer product 53 outlier 366 output layer 730 over-fitting 824 36 P Panum’s fusional area 500 parallel computer 441 parallel edges 755 parameter estimation 819, 824, 825, 845, 847 parameter selection 441 parameter vector 11 Parseval’s rule 349 Particle model 878 partition 757 Pascal’s triangle 163 passband 126 path 19, 632 in a graph 756 end vertices 756 length 756 of steepest slope 674 pattern classification pattern spectrum 647 peeling Euclidean 661 pel 13 pendant edge 755 vertex 755 perceptron 730, 732 perfect matching 777 performance analysis of computer vision algorithms performance characterization 299 performance evaluation perimeter 703 periodic extension 123 Perona-Malik filter 427 contrast parameter 442 Perona-Malik paradox 430 perspective transform 193, 196 phase 38, 74, 351, 352 phase angle 542 phase of Fourier component 38 Phong model 546 938 photogrammetric stereo 592 photometric angle 542 photometric distortion 507 photometric stereo 532 photorealistic rendering 176 picture element 13 pixel 13 pixel pipeline 883 planar embedding of a graph 759 planar graph 759 plane graph 759 point correspondence 197 point operation 4, 94, 234 point spread function 24, 100, 108, 594 point-wise maximum 631 minimum 631 polar separable 75, 349 pole 112 polygon regular 14 polygon primitives 893 polynomial interpolation 184 pose estimation 817, 821, 823–825, 827, 828 positivity 440 potential function 840 power spectrum 40 self-similar 251 pre-knee circuit 536 preprocessing 822 primitive cell 14, 177 principle of superposition 98 prior knowledge 817, 819 probabilistic model 817–819, 852 profile 10 projection of scene objects 534 projection plane 880 propagation rule 730 PSF 24, 594 PSM 532 pyramid 406, 412 pyramidal decomposition 293 pyramidal texture features 293 Index Q quadratic scale space 81 quadrature filter 294, 346 quadrature filter pair 260 quantitative image analysis Voronoi diagram 802 application 811 surface estimate 810 quantization 10, 24, 30 quantization error 31 quantum mechanics 37 queue 661 priority 677 R radial-basis functions 740 radial-basis neural network 740 radially-symmetric function 741 radiance radiosity method 877 radix-4 FFT algorithm 61 rank 230 rank filter 661 rank-value filter 114 ray-casting 884 ray-tracing 878 RBF 740 RBNN 740 RDBMS 908 real-world image receptive field 734 reciprocal 49 reciprocal base 26 reciprocal lattice 26 recognition 817 recognition rate 299 reconstruction 650 by dilation 650 by erosion 650 fast morphological 663 recursive algorithm 660 recursive filter 106, 127 reflectance map 533, 543 reflection properties 533 refractive index 910 region adjacency graph 760 region of support 94 region-based matching 354 regional extremum 652 Index regional minimum 653 regression 821, 824, 825 regression function 823 regression problem 823 regular polygon 14 regularization 430 relational database management system 908 relative resolution 40 relaxation filter 136 removal of an edge 756 rendering equation 876 rendering kernel function 896 representation-independent notation 97 residual 322, 324 residual error vector 332 resolution 904 restoration 433, 469 RF stable 574 ridge detection 255 ridge strength measure 256, 261 ridge surface 256 Rjabenki 574 Roberts operator 217 robust estimation 367 robust statistics 366 rooted tree 760 rotation 202, 358 run-length 283 running mean 158 S sampled motion 319 sampling 10 sampling theorem 27, 84, 177 temporal 318 saturated vertex 777 scalar product 36, 234 scale 3, 76 scale invariance 77 scale selection 435 for feature detection 249 for feature localization 263 for stereo matching 265 scale space 69, 77, 240, 424 scale-space derivative 241 scale-space edge 251 939 scale-space extrema 257 scale-space representation 240 scale-space ridge 256 scale-space theory 240 scaling 200 scatter matrix 432 second-moment matrix 432 second-order statistics 279 segmentation 468, 822 function 675 initial 858 marker-controlled 675 self-duality 635 self-loop 755 self-organizing map 736 self-shadow line 544 semantic network 862 consistent 862 cycle-free 862 semi-group property 77 sensor 534 separable filter 108 separable kernel 53 separation 677 sequential algorithm for discrete distance functions 659 for the reconstruction 663 set difference 631 set of modality 861 SFS 532 shadowing approaches 887 shadows 903 shape from contours applications 802 bifurcations 801 holes 801 multiple sections 801 refinements 801 shape from contours Delaunay graph 791 hierarchical contours 801 topological prerequisites 798 shape from shading 532, 592 shape from voxels Voronoi diagram 791 shape matrix 741 940 shape representation Delaunay graph 791 Voronoi diagram 791 shear 358 shift operator 37, 99 shift theorem 37, 56, 70, 181 shift-invariant system 24 sifting 667 sigmoid nonlinearity 734 sign function 50 signal processing linear signal-to-noise ratio similarity measure 354 similarity terms 444 simple neighborhood 210, 228 single-view shape recovery 550 singular point 584 skeleton by influence zones 634 geodesic 656 slant angle 557 smoothing filter 234 smoothness 434 smoothness constraint 399 Sobel operator 118, 219, 223, 289 spatial coherency measure 337 spatial domain 67 spatial width 734 spatiotemporal energy 346 spatiotemporal frequency domain 316 spatiotemporal image 314 spectral density 346 spectral moment 244, 245, 265 spectrum 10 specular 545 spline 187 spline-based interpolation 187 split-and-merge Voronoi diagram 805 geometrical model 805 method 806 quantitative image analysis 807 SQL 917 stability 108, 437 stable filter response 108 Index staircasing 430 staircasing effect 430 standard least squares 331 standard method of characteristics 561 statistical error 5, 23 statistical texture features 298 steerable filter 241 steradian 540 stereo 3, 592 feature-based 507 intensity-based 507 stereo camera head 495, 497 stereo matching 265 stochastic approximation 740 stopband 126 stopping time 442 stretching 358 structural theorem 669 structure element 94 structure tensor 330, 349, 351, 372, 432, 438 structure tensor technique 329, 342 structuring element 628, 636, 637, 709 arbitrary 661 composite 637, 656 decomposition 640, 660 linear 660 pair of points 665 transposition 631 subgraph 628, 756 vertex-induced 756 subgraph isomorphism 776 subsampling 84 successive overrelaxation 328 Sugeno measures 711 sum histogram 282 sum-of-squared difference 355 superposition principle 630 superposition principle 98 supervised network 740 surface 231 surface inspection 276, 277 surface orientation 533 surroundedness 696 symbolic description 864 Index symmetry 434, symmetry plane synapse 729 synaptic vector systematic error 941 440 556 738 T target function 190 target vergence 492 temporal aliasing 405 temporal sampling theorem 318 tensor representation 328 tensorial signal 13 tesselation 14 textural energy 291 texture 276 layered 231 oriented 231 thickening 658 thinning 658 three-point mapping 196 threshold 630 decomposition 630 double 652 hysteresis 652 threshold segmentation for 3S PSM 554 TIFF 908 tiling 793 tilt angles 557 time series 10, 106 TIN 506 TLS 332 toggle mapping 671 token tracking 320, 354 top-hat 646, 664 black 646 by closing 646 by opening 646 for removing uneven illumination 664 white 646 topographic 674 Torrance-Sparrow model 545 total coherency measure 336 total least squares 232, 331 total least squares approach 332 transfer function 101 transformation radial-basis neural network 743 translation 202 translation vector 14 transport process 425 transposition 631 TRBNN 743 tree 760 rooted 760 triangle function 50 triangulated irregular network 506 triangulation 461, 463, 592 type I FIR filter 102 type II FIR filter 103 type III FIR filter 102 type IV FIR filter 103 U uncertainty relation 48, 68, 84, 86, 232 uniform positive definiteness 434 uniformly bounded 574 union 631 unit step function 50 unit surface normal 535 unitary transform 37 Unser’s texture features 283 unsupervised mode 740 V valency of a vertex 755 variance 12 variational approach 453 vector quantization 739 vector-valued models 444 vectorial signal 12 vergence 489 version 489 vertex 632, 754 degree of a 755 pendant 755 saturated 777 valency of a 755 vertical disparity 486, 492, 506 VGL rendering pipeline 893 VGL scene 893 Vieth-Müller circle 489 942 view plane normal 880 view reference point 880 viewer navigation 898 visual front-end 245 visualization volume 665 volume data source 904 volume element 16 Volume Graphics GmbH 890 volume primitive 892 volume rendering 884 volume rendering equation 880 volumetric image 2, 16 volumetric image data geometric model 804 geometric representation 802 surface representation 802 Voronoi diagram 791 computation of 794 boundary growing procedure 795 bucketing technique 796 incremental method 794 nearest neighbor search 794 split-and-merge 805 time complexity 796 geometric model 804 quantitative image analysis 802 application 811 surface area estimate 810 shape from voxels 791 shape representation 791, 802 split-and-merge quantitative image analysis 807 Voronoi quantizer 739 vorticity 358 VOXEL 881 voxel 16 W warp 406, 413 watershed 674, 675 watershed transformation 656 wave-number domain 68 Index wavelength 10 wavelet 69 wavelet decomposition 286 wavelet-based texture features 286 weight kernel 734 weight vector 737 weighted averaging 173 well-posedness 429, 434 white balance 538 white level 536 Wigner-Seitz cell 15, 26 windowed Fourier transform 70 winning neuron 737 X XOR-problem XRay 897 731 Z z-transform 107 zero extension 123 zero-mean homogeneous noise 12 zero-phase filter 155 .. .Handbook of Computer Vision and Applications Volume Signal Processing and Pattern Recognition Handbook of Computer Vision and Applications Volume Signal Processing and Pattern Recognition. .. second volume of the Handbook on Computer Vision and Applications deals with signal processing and pattern recognition The signals processed in computer vision originate from the radiance of an... Principles of depth-from-focus algorithms 591 5 92 593 595 ix Contents 20 .4 20 .5 20 .6 20 .7 IV Multiple-view depth-from-focus Dual-view depth-from-focus Single-view depth-from-focus References