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Kanatani K. — Statistical Optimization for Geometric Computation: Theory and Practice
Kanatani K. — Statistical Optimization for Geometric Computation: Theory and Practice

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Название: Statistical Optimization for Geometric Computation: Theory and Practice

Автор: Kanatani K.

Аннотация:

This text discusses the mathematical foundations of statistical inference for building 3-dimensional models from image and sensor data that contain noise — a task involving autonomous robots guided by video cameras and sensors. The text employs a theoretical accuracy for the optimization procedure, which maximizes the reliability of estimations based on noise data. 1996 edition.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 594

Добавлена в каталог: 10.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\chi^2$ distribution      73
$\chi^2$ test      75 90 142
$\chi^2$ variable      73
$\infty$-norm      29 51
1-norm      29 51
2-norm      see “Euclidean norm Euclidean
A posteriori covariance matrix      80
A posteriori distribution      248
A posteriori probability density      80 250
A posteriori standard confidence region      140
A priori distribution      79 248
A priori probability density      250
A priori standard confidence region      140
Aberration      1
Adjugate matrix      30
Affine connection      10
Affine subspace      78 121
Affine transformation, three-dimensional      125
Affine transformation, two-dimensional      189
AIC      10 22 93 429
Akaike information criterion      see “AIC”
Algebraic variety      65
Alternative hypothesis      434
Angle (of rotation)      36
Angular velocity      37
Antisymmetric matrix      28 33
Antisymmetrization      60
Aperture problem      372
artificial intelligence      24
Asymptote      116
Asymptotic approximation      475
Asymptotic limit      429
Average      62
Axis of a parabola      117
Axis of rotation      36
Back projection      118 188 361
Base-line vector      172
Bayes estimation      80 251
Bayes formula      80 248 250
Bayesian approach      248
Bayesian standpoint      14
Beta distribution      88
Binocular stereo vision      171
Binomial distribution      88
Camera calibration      11
Canonical form      115
Cartesian coordinate system      27
Cast      55
Catastrophe theory      10
Center (of a quadric)      118
Centered quadric      118
Central limit theorem      25 71 93 429
Characteristic equation      37
Characteristic function      72
Characteristic polynomial      37
Cochran’s theorem      74
Codimension of a manifold      65 132 210 453
Codimension of a model      416
Cofactor      30 123
Cofactor expansion formula      30
Cofactor matrix      336
Coincidence test for image lines      147 229
Coincidence test for image points      145 221
Coincidence test for space lines      152 240
Coincidence test for space planes      157 246
Coincidence test for space points      151 230
Collinearity test for image points      223 298
Collinearity test for space points      233
Collineation      189 194
Comparison criterion      22
Computational projective geometry      11
Computer vision      1
Concurrency test for image lines      227
Concurrency test for space lines      239
Condition number      48
Conditional probability density      79 250
Confidence level      75 434
Congruence transformation      52 116 126
conic      11 113 300
Conic fitting      300
Conic incidence test      169
Conic locus      see “Conic”
Conic section      see “Conic”
Conic test      302
Conjugate axis      117
Conjugate direction      120 135
Conservation equation      369
Consistent equation      48
Consistent estimator      90 269
Consistent fitting      480
Consistent norm      51
Constraint      132 452
contour      129
Contragradient transformation      194
Contragradient vector      120
Contravariant vector      120
Coplanar vectors      32
Coplanarity test for space lines      242
Coplanarity test for space points      236 312 317
Correlation      61
Correlation matrix      53 366
Correspondence test      177
Cost function      251
Covariance      61
Covariance matrix      61 68
Covariance tensor      62
Covariant vector      120
Cramer formula      48
Cramer — Rao inequality      86 456 471
Cramer-Rao lower bound      9 23 86 140 215 456 471
Critical surface of finite motion      19 350
Critical surface of optical flow      22 401
Curved exponential family      88
DATA      467
Data space      131 209 249 415 452 467
Decomposability condition      17 289 336 340 350 387
Decomposable matrix      336 340 350 387
Degenerate constraint      133 455 465
Degenerate hyperboloid      350 401
Degenerate hypothesis      210 470 482
Degree of freedom of a $\chi^2$ distribution      73
Degree of freedom of a geometric model      416
Degree of freedom of a statistical model      91
Depth equation      392
Depth for finite motion      342
Depth for optical flow      392
Depth for stereo vision      180
Determinant      29
Determinate equation      48
Diagonalization      38
Diffeomorphism      65
Differential manifold      see “Manifold”
Dimension of a geometric model      416
Dimension of a manifold      65
Dimension of a matrix      27
Dimension of a tensor      54
Dimension of a vector      27
Direct sum of matrices      54
Direct sum of vectors      54
Disparity      181
Duality      11 194
Dynamical system      1
Eccentricity      117
Eddington epsilon      31
EDGE      14
Edge density      225
Edge detection      25
Edge operator      14
Edge segment      175 186 225 295
Effective gradient      257
Effective gradient approximation      14 258
Effective moment matrix      292
Effective moment tensor      303
Effective value      265 291 301
Efficient correction      463
Efficient estimator      86 463
Efficient fitting      479
Eigenmatrix      58
Eigensystem      37
Eigenvalue      37
Eigenvalue decomposition      see “Spectral decomposition”
Eigenvector      37
Eigenvector fit      15 269
Eight-point algorithm      333
ellipse      11 114
Ellipsoid      12 118
Epipolar constraint      2 7 13 172
Epipolar equation      17 173 316 325 377 435
Epipolar of optical flow      390
Epipolar of stereo vision      13 173 435
Epipolar plane      172
Epipole      13 173 180
Essential matrix      17 174 332 435
Estimator      77 85
Euclidean matrix norm      51
Euclidean motion, three-dimensional      125
Euclidean motion, two dimensional      115
Euclidean norm of a matrix      51
Euclidean norm of a vector      29
Euler’s theorem      36
Expectation      61
Expected residual      91 419
Exponential family of distributions      10 88 462 478
Exponential family, geometric correction of      23 462
Exponential family, parametric fitting of      23 478
Extended Kalman filter      15 19 263
Exterior product of a matrix and a vector      33
Exterior product of a vector and a matrix      33
Exterior product of two matrices      34
Exterior product of two vectors      see “Vector product”
Factorization      19
Feature point tracking      25
Fisher information matrix      10 23 84 455 470
Fitting parameter      467
Five-point algorithm      328
Flow matrix for general optical flow      378
Flow matrix for planar surface optical flow      403 448
Focal length      96 171 204
Focus of expansion for finite motion      329
Focus of expansion for optical flow      21 380 393
Fragile algorithm      17
Fragile computation      340
Frobenius norm      see “Euclidean matrix norm”
Fuzzy inference      24
Gamma distribution      88
Gamma function      73
Gaussian distribution      68
Gaussian random variable      68
Generalized characteristic equation      42
Generalized characteristic polynomial      42
Generalized eigensystem      42
Generalized eigenvalue      41
Generalized eigenvector      41
Generalized eigenvector fit      15 279
Generalized inverse      9 39 47
Generalized matrix inversion formula      40 258
Generalized Rayleigh quotient      43 279
Generalized spectral decomposition      42
Generated subspace      39
Geometric AIC      7 22 428 483
Geometric constraint      2
Geometric correction      2 7 12 452
Geometric correction of the exponential family      462
Geometric information criterion      see “Geometric AIC”
Geometric model      22 132 210 416 453 469
Goodness of a geometric model      7 419
Goodness of a statistical model      90
Gradient equation      370
Gradient value      370
Grassmann coordinate      see “Plucker coordinate”
Group of affine transformations      125
Group of congruence transformations      52
Group of Euclidean motions, three-dimensional      125
Group of Euclidean motions, two-dimensional      115
Group of general linear transformations      36
Group of orthogonal transformations      36
Group of projective transformations      125
Group of projective transformations, three-dimensional      125
Group of projective transformations, two-dimensional      189
Group of rotations      36
Group of similarity transformations      52
Group of special linear transformations      36
Group of special orthogonal transformations      36
Homogeneous coordinate of a space line      104
Homogeneous coordinate of a space point      102
Homogeneous coordinate of an image line      98
Homogeneous coordinate of an image point      10 95
Homotopy method      17
Hyperbola      11 114
Hyperboloid      12 118 350 351 401
Hypothesis      75 141 210 434 467
Ideal image line      98 128 129
Ideal image point      95 99 127 128 173 175
Ideal space line      111 128
Ideal space point      102 107 111 112
Ill-conditioned equation      48 465 482
Image line      95
Image line at infinity      see “Ideal image line”
Image plane      96
Image point      95
Image point at infinity      see “Ideal image point”
Image space      see “Range”
Image understanding      1
Imaginary ellipse      114
Incidence of a space line and a space plane      111
Incidence of a space point and a space line      107 110
Incidence of an image point and an image line      99
Incidence test for a space line and a space plane      162 195
Incidence test for a space point and a space plane      158 191
Incidence test for an image point and an image line      148
Incidence test for conies      169
Inconsistent equation      48
Independent random variables      61
Indeterminate equation      48
Infinity test for a space line      200
Infinity test for a space point      197
Infinity test for stereo vision      438
Information matrix      see “Fisher information matrix”
Information of finite motion      367
Information of optical flow      411
Informative part      411
Inherent constraint      11 132 452
Inlier      25
Inner product of matrices      50
Inner product of vectors      28
Innovation      82
Instantaneous axis of rotation      37
Instantaneous motion parameters      374
Invariant      52
Invariant basis      52
Inverse      30
Isotropy      64
Join of a space point and a space line      113
Join of space three points      113
Join of two image points      100
Join of two space lines      113
Join of two space points      108
Joint probability density      250
Kalman filter      9 81 260
Kalman gain      82
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