Kanatani K. — Statistical Optimization for Geometric Computation: Theory and Practice :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

Предметный указатель

Kalman — Bucy filter      9
Kernel      see “Null space”
Kronecker delta      28
Lagrange formula      31
Law of Large Numbers      62 89 93 269 429
Least-squares approximation      269
Least-squares optimization      49
Left orthonormal system      46 357
Left-handed coordinate system      27
Left-handed system      32
Levi-Civita symbol      see “Eddington epsilon”
Likelihood      77 87 211 460 475
Line fitting      295
Line of sight      96
Linear dynamical system      81
Linearization      8 15 17 288
Linearized algorithm      17 288
Local distribution      10 67 98 105 251 452
Local distribution, Gaussian      71
Logarithmic differentiation formula      84
Logarithmic likelihood ratio test      434
Loss function      251
Mahalanobis distance      74 133 185 420
Mahalanobis geometry      420
Mahalanobis projection      420 466
Major axis of a quadric      123
Major axis of an ellipse      117
Manifold      10 22 65 106
Marginal probability density      79
Matrix      27
Matrix inner product      50
Matrix inversion formula      31
Matrix norm, $\infty$ -      51
Matrix norm, 1-      51
Matrix norm, consistent      51
Matrix norm, Euclidean      51
Matrix norm, natural      see “Spectral”
Matrix norm, Schmidt      see “Euclidean”
Matrix norm, Schur      see “Euclidean”
Matrix norm, spectral      46 51
Matrix of full rank      30
Maximum a posteriori probability estimation      14 89 251
Maximum Likelihood Estimation      77 90 133 460 475
Maximum likelihood estimator      77 87 460 475
MDL principle      22
Mean square      62
Midpoint flow approximation      413
Minimum description length principle      see “MDL principle”
Minimum mean square estimation      83
Minkowski norm      see “p-norm”
Minor axis      117
Mixed tensor      54
Model, geometric      7 210 416 453 469
Model, statistical      90
Modified $\chi^2$ distribution      143 219
Modified $\chi^2$ test      76
Modified $\chi^2$ variable      143 219
moment      72
Moment generating function      72
Moment matrix      214 225 235 237 269 311 426 471 303 333 384
Moore — Penrose generalized inverse      see “Generalized inverse”
Motion parallax      21 367
Motion parameter, finite      17 124 172
Motion parameter, instantaneous      374
Multidimensional moments      72
Natural norm      46 (see also “Spectral norm”)
Negative definite matrix      39
Negative semi-definite matrix      39
Neuro-computing      24
Newton iteration      284
Neyman — Scott problem      23
noise level      142 178 218 267 296 309 333 429
Non-Bayesian approach      248
Non-Euclidean distance      185
Nonsingular conic      114
Nonsingular constraint      132 455
Nonsingular data      210
Nonsingular generalized eigenvalue problem      42
Nonsingular hypothesis      210 425 469
Nonsingular matrix      30
Nonsingular quadric      119
Norm of a matrix      see “Matrix norm”
Norm of a vector      29
Norm of a vector, $\infty$ -      29
Norm of a vector, 1-      29
Norm of a vector, Euclidean      29
Norm of a vector, p-      29
Normal distribution      68
Normal flow      372
Normal space      66
Normalization      29 51
Normalized covariance matrix      142 178 218 267 333 429
Normalized covariance tensor      337 388
Normalized geometric AIC      429
Normalized residual      429
Nuisance parameter      8 23
Null hypothesis      434
Null space      11 39 46
Observation vector      81
Occluding contour      129
Optical flow      20 369 375
Optical flow equation      375
Optimal filter      8 14 254
Order symbol      30
Ordinary datum      469
Ordinary value      455
Orthogonal complement      34
Orthogonal matrix      35
Orthogonal projection      35 83
Orthogonality of matrices      50
Orthogonality of vectors      28
Orthogonality test for three orientations      167
Orthogonality test for two orientations      164
Orthonormal system      29
Outer product      28
Outlier      25
Outlier, detection      25
Overspecification      286 289
p-Norm      29
parabola      11 114
Paraboloid      12 118
Parallel stereo system      174
Parallelism      29
Parameter of interest      23
Parameter space      209 249 416 467
Parametric fitting      2 7 467
Parametric fitting of the exponential family      478
Parity      27
Perspective projection      11 96 171
Perturbation theorem      44 274
Photometric stereo      25
Planarity test for finite motion      19 351 353 442 443
Planarity test for optical flow      402 450
Planarity test for stereo vision      438
Plucker coordinate      104
Poisson distribution      88
Poisson-gamma distribution      88
polar      114 120 169
Pole      114 120 169
Positive definite matrix      39
Positive semi-definite matrix      39
Posterior      see “A posteriori probability density”
Primary deviation pair      12 71 101 124 183 286
Principal axis      117 119
Prior      see “A priori probability density”
Probabilistic relaxation      3
Projection      10
Projection matrix      34
Projection tensor      302
Projective geometry      10 98 194

Projective space, three-dimensional      102 125
Projective space, two-dimensional      95 175
Projective transformation, three-dimensional      125
Projective transformation, two-dimensional      116 126 175 189 194
Pseudo inverse      see “Generalized inverse”
Pull-back      185
Purposive vision      24
Pythagoras theorem      421
Quadratic convergence      284
Quadratic form      41
Quadric      11 118
Qualitative vision      24
Quaternion      67
Radius of curvature      420
RANGE      39 46
Range data      309
Range finder      16 309
Range sensing      309
Rank of a constraint      453
Rank of a hypothesis      210 425 468
Rank of a non-symmetric matrix      45
Rank of a symmetric matrix      37
Rank of equations      132
Rank of vectors      372
Rank-constrained generalized inverse      8 40 47 136
Rayleigh quotient      40
Real conic      114
Real optical flow      412
Rectangular hyperbola      117
Regression      5 448
Regular distribution      85 455 470
Regularization      3 20
Rejection region      75
Renormalization      8 15 285
Residual      49 91 142 429
Riemannian curvature      185
Riemannian distance      185
Riemannian metric      10 13
Riemannian space      185
Right orthonormal system      46
Right-handed coordinate system      27
Right-handed system      32
Rigidity test for finite motion      328
Rigidity test for optical flow      380
Robust computation      340
Root mean square      62
Rotation matrix      35 365
Rotation test for finite motion      19 326 364 442 443
Rotation test for optical flow      378 408 450
Rotation velocity      37 374
Satisfiability      50 133
Satisfiable constraint      133
Scalar triple product      32
Schmidt norm      see “Euclidean matrix norm”
Schur norm      see “Euclidean matrix norm”
Schwarz inequality of matrices      51
Schwarz inequality of vectors      29
Score      83 455 470
Second fundamental form      86
Second order renormalization      15 294
Shape from motion      see “Structure from motion”
Shape from shading      25
Signature      52 114
Signature symbol      29
Significance level      75 434
Similarity transformation      52
Singular conic      114
Singular constraint      132 337 455
Singular datum      210 469
Singular generalized eigenvalue problem      42
Singular hypothesis      469
Singular matrix      30
Singular quadric      119
Singular value      45 336 357 455
Singular value decomposition      45
Skew-symmetric matrix      28
Smoothness constraint      20
Solvable equation      48
Space conic      118
Space line      95
Space line at infinity      see “Ideal space line”
Space point      95
Space point at infinity      see “Ideal space point”
Space-time velocity      370
Spanned subspace      39
Spatio-temporal gradient equation      370
Spatio-temporal gradient value      370
Spectral decomposition      37
Spectral norm      46 51
Square matrix      27
Standard confidence interval      69
Standard confidence region      122 140 182
Standard deviation      69
Standard deviation pair      69
Standard Gaussian distribution      69
Standard normal distribution      69
State transition      15
State vector      81
Statistical bias      263 269
Statistical estimation      90
Statistical geometry      10
Statistical model      90
Statistical test      90
Stereo matching matching      25
Stereo vision      13 171
Stochastic relaxation      3
Strong critical surface for finite motion      19 350
Strong critical surface for optical flow      22 401
Strong hypothesis      276 282
Structural stability      66
Structure from motion      17
Structure parameter      23
Submanifold      65
Sylvester’s law of inertia      52 116
Symmetric matrix      28
Symmetrization      60
Tangent      115 120
Tangent bundle      65
Tangent space      10 65 131 185
Tangential flow      372
Tensor      54
Tensor of mixed dimensions      see “Mixed tensor”
Tensor product      54
Testing of hypotheses      75 141 275 434
Theoretical optical flow      412
Total curvature      420
Trace      28
Translation velocity      374
Transversal intersection      10 66 132 228 425 452 469
Transverse axis      117
Triangle inequality of matrices      51
Triangle inequality of vectors      29
Trinocular stereo vision      171
TYPE      27 54
Type transformation      55
Unbiased eigenvector fit      15 273
Unbiased estimator      77 85 456 471
Unbiased least-squares approximation      273
Unbiased moment matrix      273 293 311 304
Uncertainty field      183
Underspecification      289
Uninformative part      411
Unit matrix      28
Unit vector      29
Unsolvable equation      48
Upper a% point      434
Vanishing line      128 360
Vanishing point      14 127
Variance      61
Variance-covariance matrix      61

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