Pattern theory: from representation to inference
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 596 S. Ill., graph. Darst. |
| ISBN: | 0198505701 9780198505709 9780199297061 0199297061 |
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MARC
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| 100 | 1 | |a Grenander, Ulf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Pattern theory |b from representation to inference |c Ulf Grenander and Michael I. Miller |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2007 | |
| 300 | |a XII, 596 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Perception des structures | |
| 650 | 4 | |a Reconnaissance des formes (Informatique) | |
| 650 | 4 | |a Pattern perception | |
| 650 | 4 | |a Pattern recognition systems | |
| 650 | 0 | 7 | |a Mustererkennung |0 (DE-588)4040936-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mustererkennung |0 (DE-588)4040936-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Miller, Michael I. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch Darmstadt |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015468996&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Record in the Search Index
| _version_ | 1804136257354203136 |
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| adam_text | PATTERN THEORY: FROM REPRESENTATION TO INFERENCE ULF GRENANDER AND
MICHAEL I. MILLER OXFORD UNIVERSITY PRESS CONTENTS INTRODUCTION 1 1.1
ORGANIZATION 3 THE BAYES PARADIGM, ESTIMATION AND INFORMATION MEASURES 5
2.1 BAYES POSTERIOR DISTRIBUTION 5 2.1.1 MINIMUM RISK ESTIMATION 6 2.1.2
INFORMATION MEASURES 7 2.2 MATHEMATICAL PRELIMINARIES 8 2.2.1
PROBABILITY SPACES, RANDOM VARIABLES, DISTRIBUTIONS, DENSITIES, AND
EXPECTATION 8 2.2.2 TRANSFORMATIONS OF VARIABLES 10 2.2.3 THE
MULTIVARIATE NORMAL DISTRIBUTION 10 2.2.4 CHARACTERISTIC FUNCTION 11 2.3
MINIMUM RISK HYPOTHESIS TESTING ON DISCRETE SPACES 12 2.3.1 MINIMUM
PROBABILITY OF ERROR VIA MAXIMUM A POSTERIORI HYPOTHESIS TESTING 13
2.3.2 NEYMAN-PEARSON AND THE OPTIMALITY OF THE LIKELIHOOD RATIO TEST 14
2.4 MINIMUM MEAN-SQUARED ERROR RISK ESTIMATION IN VECTOR SPACES 16 2.4.1
NORMED LINEAR AND HILBERT SPACES 17 2.4.2 LEAST-SQUARES ESTIMATION 20
2.4.3 CONDITIONAL MEAN ESTIMATION AND GAUSSIAN PROCESSES 22 2.5 THE
FISHER INFORMATION OF ESTIMATORS 24 2.6 MAXIMUM-LIKELIHOOD AND ITS
CONSISTENCY 26 2.6.1 CONSISTENCY VIA UNIFORM CONVERGENCE OF EMPIRICAL
LOG-LIKELIHOOD 27 2.6.2 ASYMPTOTIC NORMALITY AND *JN CONVERGENCE RATE OF
THE MLE 28 2.7 COMPLETE-INCOMPLETE DATA PROBLEMS AND THE EM ALGORITHM 30
2.8 HYPOTHESIS TESTING AND MODEL COMPLEXITY 38 2.8.1 MODEL-ORDER
ESTIMATION AND THE D/2 LOG SAMPLE-SIZE COMPLEXITY 38 2.8.2 THE GAUSSIAN
CASE IS SPECIAL 41 2.8.3 MODEL COMPLEXITY AND THE GAUSSIAN CASE 42 2.9
BUILDING PROBABILITY MODELS VIA THE PRINCIPLE OF MAXIMUM ENTROPY 43
2.9.1 PRINCIPLE OF MAXIMUM ENTROPY 44 2.9.2 MAXIMUM ENTROPY MODELS 45
2.9.3 CONDITIONAL DISTRIBUTIONS ARE MAXIMUM ENTROPY 47 PROBABILISTIC
DIRECTED ACYCLIC GRAPHS AND THEIR ENTROPIES 49 3.1 DIRECTED ACYCLIC
GRAPHS (DAGS) 49 3/2 PROBABILITIES ON DIRECTED ACYCLIC GRAPHS (PDAGS) 51
3.3 FINITE STATE MARKOV CHAINS 54 3.4 MULTI-TYPE BRANCHING PROCESSES 56
3.4.1 THE BRANCHING MATRIX 59 3.4.2 THE MOMENT-GENERATING FUNCTION 60
3.5 EXTINCTION FOR FINITE-STATE MARKOV CHAINS AND BRANCHING PROCESSES 62
3.5.1 EXTINCTION IN MARKOV CHAINS 62 3.5.2 EXTINCTION IN BRANCHING
PROCESSES 63 3.6 ENTROPIES OF DIRECTED ACYCLIC GRAPHS 64 3.7
COMBINATORICS OF INDEPENDENT, IDENTICALLY DISTRIBUTED STRINGS VIA THE
AYMPTOTIC EQUIPARTITION THEOREM 65 VI CONTENTS 3.8 ENTROPY AND
COMBINATORICS OF MARKOV CHAINS 3.9 ENTROPIES OF BRANCHING PROCESSES
3.9.1 TREE STRUCTURE OF MULTI-TYPE BRANCHING PROCESSES 3.9.2 ENTROPIES
OF SUB-CRITICAL, CRITICAL, AND SUPER-CRITICAL PROCESSES 3.9.3 TYPICAL
TREES AND THE EQUIPARTITION THEOREM 3.10 FORMAL LANGUAGES AND STOCHASTIC
GRAMMARS 3.11 DAGS FOR NATURAL LANGUAGE MODELLING 3.11.1 MARKOV CHAINS
AND M-GRAMS 3.11.2 CONTEXT-FREE MODELS 3.11.3 HIERARCHICAL DIRECTED
ACYCLIC GRAPH MODEL 3.12 EM ALGORITHMS FOR PARAMETER ESTIMATION IN
HIDDEN MARKOV MODELS 3.12.1 MAP DECODING OF THE HIDDEN STATE SEQUENCE
3.12.2 ML ESTIMATION OF HMM PARAMETERS VIA EM FORWARD/BACKWARD ALGORITHM
3.13 EM ALGORITHMS FOR PARAMETER ESTIMATION IN NATURAL LANGUAGE MODELS
3.13.1 EM ALGORITHM FOR CONTEXT-FREE CHOMSKY NORMAL FORM 3.13.2 GENERAL
CONTEXT-FREE GRAMMARS AND THE TRELLIS ALGORITHM OF KUPIEC 4 MARKOV
RANDOM FIELDS ON UNDIRECTED GRAPHS 4.1 UNDIRECTED GRAPHS 4.2 MARKOV
RANDOM FIELDS 4.3 GIBBS RANDOM FIELDS 4.4 THE SPLITTING PROPERTY OF
GIBBS DISTRIBUTIONS 4.5 BAYESIAN TEXTURE SEGMENTATION: THE
LOG-NORMALIZER PROBLEM 4.5.1 THE GIBBS PARTITION FUNCTION PROBLEM 4.6
MAXIMUM-ENTROPY TEXTURE REPRESENTATION 4.6.1 EMPIRICAL MAXIMUM ENTROPY
TEXTURE CODING 4.7 STATIONARY GIBBS RANDOM FIELDS 4.7.1 THE
DOBRUSHIN/LANFORD/RUELLE DEFINITION 4.7.2 GIBBS DISTRIBUTIONS EXHIBIT
MULTIPLE LAWS WITH THE SAME INTERACTIONS (PHASE TRANSITIONS): THE ISING
MODEL AT LOW TEMPERATURE 4.8 ID RANDOM FIELDS ARE MARKOV CHAINS 4.9
MARKOV CHAINS HAVE A UNIQUE GIBBS DISTRIBUTION 4.10 ENTROPY OF
STATIONARY GIBBS FIELDS 5 GAUSSIAN RANDOM FIELDS ON UNDIRECTED GRAPHS
5.1 GAUSSIAN RANDOM FIELDS 5.2 DIFFERENCE OPERATORS AND ADJOINTS 5.3
GAUSSIAN FIELDS INDUCED VIA DIFFERENCE OPERATORS/ 5.4 STATIONARY
GAUSSIAN PROCESSES ON Z D AND THEIR SPECTRUM 5.5 CYCLO-STATIONARY
GAUSSIAN PROCESSES AND THEIR SPECTRUM 5.6 THE LOG-DETERMINANT COVARIANCE
AND THE ASYMPTOTIC NORMALIZER 5.6.1 ASYMPTOTICS OF THE GAUSSIAN
PROCESSES AND THEIR COVARIANCE 5.6.2 THE ASYMPTOTIC COVARIANCE AND
LOG-NORMALIZER 5.7 THE ENTROPY RATES OF THE STATIONARY PROCESS 5.7.1
BURG S MAXIMUM ENTROPY AUTO-REGRESSIVE PROCESSES ON IR 5.8 GENERALIZED
AUTO-REGRESSIVE IMAGE MODELLING VIA MAXIMUM-LIKELIHOOD ESTIMATION 5.8.1
ANISOTROPIC TEXTURES CONTENTS VM THE CANONICAL REPRESENTATIONS OF
GENERAL PATTERN THEORY 154 6.1 THE GENERATORS, CONFIGURATIONS, AND
REGULARITY OF PATTERNS 154 6.2 THE GENERATORS OF FORMAL LANGUAGES AND
GRAMMARS 158 6.3 GRAPH TRANSFORMATIONS 162 6.4 THE CANONICAL
REPRESENTATION OF PATTERNS: DAGS, MRFS, GAUSSIAN RANDOM FIELDS 166 6.4.1
DIRECTED ACYCLIC GRAPHS 167 6.4.2 MARKOV RANDOM FIELDS 169 6.4.3
GAUSSIAN RANDOM FIELDS: GENERATORS INDUCED VIA DIFFERENCE OPERATORS 170
MATRIX GROUP ACTIONS TRANSFORMING PATTERNS 174 7.1 GROUPS TRANSFORMING
CONFIGURATIONS 174 7.1.1 SIMILARITY GROUPS 174 7.1.2 GROUP ACTIONS
DEFINING EQUIVALENCE 175 7.1.3 GROUPS ACTIONS ON GENERATORS AND
DEFORMABLE TEMPLATES 177 7.2 THE MATRIX GROUPS 177 7.2.1 LINEAR MATRIX
AND AFFINE GROUPS OF TRANSFORMATION 177 7.2.2 MATRIX GROUPS ACTING ON R
D 179 7.3 TRANSFORMATIONS CONSTRUCTED FROM PRODUCTS OF GROUPS 181 7.4
RANDOM REGULARITY ON THE SIMILARITIES 184 7.5 CURVES AS SUBMANIFOLDS AND
THE FRENET FRAME 190 7.6 2D SURFACES IN R 3 AND THE SHAPE OPERATOR 195
7.6.1 THE SHAPE OPERATOR 196 7.7 FITTING QUADRATIC CHARTS AND CURVATURES
ON SURFACES 198 7.7.1 GAUSSIAN AND MEAN CURVATURE 198 7.7.2 SECOND ORDER
QUADRATIC CHARTS 200 7.7.3 ISOSURFACE ALGORITHM 201 7.8 RIDGE CURVES AND
CREST LINES 205 7.8.1 DEFINITION OF SULCUS, GYRUS, AND GEODESIC CURVES
ON TRIANGULATED GRAPHS 205 7.8.2 DYNAMIC PROGRAMMING 207 7.9 BIJECTIONS
AND SMOOTH MAPPINGS FOR COORDINATIZING MANIFOLDS VIA LOCAL COORDINATES
210 MANIFOLDS, ACTIVE MODELS, AND DEFORMABLE TEMPLATES 214 8.1 MANIFOLDS
AS GENERATORS, TANGENT SPACES, AND VECTOR FIELDS 214 8.1.1 MANIFOLDS 214
8.1.2 TANGENT SPACES 215 8.1.3 VECTOR FIELDS ON M 217 8.1.4 CURVES AND
THE TANGENT SPACE 218 8.2 SMOOTH MAPPINGS, THE JACOBIAN, AND
DIFFEOMORPHISMS 219 8.2.1 SMOOTH MAPPINGS AND THE JACOBIAN 219 8.2.2 THE
JACOBIAN AND LOCAL DIFFEOMORPHIC PROPERTIES 221 8.3 MATRIX GROUPS ARE
DIFFEOMORPHISMS WHICH ARE A SMOOTH MANIFOLD 222 8.3.1 DIFFEOMORPHISMS
222 8.3.2 MATRIX GROUP ACTIONS ARE DIFFEOMORPHISMS ON THE BACKGROUND
SPACE 8.3.3 THE MATRIX GROUPS ARE SMOOTH MANIFOLDS (LIE GROUPS) 8.4
ACTIVE MODELS AND DEFORMABLE TEMPLATES AS IMMERSIONS 8.4.1 SNAKES AND
ACTIVE CONTOURS 8.4.2 DEFORMING CLOSED CONTOURS IN THE PLANE 8.4.3
NORMAL DEFORMABLE SURFACES 8.5 ACTIVATING SHAPES IN DEFORMABLE MODELS
8.5.1 LIKELIHOOD OF SHAPES PARTITIONING IMAGE 8.5.2 A GENERAL CALCULUS
FOR SHAPE ACTIVATION VRII CONTENTS 8.5.3 ACTIVE CLOSED CONTOURS IN M 2
8.5.4 ACTIVE UNCLOSED SNAKES AND ROADS 8.5.5 NORMAL DEFORMATION OF
CIRCLES AND SPHERES 8.5.6 ACTIVE DEFORMABLE SPHERES 8.6 LEVEL SET ACTIVE
CONTOUR MODELS 8.7 GAUSSIAN RANDOM FIELD MODELS FOR ACTIVE SHAPES 9
SECOND ORDER AND GAUSSIAN FIELDS 9.1 SECOND ORDER PROCESSES (SOP) AND
THE HILBERT SPACE OF RANDOM VARIABLES 9.1.1 MEASURABILITY, SEPARABILITY,
CONTINUITY 9.1.2 HILBERT SPACE OF RANDOM VARIABLES 9.1.3 COVARIANCE AND
SECOND ORDER PROPERTIES 9.1.4 QUADRATIC MEAN CONTINUITY AND INTEGRATION
9.2 ORTHOGONAL PROCESS REPRESENTATIONS ON BOUNDED DOMAINS 9.2.1 COMPACT
OPERATORS AND COVARIANCES 9.2.2 ORTHOGONAL REPRESENTATIONS FOR RANDOM
PROCESSES AND FIELDS 9.2.3 STATIONARY PERIODIC PROCESSES AND FIELDS ON
BOUNDED DOMAINS 9.3 GAUSSIAN FIELDS ON THE CONTINUUM 9.4 SOBOLEV SPACES,
GREEN S FUNCTIONS, AND REPRODUCING KERNEL HILBERT SPACES 9.4.1
REPRODUCING KERNEL HILBERT SPACES 9.4.2 SOBOLEV NORMED SPACES 9.4.3
RELATION TO GREEN S FUNCTIONS 9.4.4 GRADIENT AND LAPLACIAN INDUCED
GREEN S KERNELS 9.5 GAUSSIAN PROCESSES INDUCED VIA LINEAR DIFFERENTIAL
OPERATORS 9.6 GAUSSIAN FIELDS IN THE UNIT CUBE 9.6.1 MAXIMUM LIKELIHOOD
ESTIMATION OF THE FIELDS: GENERALIZED ARMA MODELLING 9.6.2 SMALL
DEFORMATION VECTOR FIELDS MODELS IN THE PLANE AND CUBE 9.7 DISCRETE
LATTICES AND REACHABILITY OF CYCLO-STATIONARY SPECTRA 9.8 STATIONARY
PROCESSES ON THE SPHERE 9.8.1 LAPLACIAN OPERATOR INDUCED GAUSSIAN FIELDS
ON THE SPHERE 9.9 GAUSSIAN RANDOM FIELDS ON AN ARBITRARY SMOOTH SURFACE
9.9.1 LAPLACE-BELTRAMI OPERATOR WITH NEUMANN BOUNDARY CONDITIONS 9.9.2
SMOOTHING AN ARBITRARY FUNCTION ON MANIFOLDS BY ORTHONORMAL BASES OF THE
LAPLACE-BELTRAMI OPERATOR 9.10 SAMPLE PATH PROPERTIES AND CONTINUITY
9.11 GAUSSIAN RANDOM FIELDS AS PRIOR DISTRIBUTIONS IN POINT PROCESS
IMAGE RECONSTRUCTION 9.11.1 THE NEED FOR REGULARIZATION IN IMAGE
RECONSTRUCTION 9.11.2 SMOOTHNESS AND GAUSSIAN PRIORS 9.11.3 GOOD S
ROUGHNESS AS A GAUSSIAN PRIOR 9.11.4 EXPONENTIAL SPLINE SMOOTHING VIA
GOOD S ROUGHNESS 9.12 NON-COMPACT OPERATORS AND ORTHOGONAL
REPRESENTATIONS 9.12.1 CRAMER DECOMPOSITION FOR STATIONARY PROCESSES
9.12.2 ORTHOGONAL SCALE REPRESENTATION 10 METRICS SPACES FOR THE MATRIX
GROUPS 10.1 RIEMANNIAN MANIFOLDS AS METRIC SPACES 10.1.1 METRIC SPACES
AND SMOOTH MANIFOLDS 10.1.2 RIEMANNIAN MANIFOLD, GEODESIC METRIC, AND
MINIMUM ENERGY 10.2 VECTOR SPACES AS METRIC SPACES 10.3 COORDINATE
FRAMES ON THE MATRIX GROUPS AND THE EXPONENTIAL MAP CONTENTS IX 10.3.1
LEFT AND RIGHT GROUP ACTION 320 10.3.2 THE COORDINATE FRAMES 321 10.3.3
LOCAL OPTIMIZATION VIA DIRECTIONAL DERIVATIVES AND THE EXPONENTIAL MAP
323 10.4 METRIC SPACE STRUCTURE FOR THE LINEAR MATRIX GROUPS 324 10.4.1
GEODESIES IN THE MATRIX GROUPS 324 10.5 CONSERVATION OF MOMENTUM AND
GEODESIC EVOLUTION OF THE MATRIX GROUPS VIA THE TANGENT AT THE IDENTITY
326 10.6 METRICS IN THE MATRIX GROUPS 327 10.7 VIEWING THE MATRIX GROUPS
IN EXTRINSIC EUCLIDEAN COORDINATES 329 10.7.1 THE FROBENIUS METRIC 329
10.7.2 COMPARING INTRINSIC AND EXTRINSIC METRICS IN SO(2,3) 330 11
METRICS SPACES FOR THE INFINITE DIMENSIONAL DIFFEOMORPHISMS 332 11.1
LAGRANGIAN AND EULERIAN GENERATION OF DIFFEOMORPHISMS 332 11.1.1 ON
CONDITIONS FOR GENERATING FLOWS OF DIFFEOMORPHISMS 333 11.1.2 MODELING
VIA DIFFERENTIAL OPERATORS AND THE REPRODUCING KERNEL HILBERT SPACE 335
11.2 THE METRIC ON THE SPACE OF DIFFEOMORPHISMS 336 11.3 MOMENTUM
CONSERVATION FOR GEODESIES 338 11.4 CONSERVATION OF MOMENTUM FOR
DIFFEOMORPHISM SPLINES SPECIFIED ON SPARSE LANDMARK POINTS 340 11.4.1 AN
ODE FOR DIFFEOMORPHIC LANDMARK MAPPING 343 12 METRICS ON PHOTOMETRIC AND
GEOMETRIC DEFORMABLE TEMPLATES 346 12.1 METRICS ON DENSE DEFORMABLE
TEMPLATES: GEOMETRIC GROUPS ACTING ON IMAGES 346 12.1.1 GROUP ACTIONS ON
THE IMAGES 346 12.1.2 INVARIANT METRIC DISTANCES 347 12.2 THE
DIFFEOMORPHISM METRIC FOR THE IMAGE ORBIT 349 12.3 NORMAL MOMENTUM
MOTION FOR GEODESIC CONNECTION VIA INEXACT MATCHING 350 12.4 NORMAL
MOMENTUM MOTION FOR TEMPORAL SEQUENCES 354 12.5 METRIC DISTANCES BETWEEN
ORBITS DEFINED THROUGH INVARIANCE OF THE METRIC 356 12.6 FINITE
DIMENSIONAL LANDMARKED SHAPE SPACES 357 12.6.1 THE EUCLIDEAN METRIC 357
12.6.2 KENDALL S SIMILITUDE INVARIANT DISTANCE 359 12.7 THE
DIFFEOMORPHISM METRIC AND DIFFEOMORPHISM SPLINES ON LANDMARK SHAPES 361
12.7.1 SMALL DEFORMATION SPLINES 361 12.8 THE DEFORMABLE TEMPLATE:
ORBITS OF PHOTOMETRIC AND GEOMETRIC VARIATION 365 12.8.1 METRIC SPACES
FOR PHOTOMETRIC VARIABILITY 365 12.8.2 THE METRICS INDUCED VIA
PHOTOMETRIC AND GEOMETRIC FLOW 366 12.9 THE EULER EQUATIONS FOR
PHOTOMETRIC AND GEOMETRIC VARIATION 369 12.10 METRICS BETWEEN ORBITS OF
THE SPECIAL EUCLIDEAN GROUP 373 12.11 THE MATRIX GROUPS (EUCLIDEAN AND
AFFINE MOTIONS) 374 12.11.1 COMPUTING THE AFFINE MOTIONS 376 13
ESTIMATION BOUNDS FOR AUTOMATED OBJECT RECOGNITION 378 13.1 THE
COMMUNICATIONS MODEL FOR IMAGE TRANSMISSION 378 13.1.1 THE SOURCE MODEL:
OBJECTS UNDER MATRIX GROUP ACTIONS 379 : 13.1.2 THE SENSING MODELS:
PROJECTIVE TRANSFORMATIONS IN NOISE 379 13.1.3 THE LIKELIHOOD AND
POSTERIOR 379 CONTIFJTS 13.2 CONDITIONAL MEAN MINIMUM RISK ESTIMATION
13.2.1 METRICS (RISK) ON THE MATRIX GROUPS 13.2.2 CONDITIONAL MEAN
MINIMUM RISK ESTIMATORS 13.2.3 COMPUTATION OF THE HSE FOR SE(2,3) 13.2.4
DISCRETE INTEGRATION ON SO(3) 13.3 MMSE ESTIMATORS FOR PROJECTIVE
IMAGERY MODELS 13.3.1 3D TO 2D PROJECTIONS IN GAUSSIAN NOISE 13.3.2 3D
TO 2D SYNTHETIC APERTURE RADAR IMAGING 13.3.3 3D TO 2D LADAR IMAGING
13.3.4 3D TO 2D POISSON PROJECTION MODEL 13.3.5 3D TO ID PROJECTIONS
13.3.6 3D(2D) TO 3D(2D) MEDICAL IMAGING REGISTRATION 13.4 PARAMETER
ESTIMATION AND FISHER INFORMATION 13.5 BAYESIAN FUSION OF INFORMATION
13.6 ASYMPTOTIC CONSISTENCY OF INFERENCE AND SYMMETRY GROUPS 13.6.1
CONSISTENCY 13.6.2 SYMMETRY GROUPS AND SENSOR SYMMETRY 13.7 HYPOTHESIS
TESTING AND ASYMPTOTIC ERROR-EXPONENTS 13.7.1 ANALYTICAL REPRESENTATIONS
OF THE ERROR PROBABILITIES AND THE BAYESIAN INFORMATION CRITERION 13.7.2
M-ARY MULTIPLE HYPOTHESES 14 ESTIMATION ON METRIC SPACES WITH
PHOTOMETRIC VARIATION 14.1 THE DEFORMABLE TEMPLATE: ORBITS OF SIGNATURE
AND GEOMETRIC VARIATION 14.1.1 THE ROBUST DEFORMABLE TEMPLATES 14.1.2
THE METRIC SPACE OF THE ROBUST DEFORMABLE TEMPLATE 14.2 EMPIRICAL
COVARIANCE OF PHOTOMETRIC VARIABILITY VIA PRINCIPLE COMPONENTS 14.2.1
SIGNATURES AS A GAUSSIAN RANDOM FIELD CONSTRUCTED FROM PRINCIPLE
COMPONENTS 14.2.2 ALGORITHM FOR EMPIRICAL CONSTRUCTION OF BASES 14.3
ESTIMATION OF PARAMETERS ON THE CONDITIONALLY GAUSSIAN RANDOM FIELD
MODELS 14.4 ESTIMATION OF POSE BY INTEGRATING OUT EIGENSIGNATURES 14.4.1
BAYES INTEGRATION 14.5 MULTIPLE MODALITY SIGNATURE REGISTRATION 14.6
MODELS FOR CLUTTER: THE TRANSPORTED GENERATOR MODEL 14.6.1
CHARACTERISTIC FUNCTIONS AND CUMULANTS 14.7 ROBUST DEFORMABLE TEMPLATES
FOR NATURAL CLUTTER 14.7.1 THE EUCLIDEAN METRIC 14.7.2 METRIC SPACE
NORMS FOR CLUTTER 14.7.3 COMPUTATIONAL SCHEME 14.7.4 EMPIRICAL
CONSTRUCTION OF THE METRIC FROM RENDERED IMAGES 14.8 TARGET
DETECTION/IDENTIFICATION IN EO IMAGERY 15 INFORMATION BOUNDS FOR
AUTOMATED OBJECT RECOGNITION 15.1 MUTUAL INFORMATION FOR SENSOR SYSTEMS
15.1.1 QUANTIFYING MULTIPLE-SENSOR INFORMATION GAIN VIA MUTUAL
INFORMATION 15.1.2 QUANTIFYING INFORMATION LOSS WITH MODEL UNCERTAINTY
15.1.3 ASYMPTOTIC APPROXIMATION OF INFORMATION MEASURES CONTENTS XI 15.2
RATE-DISTORTION THEORY 456 15.2.1 THE RATE-DISTORTION PROBLEM 456 15.3
THE BLAHUT ALGORITHM 457 15.4 THE REMOTE RATE DISTORTION PROBLEM 459
15.4.1 BLAHUT ALGORITHM EXTENDED 460 15.5 OUTPUT SYMBOL DISTRIBUTION 465
16 COMPUTATIONAL ANATOMY: SHAPE, GROWTH AND ATROPHY COMPARISON VIA
DIFFEOMORPHISMS 468 16.1 COMPUTATIONAL ANATOMY 468 16.1.1 DIFFEOMORPHIC
STUDY OF ANATOMICAL SUBMANIFOLDS 469 16.2 THE ANATOMICAL SOURCE MODEL OF
C A 470 16.2.1 GROUP ACTIONS FOR THE ANATOMICAL SOURCE MODEL 472 16.2.2
THE DATA CHANNEL MODEL 473 16.3 NORMAL MOMENTUM MOTION FOR LARGE
DEFORMATION METRIC MAPPING (LDDMM) FOR GROWTH AND ATROPHY 474 16.4
CHRISTENSEN NON-GEODESIC MAPPING ALGORITHM 478 16.5 EXTRINSIC MAPPING OF
SURFACE AND VOLUME SUBMANIFOLDS 480 16.5.1 DIFFEOMORPHIC MAPPING OF THE
FACE 481 16.5.2 DIFFEOMORPHIC MAPPING OF BRAIN SUBMANIFOLDS 481 16.5.3
EXTRINSIC MAPPING OF SUBVOLUMES FOR AUTOMATED SEGMENTATION 481 16.5.4
METRIC MAPPING OF CORTICAL ATLASES 483 16.6 HEART MAPPING AND DIFFUSION
TENSOR MAGNETIC RESONANCE IMAGING 484 16.7 VECTOR FIELDS FOR GROWTH 488
16.7.1 GROWTH FROM LANDMARKED SHAPE SPACES 488 17 COMPUTATIONAL ANATOMY:
HYPOTHESIS TESTING ON DISEASE 494 17.1 STATISTICS ANALYSIS FOR SHAPE
SPACES 494 17.2 GAUSSIAN RANDOM FIELDS 495 17.2.1 EMPIRICAL ESTIMATION
OF RANDOM VARIABLES 496 17.3 SHAPE REPRESENTATION OF THE ANATOMICAL
ORBIT UNDER LARGE DEFORMATION DIFFEOMORPHISMS 496 17.3.1 PRINCIPAL
COMPONENT SELECTION OF THE BASIS FROM EMPIRICAL OBSERVATIONS 497 17.4
THE MOMENTUM OF LANDMARKED SHAPE SPACES 498 17.4.1 GEODESIC EVOLUTION
EQUATIONS FOR LANDMARKS 498 17.4.2 SMALL DEFORMATION PCA VERSUS LARGE
DEFORMATION PCA 499 17.5 THE SMALL DEFORMATION SETTING 502 17.6 SMALL
DEFORMATION GAUSSIAN FIELDS ON SURFACE SUBMANIFOLDS 502 17.7 DISEASE
TESTING OF AUTOMORPHIC PATHOLOGY * 503 17.7.1 HYPOTHESIS TESTING ON
DISEASE IN THE SMALL NOISE LIMIT 503 17.7.2 STATISTICAL TESTING 505
DISTRIBUTION FREE TESTING 510 17.9 HETEROMORPHIC TUMORS 511 JV PROCESSES
AND RANDOM SAMPLING 514 |4 MARKOV JUMP PROCESSES 514 18.1.1 JUMP
PROCESSES 515 RANDOM SAMPLING AND STOCHASTIC INFERENCE 516 18.2.1
STATIONARY OR INVARIANT MEASURES 517 18.2.2 GENERATOR FOR MARKOV JUMP
PROCESSES 519 J8.2.3 JUMP PROCESS SIMULATION 520 1S.2.4
METROPOLIS-HASTINGS ALGORITHM 521 XII CONTENTS 18.3 DIFFUSION PROCESSES
FOR SIMULATION 18.3.1 GENERATORS OF ID DIFFUSIONS 18.3.2 DIFFUSIONS AND
SDES FOR SAMPLING 18.4 JUMP-DIFFUSION INFERENCE ON COUNTABLE UNIONS OF
SPACES 18.4.1 THE BASIC PROBLEM 19 JUMP DIFFUSION INFERENCE IN COMPLEX
SCENES 19.1 RECOGNITION OF GROUND VEHICLES 19.1.1 CAD MODELS AND THE
PARAMETER SPACE 19.1.2 THE FLIR SENSOR MODEL 19.2 JUMP DIFFUSION FOR
SAMPLING THE TARGET RECOGNITION POSTERIOR 19.2.1 THE POSTERIOR
DISTRIBUTION 19.2.2 THE JUMP DIFFUSION ALGORITHMS 19.2.3 JUMPS VIA
GIBBS SAMPLING 19.2.4 JUMPS VIA METROPOLIS-HASTINGS
ACCEPTANCE/REJECTION 19.3 EXPERIMENTAL RESULTS FOR FLIR AND LADAR 19.3.1
DETECTION AND REMOVAL OF OBJECTS 19.3.2 IDENTIFICATION 19.3.3 POSE AND
IDENTIFICATION 19.3.4 IDENTIFICATION AND RECOGNITION VIA HIGH RESOLUTION
RADAR (HRR) 19.3.5 THE DYNAMICS OF POSE ESTIMATION VIA THE
JUMP-DIFFUSION PROCESS 19.3.6 LADAR RECOGNITION 19.4 POWERFUL PRIOR
DYNAMICS FOR AIRPLANE TRACKING 19.4.1 THE EULER-EQUATIONS INDUCING THE
PRIOR ON AIRPLANE DYNAMICS 19.4.2 DETECTION OF AIRFRAMES 19.4.3 PRUNING
VIA THE PRIOR DISTRIBUTION 19.5 DEFORMABLE ORGANELLES: MITOCHONDRIA AND
MEMBRANES 19.5.1 THE PARAMETER SPACE FOR CONTOUR MODELS 19.5.2
STATIONARY GAUSSIAN CONTOUR MODEL 19.5.3 THE ELECTRON MICROGRAPH DATA
MODEL: CONDITIONAL GAUSSIAN RANDOM FIELDS 19.6 JUMP-DIFFUSION FOR
MITOCHONDRIA 19.6.1 THE JUMP PARAMETERS 19.6.2 COMPUTING GRADIENTS FOR
THE DRIFTS 19.6.3 JUMP DIFFUSION FOR MITOCHONDRIA DETECTION AND
DEFORMATION 19.6.4 PSEUDOLIKELIHOOD FOR DEFORMATION REFERENCES INDEX
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PATTERN THEORY: FROM REPRESENTATION TO INFERENCE ULF GRENANDER AND
MICHAEL I. MILLER OXFORD UNIVERSITY PRESS CONTENTS INTRODUCTION 1 1.1
ORGANIZATION 3 THE BAYES PARADIGM, ESTIMATION AND INFORMATION MEASURES 5
2.1 BAYES POSTERIOR DISTRIBUTION 5 2.1.1 MINIMUM RISK ESTIMATION 6 2.1.2
INFORMATION MEASURES 7 2.2 MATHEMATICAL PRELIMINARIES 8 2.2.1
PROBABILITY SPACES, RANDOM VARIABLES, DISTRIBUTIONS, DENSITIES, AND
EXPECTATION 8 2.2.2 TRANSFORMATIONS OF VARIABLES 10 2.2.3 THE
MULTIVARIATE NORMAL DISTRIBUTION 10 2.2.4 CHARACTERISTIC FUNCTION 11 2.3
MINIMUM RISK HYPOTHESIS TESTING ON DISCRETE SPACES 12 2.3.1 MINIMUM
PROBABILITY OF ERROR VIA MAXIMUM A POSTERIORI HYPOTHESIS TESTING 13
2.3.2 NEYMAN-PEARSON AND THE OPTIMALITY OF THE LIKELIHOOD RATIO TEST 14
2.4 MINIMUM MEAN-SQUARED ERROR RISK ESTIMATION IN VECTOR SPACES 16 2.4.1
NORMED LINEAR AND HILBERT SPACES 17 2.4.2 LEAST-SQUARES ESTIMATION 20
2.4.3 CONDITIONAL MEAN ESTIMATION AND GAUSSIAN PROCESSES 22 2.5 THE
FISHER INFORMATION OF ESTIMATORS 24 2.6 MAXIMUM-LIKELIHOOD AND ITS
CONSISTENCY 26 2.6.1 CONSISTENCY VIA UNIFORM CONVERGENCE OF EMPIRICAL
LOG-LIKELIHOOD 27 2.6.2 ASYMPTOTIC NORMALITY AND *JN CONVERGENCE RATE OF
THE MLE 28 2.7 COMPLETE-INCOMPLETE DATA PROBLEMS AND THE EM ALGORITHM 30
2.8 HYPOTHESIS TESTING AND MODEL COMPLEXITY 38 2.8.1 MODEL-ORDER
ESTIMATION AND THE D/2 LOG SAMPLE-SIZE COMPLEXITY 38 2.8.2 THE GAUSSIAN
CASE IS SPECIAL 41 2.8.3 MODEL COMPLEXITY AND THE GAUSSIAN CASE 42 2.9
BUILDING PROBABILITY MODELS VIA THE PRINCIPLE OF MAXIMUM ENTROPY 43
2.9.1 PRINCIPLE OF MAXIMUM ENTROPY 44 2.9.2 MAXIMUM ENTROPY MODELS 45
2.9.3 CONDITIONAL DISTRIBUTIONS ARE MAXIMUM ENTROPY 47 PROBABILISTIC
DIRECTED ACYCLIC GRAPHS AND THEIR ENTROPIES 49 3.1 DIRECTED ACYCLIC
GRAPHS (DAGS) 49 3/2 PROBABILITIES ON DIRECTED ACYCLIC GRAPHS (PDAGS) 51
3.3 FINITE STATE MARKOV CHAINS 54 3.4 MULTI-TYPE BRANCHING PROCESSES 56
3.4.1 THE BRANCHING MATRIX 59 3.4.2 THE MOMENT-GENERATING FUNCTION 60
3.5 EXTINCTION FOR FINITE-STATE MARKOV CHAINS AND BRANCHING PROCESSES 62
3.5.1 EXTINCTION IN MARKOV CHAINS 62 3.5.2 EXTINCTION IN BRANCHING
PROCESSES 63 3.6 ENTROPIES OF DIRECTED ACYCLIC GRAPHS 64 3.7
COMBINATORICS OF INDEPENDENT, IDENTICALLY DISTRIBUTED STRINGS VIA THE
AYMPTOTIC EQUIPARTITION THEOREM 65 VI CONTENTS 3.8 ENTROPY AND
COMBINATORICS OF MARKOV CHAINS 3.9 ENTROPIES OF BRANCHING PROCESSES
3.9.1 TREE STRUCTURE OF MULTI-TYPE BRANCHING PROCESSES 3.9.2 ENTROPIES
OF SUB-CRITICAL, CRITICAL, AND SUPER-CRITICAL PROCESSES 3.9.3 TYPICAL
TREES AND THE EQUIPARTITION THEOREM 3.10 FORMAL LANGUAGES AND STOCHASTIC
GRAMMARS 3.11 DAGS FOR NATURAL LANGUAGE MODELLING 3.11.1 MARKOV CHAINS
AND M-GRAMS 3.11.2 CONTEXT-FREE MODELS 3.11.3 HIERARCHICAL DIRECTED
ACYCLIC GRAPH MODEL 3.12 EM ALGORITHMS FOR PARAMETER ESTIMATION IN
HIDDEN MARKOV MODELS 3.12.1 MAP DECODING OF THE HIDDEN STATE SEQUENCE
3.12.2 ML ESTIMATION OF HMM PARAMETERS VIA EM FORWARD/BACKWARD ALGORITHM
3.13 EM ALGORITHMS FOR PARAMETER ESTIMATION IN NATURAL LANGUAGE MODELS
3.13.1 EM ALGORITHM FOR CONTEXT-FREE CHOMSKY NORMAL FORM 3.13.2 GENERAL
CONTEXT-FREE GRAMMARS AND THE TRELLIS ALGORITHM OF KUPIEC 4 MARKOV
RANDOM FIELDS ON UNDIRECTED GRAPHS 4.1 UNDIRECTED GRAPHS 4.2 MARKOV
RANDOM FIELDS 4.3 GIBBS RANDOM FIELDS 4.4 THE SPLITTING PROPERTY OF
GIBBS DISTRIBUTIONS 4.5 BAYESIAN TEXTURE SEGMENTATION: THE
LOG-NORMALIZER PROBLEM 4.5.1 THE GIBBS PARTITION FUNCTION PROBLEM 4.6
MAXIMUM-ENTROPY TEXTURE REPRESENTATION 4.6.1 EMPIRICAL MAXIMUM ENTROPY
TEXTURE CODING 4.7 STATIONARY GIBBS RANDOM FIELDS 4.7.1 THE
DOBRUSHIN/LANFORD/RUELLE DEFINITION 4.7.2 GIBBS DISTRIBUTIONS EXHIBIT
MULTIPLE LAWS WITH THE SAME INTERACTIONS (PHASE TRANSITIONS): THE ISING
MODEL AT LOW TEMPERATURE 4.8 ID RANDOM FIELDS ARE MARKOV CHAINS 4.9
MARKOV CHAINS HAVE A UNIQUE GIBBS DISTRIBUTION 4.10 ENTROPY OF
STATIONARY GIBBS FIELDS 5 GAUSSIAN RANDOM FIELDS ON UNDIRECTED GRAPHS
5.1 GAUSSIAN RANDOM FIELDS 5.2 DIFFERENCE OPERATORS AND ADJOINTS 5.3
GAUSSIAN FIELDS INDUCED VIA DIFFERENCE OPERATORS/ 5.4 STATIONARY
GAUSSIAN PROCESSES ON Z D AND THEIR SPECTRUM 5.5 CYCLO-STATIONARY
GAUSSIAN PROCESSES AND THEIR SPECTRUM 5.6 THE LOG-DETERMINANT COVARIANCE
AND THE ASYMPTOTIC NORMALIZER 5.6.1 ASYMPTOTICS OF THE GAUSSIAN
PROCESSES AND THEIR COVARIANCE 5.6.2 THE ASYMPTOTIC COVARIANCE AND
LOG-NORMALIZER 5.7 THE ENTROPY RATES OF THE STATIONARY PROCESS 5.7.1
BURG'S MAXIMUM ENTROPY AUTO-REGRESSIVE PROCESSES ON IR 5.8 GENERALIZED
AUTO-REGRESSIVE IMAGE MODELLING VIA MAXIMUM-LIKELIHOOD ESTIMATION 5.8.1
ANISOTROPIC TEXTURES CONTENTS VM THE CANONICAL REPRESENTATIONS OF
GENERAL PATTERN THEORY 154 6.1 THE GENERATORS, CONFIGURATIONS, AND
REGULARITY OF PATTERNS 154 6.2 THE GENERATORS OF FORMAL LANGUAGES AND
GRAMMARS 158 6.3 GRAPH TRANSFORMATIONS 162 6.4 THE CANONICAL
REPRESENTATION OF PATTERNS: DAGS, MRFS, GAUSSIAN RANDOM FIELDS 166 6.4.1
DIRECTED ACYCLIC GRAPHS 167 6.4.2 MARKOV RANDOM FIELDS 169 6.4.3
GAUSSIAN RANDOM FIELDS: GENERATORS INDUCED VIA DIFFERENCE OPERATORS 170
MATRIX GROUP ACTIONS TRANSFORMING PATTERNS 174 7.1 GROUPS TRANSFORMING
CONFIGURATIONS 174 7.1.1 SIMILARITY GROUPS 174 7.1.2 GROUP ACTIONS
DEFINING EQUIVALENCE 175 7.1.3 GROUPS ACTIONS ON GENERATORS AND
DEFORMABLE TEMPLATES 177 7.2 THE MATRIX GROUPS 177 7.2.1 LINEAR MATRIX
AND AFFINE GROUPS OF TRANSFORMATION 177 7.2.2 MATRIX GROUPS ACTING ON R
D 179 7.3 TRANSFORMATIONS CONSTRUCTED FROM PRODUCTS OF GROUPS 181 7.4
RANDOM REGULARITY ON THE SIMILARITIES 184 7.5 CURVES AS SUBMANIFOLDS AND
THE FRENET FRAME 190 7.6 2D SURFACES IN R 3 AND THE SHAPE OPERATOR 195
7.6.1 THE SHAPE OPERATOR 196 7.7 FITTING QUADRATIC CHARTS AND CURVATURES
ON SURFACES 198 7.7.1 GAUSSIAN AND MEAN CURVATURE 198 7.7.2 SECOND ORDER
QUADRATIC CHARTS 200 7.7.3 ISOSURFACE ALGORITHM 201 7.8 RIDGE CURVES AND
CREST LINES 205 7.8.1 DEFINITION OF SULCUS, GYRUS, AND GEODESIC CURVES
ON TRIANGULATED GRAPHS 205 7.8.2 DYNAMIC PROGRAMMING 207 7.9 BIJECTIONS
AND SMOOTH MAPPINGS FOR COORDINATIZING MANIFOLDS VIA LOCAL COORDINATES
210 MANIFOLDS, ACTIVE MODELS, AND DEFORMABLE TEMPLATES 214 8.1 MANIFOLDS
AS GENERATORS, TANGENT SPACES, AND VECTOR FIELDS 214 8.1.1 MANIFOLDS 214
8.1.2 TANGENT SPACES 215 8.1.3 VECTOR FIELDS ON M 217 8.1.4 CURVES AND
THE TANGENT SPACE 218 8.2 SMOOTH MAPPINGS, THE JACOBIAN, AND
DIFFEOMORPHISMS 219 8.2.1 SMOOTH MAPPINGS AND THE JACOBIAN 219 8.2.2 THE
JACOBIAN AND LOCAL DIFFEOMORPHIC PROPERTIES 221 8.3 MATRIX GROUPS ARE
DIFFEOMORPHISMS WHICH ARE A SMOOTH MANIFOLD 222 8.3.1 DIFFEOMORPHISMS
222 8.3.2 MATRIX GROUP ACTIONS ARE DIFFEOMORPHISMS ON THE BACKGROUND
SPACE 8.3.3 THE MATRIX GROUPS ARE SMOOTH MANIFOLDS (LIE GROUPS) 8.4
ACTIVE MODELS AND DEFORMABLE TEMPLATES AS IMMERSIONS 8.4.1 SNAKES AND
ACTIVE CONTOURS 8.4.2 DEFORMING CLOSED CONTOURS IN THE PLANE 8.4.3
NORMAL DEFORMABLE SURFACES 8.5 ACTIVATING SHAPES IN DEFORMABLE MODELS
8.5.1 LIKELIHOOD OF SHAPES PARTITIONING IMAGE 8.5.2 A GENERAL CALCULUS
FOR SHAPE ACTIVATION VRII CONTENTS 8.5.3 ACTIVE CLOSED CONTOURS IN M 2
8.5.4 ACTIVE UNCLOSED SNAKES AND ROADS 8.5.5 NORMAL DEFORMATION OF
CIRCLES AND SPHERES 8.5.6 ACTIVE DEFORMABLE SPHERES 8.6 LEVEL SET ACTIVE
CONTOUR MODELS 8.7 GAUSSIAN RANDOM FIELD MODELS FOR ACTIVE SHAPES 9
SECOND ORDER AND GAUSSIAN FIELDS 9.1 SECOND ORDER PROCESSES (SOP) AND
THE HILBERT SPACE OF RANDOM VARIABLES 9.1.1 MEASURABILITY, SEPARABILITY,
CONTINUITY 9.1.2 HILBERT SPACE OF RANDOM VARIABLES 9.1.3 COVARIANCE AND
SECOND ORDER PROPERTIES 9.1.4 QUADRATIC MEAN CONTINUITY AND INTEGRATION
9.2 ORTHOGONAL PROCESS REPRESENTATIONS ON BOUNDED DOMAINS 9.2.1 COMPACT
OPERATORS AND COVARIANCES 9.2.2 ORTHOGONAL REPRESENTATIONS FOR RANDOM
PROCESSES AND FIELDS 9.2.3 STATIONARY PERIODIC PROCESSES AND FIELDS ON
BOUNDED DOMAINS 9.3 GAUSSIAN FIELDS ON THE CONTINUUM 9.4 SOBOLEV SPACES,
GREEN'S FUNCTIONS, AND REPRODUCING KERNEL HILBERT SPACES 9.4.1
REPRODUCING KERNEL HILBERT SPACES 9.4.2 SOBOLEV NORMED SPACES 9.4.3
RELATION TO GREEN'S FUNCTIONS 9.4.4 GRADIENT AND LAPLACIAN INDUCED
GREEN'S KERNELS 9.5 GAUSSIAN PROCESSES INDUCED VIA LINEAR DIFFERENTIAL
OPERATORS 9.6 GAUSSIAN FIELDS IN THE UNIT CUBE 9.6.1 MAXIMUM LIKELIHOOD
ESTIMATION OF THE FIELDS: GENERALIZED ARMA MODELLING 9.6.2 SMALL
DEFORMATION VECTOR FIELDS MODELS IN THE PLANE AND CUBE 9.7 DISCRETE
LATTICES AND REACHABILITY OF CYCLO-STATIONARY SPECTRA 9.8 STATIONARY
PROCESSES ON THE SPHERE 9.8.1 LAPLACIAN OPERATOR INDUCED GAUSSIAN FIELDS
ON THE SPHERE 9.9 GAUSSIAN RANDOM FIELDS ON AN ARBITRARY SMOOTH SURFACE
9.9.1 LAPLACE-BELTRAMI OPERATOR WITH NEUMANN BOUNDARY CONDITIONS 9.9.2
SMOOTHING AN ARBITRARY FUNCTION ON MANIFOLDS BY ORTHONORMAL BASES OF THE
LAPLACE-BELTRAMI OPERATOR 9.10 SAMPLE PATH PROPERTIES AND CONTINUITY
9.11 GAUSSIAN RANDOM FIELDS AS PRIOR DISTRIBUTIONS IN POINT PROCESS
IMAGE RECONSTRUCTION 9.11.1 THE NEED FOR REGULARIZATION IN IMAGE
RECONSTRUCTION 9.11.2 SMOOTHNESS AND GAUSSIAN PRIORS 9.11.3 GOOD'S
ROUGHNESS AS A GAUSSIAN PRIOR 9.11.4 EXPONENTIAL SPLINE SMOOTHING VIA
GOOD'S ROUGHNESS 9.12 NON-COMPACT OPERATORS AND ORTHOGONAL
REPRESENTATIONS 9.12.1 CRAMER DECOMPOSITION FOR STATIONARY PROCESSES
9.12.2 ORTHOGONAL SCALE REPRESENTATION 10 METRICS SPACES FOR THE MATRIX
GROUPS 10.1 RIEMANNIAN MANIFOLDS AS METRIC SPACES 10.1.1 METRIC SPACES
AND SMOOTH MANIFOLDS 10.1.2 RIEMANNIAN MANIFOLD, GEODESIC METRIC, AND
MINIMUM ENERGY 10.2 VECTOR SPACES AS METRIC SPACES 10.3 COORDINATE
FRAMES ON THE MATRIX GROUPS AND THE EXPONENTIAL MAP CONTENTS IX 10.3.1
LEFT AND RIGHT GROUP ACTION 320 10.3.2 THE COORDINATE FRAMES 321 10.3.3
LOCAL OPTIMIZATION VIA DIRECTIONAL DERIVATIVES AND THE EXPONENTIAL MAP
323 10.4 METRIC SPACE STRUCTURE FOR THE LINEAR MATRIX GROUPS 324 10.4.1
GEODESIES IN THE MATRIX GROUPS 324 10.5 CONSERVATION OF MOMENTUM AND
GEODESIC EVOLUTION OF THE MATRIX GROUPS VIA THE TANGENT AT THE IDENTITY
326 10.6 METRICS IN THE MATRIX GROUPS 327 10.7 VIEWING THE MATRIX GROUPS
IN EXTRINSIC EUCLIDEAN COORDINATES 329 10.7.1 THE FROBENIUS METRIC 329
10.7.2 COMPARING INTRINSIC AND EXTRINSIC METRICS IN SO(2,3) 330 11
METRICS SPACES FOR THE INFINITE DIMENSIONAL DIFFEOMORPHISMS 332 11.1
LAGRANGIAN AND EULERIAN GENERATION OF DIFFEOMORPHISMS 332 11.1.1 ON
CONDITIONS FOR GENERATING FLOWS OF DIFFEOMORPHISMS 333 11.1.2 MODELING
VIA DIFFERENTIAL OPERATORS AND THE REPRODUCING KERNEL HILBERT SPACE 335
11.2 THE METRIC ON THE SPACE OF DIFFEOMORPHISMS 336 11.3 MOMENTUM
CONSERVATION FOR GEODESIES 338 11.4 CONSERVATION OF MOMENTUM FOR
DIFFEOMORPHISM SPLINES SPECIFIED ON SPARSE LANDMARK POINTS 340 11.4.1 AN
ODE FOR DIFFEOMORPHIC LANDMARK MAPPING 343 12 METRICS ON PHOTOMETRIC AND
GEOMETRIC DEFORMABLE TEMPLATES 346 12.1 METRICS ON DENSE DEFORMABLE
TEMPLATES: GEOMETRIC GROUPS ACTING ON IMAGES 346 12.1.1 GROUP ACTIONS ON
THE IMAGES 346 12.1.2 INVARIANT METRIC DISTANCES 347 12.2 THE
DIFFEOMORPHISM METRIC FOR THE IMAGE ORBIT 349 12.3 NORMAL MOMENTUM
MOTION FOR GEODESIC CONNECTION VIA INEXACT MATCHING 350 12.4 NORMAL
MOMENTUM MOTION FOR TEMPORAL SEQUENCES 354 12.5 METRIC DISTANCES BETWEEN
ORBITS DEFINED THROUGH INVARIANCE OF THE METRIC 356 12.6 FINITE
DIMENSIONAL LANDMARKED SHAPE SPACES 357 12.6.1 THE EUCLIDEAN METRIC 357
12.6.2 KENDALL'S SIMILITUDE INVARIANT DISTANCE 359 12.7 THE
DIFFEOMORPHISM METRIC AND DIFFEOMORPHISM SPLINES ON LANDMARK SHAPES 361
12.7.1 SMALL DEFORMATION SPLINES 361 12.8 THE DEFORMABLE TEMPLATE:
ORBITS OF PHOTOMETRIC AND GEOMETRIC VARIATION ' 365 12.8.1 METRIC SPACES
FOR PHOTOMETRIC VARIABILITY 365 12.8.2 THE METRICS INDUCED VIA
PHOTOMETRIC AND GEOMETRIC FLOW 366 12.9 THE EULER EQUATIONS FOR
PHOTOMETRIC AND GEOMETRIC VARIATION 369 12.10 METRICS BETWEEN ORBITS OF
THE SPECIAL EUCLIDEAN GROUP 373 12.11 THE MATRIX GROUPS (EUCLIDEAN AND
AFFINE MOTIONS) 374 12.11.1 COMPUTING THE AFFINE MOTIONS 376 13
ESTIMATION BOUNDS FOR AUTOMATED OBJECT RECOGNITION 378 13.1 THE
COMMUNICATIONS MODEL FOR IMAGE TRANSMISSION 378 13.1.1 THE SOURCE MODEL:
OBJECTS UNDER MATRIX GROUP ACTIONS 379 : 13.1.2 THE SENSING MODELS:
PROJECTIVE TRANSFORMATIONS IN NOISE 379 13.1.3 THE LIKELIHOOD AND
POSTERIOR 379 CONTIFJTS 13.2 CONDITIONAL MEAN MINIMUM RISK ESTIMATION
13.2.1 METRICS (RISK) ON THE MATRIX GROUPS 13.2.2 CONDITIONAL MEAN
MINIMUM RISK ESTIMATORS 13.2.3 COMPUTATION OF THE HSE FOR SE(2,3) 13.2.4
DISCRETE INTEGRATION ON SO(3) 13.3 MMSE ESTIMATORS FOR PROJECTIVE
IMAGERY MODELS 13.3.1 3D TO 2D PROJECTIONS IN GAUSSIAN NOISE 13.3.2 3D
TO 2D SYNTHETIC APERTURE RADAR IMAGING 13.3.3 3D TO 2D LADAR IMAGING
13.3.4 3D TO 2D POISSON PROJECTION MODEL 13.3.5 3D TO ID PROJECTIONS
13.3.6 3D(2D) TO 3D(2D) MEDICAL IMAGING REGISTRATION 13.4 PARAMETER
ESTIMATION AND FISHER INFORMATION 13.5 BAYESIAN FUSION OF INFORMATION
13.6 ASYMPTOTIC CONSISTENCY OF INFERENCE AND SYMMETRY GROUPS 13.6.1
CONSISTENCY 13.6.2 SYMMETRY GROUPS AND SENSOR SYMMETRY 13.7 HYPOTHESIS
TESTING AND ASYMPTOTIC ERROR-EXPONENTS 13.7.1 ANALYTICAL REPRESENTATIONS
OF THE ERROR PROBABILITIES AND THE BAYESIAN INFORMATION CRITERION 13.7.2
M-ARY MULTIPLE HYPOTHESES 14 ESTIMATION ON METRIC SPACES WITH
PHOTOMETRIC VARIATION 14.1 THE DEFORMABLE TEMPLATE: ORBITS OF SIGNATURE
AND GEOMETRIC VARIATION 14.1.1 THE ROBUST DEFORMABLE TEMPLATES 14.1.2
THE METRIC SPACE OF THE ROBUST DEFORMABLE TEMPLATE 14.2 EMPIRICAL
COVARIANCE OF PHOTOMETRIC VARIABILITY VIA PRINCIPLE COMPONENTS 14.2.1
SIGNATURES AS A GAUSSIAN RANDOM FIELD CONSTRUCTED FROM PRINCIPLE
COMPONENTS 14.2.2 ALGORITHM FOR EMPIRICAL CONSTRUCTION OF BASES 14.3
ESTIMATION OF PARAMETERS ON THE CONDITIONALLY GAUSSIAN RANDOM FIELD
MODELS 14.4 ESTIMATION OF POSE BY INTEGRATING OUT EIGENSIGNATURES 14.4.1
BAYES INTEGRATION 14.5 MULTIPLE MODALITY SIGNATURE REGISTRATION 14.6
MODELS FOR CLUTTER: THE TRANSPORTED GENERATOR MODEL 14.6.1
CHARACTERISTIC FUNCTIONS AND CUMULANTS 14.7 ROBUST DEFORMABLE TEMPLATES
FOR NATURAL CLUTTER 14.7.1 THE EUCLIDEAN METRIC 14.7.2 METRIC SPACE
NORMS FOR CLUTTER 14.7.3 COMPUTATIONAL SCHEME 14.7.4 EMPIRICAL
CONSTRUCTION OF THE METRIC FROM RENDERED IMAGES 14.8 TARGET
DETECTION/IDENTIFICATION IN EO IMAGERY 15 INFORMATION BOUNDS FOR
AUTOMATED OBJECT RECOGNITION 15.1 MUTUAL INFORMATION FOR SENSOR SYSTEMS
15.1.1 QUANTIFYING MULTIPLE-SENSOR INFORMATION GAIN VIA MUTUAL
INFORMATION 15.1.2 QUANTIFYING INFORMATION LOSS WITH MODEL UNCERTAINTY
15.1.3 ASYMPTOTIC APPROXIMATION OF INFORMATION MEASURES CONTENTS XI 15.2
RATE-DISTORTION THEORY 456 15.2.1 THE RATE-DISTORTION PROBLEM 456 15.3
THE BLAHUT ALGORITHM 457 15.4 THE REMOTE RATE DISTORTION PROBLEM 459
15.4.1 BLAHUT ALGORITHM EXTENDED 460 15.5 OUTPUT SYMBOL DISTRIBUTION 465
16 COMPUTATIONAL ANATOMY: SHAPE, GROWTH AND ATROPHY COMPARISON VIA
DIFFEOMORPHISMS 468 16.1 COMPUTATIONAL ANATOMY 468 16.1.1 DIFFEOMORPHIC
STUDY OF ANATOMICAL SUBMANIFOLDS 469 16.2 THE ANATOMICAL SOURCE MODEL OF
C A 470 16.2.1 GROUP ACTIONS FOR THE ANATOMICAL SOURCE MODEL 472 16.2.2
THE DATA CHANNEL MODEL 473 16.3 NORMAL MOMENTUM MOTION FOR LARGE
DEFORMATION METRIC MAPPING (LDDMM) FOR GROWTH AND ATROPHY 474 16.4
CHRISTENSEN NON-GEODESIC MAPPING ALGORITHM 478 16.5 EXTRINSIC MAPPING OF
SURFACE AND VOLUME SUBMANIFOLDS 480 16.5.1 DIFFEOMORPHIC MAPPING OF THE
FACE 481 16.5.2 DIFFEOMORPHIC MAPPING OF BRAIN SUBMANIFOLDS 481 16.5.3
EXTRINSIC MAPPING OF SUBVOLUMES FOR AUTOMATED SEGMENTATION 481 16.5.4
METRIC MAPPING OF CORTICAL ATLASES 483 16.6 HEART MAPPING AND DIFFUSION
TENSOR MAGNETIC RESONANCE IMAGING 484 16.7 VECTOR FIELDS FOR GROWTH 488
16.7.1 GROWTH FROM LANDMARKED SHAPE SPACES 488 17 COMPUTATIONAL ANATOMY:
HYPOTHESIS TESTING ON DISEASE 494 17.1 STATISTICS ANALYSIS FOR SHAPE
SPACES 494 17.2 GAUSSIAN RANDOM FIELDS 495 17.2.1 EMPIRICAL ESTIMATION
OF RANDOM VARIABLES 496 17.3 SHAPE REPRESENTATION OF THE ANATOMICAL
ORBIT UNDER LARGE DEFORMATION DIFFEOMORPHISMS 496 17.3.1 PRINCIPAL
COMPONENT SELECTION OF THE BASIS FROM EMPIRICAL OBSERVATIONS 497 17.4
THE MOMENTUM OF LANDMARKED SHAPE SPACES 498 17.4.1 GEODESIC EVOLUTION
EQUATIONS FOR LANDMARKS 498 17.4.2 SMALL DEFORMATION PCA VERSUS LARGE
DEFORMATION PCA 499 17.5 THE SMALL DEFORMATION SETTING 502 17.6 SMALL
DEFORMATION GAUSSIAN FIELDS ON SURFACE SUBMANIFOLDS 502 17.7 DISEASE
TESTING OF AUTOMORPHIC PATHOLOGY * 503 17.7.1 HYPOTHESIS TESTING ON
DISEASE IN THE SMALL NOISE LIMIT 503 17.7.2 STATISTICAL TESTING 505
DISTRIBUTION FREE TESTING 510 17.9 HETEROMORPHIC TUMORS 511 JV PROCESSES
AND RANDOM SAMPLING 514 |4 MARKOV JUMP PROCESSES 514 18.1.1 JUMP
PROCESSES 515 RANDOM SAMPLING AND STOCHASTIC INFERENCE 516 18.2.1
STATIONARY OR INVARIANT MEASURES 517 18.2.2 GENERATOR FOR MARKOV JUMP
PROCESSES 519 J8.2.3 JUMP PROCESS SIMULATION 520 1S.2.4
METROPOLIS-HASTINGS ALGORITHM 521 XII CONTENTS 18.3 DIFFUSION PROCESSES
FOR SIMULATION 18.3.1 GENERATORS OF ID DIFFUSIONS 18.3.2 DIFFUSIONS AND
SDES FOR SAMPLING 18.4 JUMP-DIFFUSION INFERENCE ON COUNTABLE UNIONS OF
SPACES 18.4.1 THE BASIC PROBLEM 19 JUMP DIFFUSION INFERENCE IN COMPLEX
SCENES 19.1 RECOGNITION OF GROUND VEHICLES 19.1.1 CAD MODELS AND THE
PARAMETER SPACE 19.1.2 THE FLIR SENSOR MODEL 19.2 JUMP DIFFUSION FOR
SAMPLING THE TARGET RECOGNITION POSTERIOR 19.2.1 THE POSTERIOR
DISTRIBUTION 19.2.2 THE JUMP DIFFUSION ALGORITHMS 19.2.3 JUMPS VIA
GIBBS' SAMPLING 19.2.4 JUMPS VIA METROPOLIS-HASTINGS
ACCEPTANCE/REJECTION 19.3 EXPERIMENTAL RESULTS FOR FLIR AND LADAR 19.3.1
DETECTION AND REMOVAL OF OBJECTS 19.3.2 IDENTIFICATION 19.3.3 POSE AND
IDENTIFICATION 19.3.4 IDENTIFICATION AND RECOGNITION VIA HIGH RESOLUTION
RADAR (HRR) 19.3.5 THE DYNAMICS OF POSE ESTIMATION VIA THE
JUMP-DIFFUSION PROCESS 19.3.6 LADAR RECOGNITION 19.4 POWERFUL PRIOR
DYNAMICS FOR AIRPLANE TRACKING 19.4.1 THE EULER-EQUATIONS INDUCING THE
PRIOR ON AIRPLANE DYNAMICS 19.4.2 DETECTION OF AIRFRAMES 19.4.3 PRUNING
VIA THE PRIOR DISTRIBUTION 19.5 DEFORMABLE ORGANELLES: MITOCHONDRIA AND
MEMBRANES 19.5.1 THE PARAMETER SPACE FOR CONTOUR MODELS 19.5.2
STATIONARY GAUSSIAN CONTOUR MODEL 19.5.3 THE ELECTRON MICROGRAPH DATA
MODEL: CONDITIONAL GAUSSIAN RANDOM FIELDS 19.6 JUMP-DIFFUSION FOR
MITOCHONDRIA 19.6.1 THE JUMP PARAMETERS 19.6.2 COMPUTING GRADIENTS FOR
THE DRIFTS 19.6.3 JUMP DIFFUSION FOR MITOCHONDRIA DETECTION AND
DEFORMATION 19.6.4 PSEUDOLIKELIHOOD FOR DEFORMATION REFERENCES INDEX |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Grenander, Ulf Miller, Michael I. |
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| callnumber-first | Q - Science |
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| classification_rvk | ST 330 |
| classification_tum | DAT 770f |
| ctrlnum | (OCoLC)65467603 (DE-599)BVBBV022258308 |
| dewey-full | 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.33 |
| dewey-search | 511.33 |
| dewey-sort | 3511.33 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV022258308 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:41:54Z |
| indexdate | 2024-07-09T20:53:31Z |
| institution | BVB |
| isbn | 0198505701 9780198505709 9780199297061 0199297061 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015468996 |
| oclc_num | 65467603 |
| open_access_boolean | |
| owner | DE-29T DE-91G DE-BY-TUM DE-11 DE-83 |
| owner_facet | DE-29T DE-91G DE-BY-TUM DE-11 DE-83 |
| physical | XII, 596 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Grenander, Ulf Verfasser aut Pattern theory from representation to inference Ulf Grenander and Michael I. Miller 1. publ. Oxford [u.a.] Oxford Univ. Press 2007 XII, 596 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Perception des structures Reconnaissance des formes (Informatique) Pattern perception Pattern recognition systems Mustererkennung (DE-588)4040936-3 gnd rswk-swf Mustererkennung (DE-588)4040936-3 s DE-604 Miller, Michael I. Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015468996&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grenander, Ulf Miller, Michael I. Pattern theory from representation to inference Perception des structures Reconnaissance des formes (Informatique) Pattern perception Pattern recognition systems Mustererkennung (DE-588)4040936-3 gnd |
| subject_GND | (DE-588)4040936-3 |
| title | Pattern theory from representation to inference |
| title_auth | Pattern theory from representation to inference |
| title_exact_search | Pattern theory from representation to inference |
| title_exact_search_txtP | Pattern theory from representation to inference |
| title_full | Pattern theory from representation to inference Ulf Grenander and Michael I. Miller |
| title_fullStr | Pattern theory from representation to inference Ulf Grenander and Michael I. Miller |
| title_full_unstemmed | Pattern theory from representation to inference Ulf Grenander and Michael I. Miller |
| title_short | Pattern theory |
| title_sort | pattern theory from representation to inference |
| title_sub | from representation to inference |
| topic | Perception des structures Reconnaissance des formes (Informatique) Pattern perception Pattern recognition systems Mustererkennung (DE-588)4040936-3 gnd |
| topic_facet | Perception des structures Reconnaissance des formes (Informatique) Pattern perception Pattern recognition systems Mustererkennung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015468996&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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