User:Papadim.G/Computer Vision Geometry Summary

This is a list of computer vision geometry and mathematics that shows an organisation of the geometric and mathematical topics central to computer vision and image processing. This was originally proposed in the CVonline resource.

Vision Geometry and Mathematics

 * 1) Basic Representations
 * 2) Coordinate systems
 * 3) Cartesian coordinate system
 * 4) Cylindrical coordinate system
 * 5) Hexagonal coordinate system
 * 6) Log-Polar coordinate system
 * 7) Polar coordinate system
 * 8) Spherical coordinate system
 * 9) Digital topology
 * 10) Dual space
 * 11) Homogeneous coordinates
 * 12) Pose/Rotation/Orientation Representations
 * 13) Axis-angle representation
 * 14) Clifford algebra
 * 15) Euler angles
 * 16) Exponential map
 * 17) Quaternion/Dual quaternion
 * 18) Rotation matrix
 * 19) Pitch/Yaw/Roll
 * 20) Distance metrics
 * 21) Affine
 * 22) Algebraic distance
 * 23) Bhattacharyya distance
 * 24) Chi-square test/metric
 * 25) Curse of dimensionality
 * 26) Earth mover's distance
 * 27) Euclidean distance
 * 28) Fuzzy intersection
 * 29) Hausdorff distance
 * 30) Jeffrey-divergence
 * 31) Kullback–Leibler divergence
 * 32) Mahalanobis distance
 * 33) Manhattan/City block distance
 * 34) Minkowski distance
 * 35) Procrustes analysis
 * 36) Procrustes average
 * 37) Quadratic form
 * 38) Specific structure similarity
 * 39) Curve similarity
 * 40) Region similarity
 * 41) Volume similarity
 * 42) Elementary mathematics for Vision
 * 43) Coordinate systems/Vectors/Matrices/Derivatives/Gradients/Probability
 * 44) Derivatives in sampled images
 * 45) Mathematical optimization
 * 46) Golden section search
 * 47) Lagrange multipliers/Constraint optimization
 * 48) Multi-Dimensional Optimization
 * 49) Derivative Free Search
 * 50) Global optimization
 * 51) Ant colony optimization
 * 52) Downhill simplex
 * 53) Genetic algorithms
 * 54) Graduated optimization
 * 55) Markov random field optimization
 * 56) Particle swarm optimization
 * 57) Simulated annealing
 * 58) Optimization with derivatives
 * 59) Levenberg–Marquardt
 * 60) Gradient descent/Quasi-Newton method
 * 61) Model selection
 * 62) Variational methods
 * 63) Linear algebra for computer vision
 * 64) Eigenfunction
 * 65) Eigenvalues and eigenvectors
 * 66) Principal Component and Related Approaches
 * 67) Dimensionality reduction
 * 68) Linear discriminant analysis
 * 69) Factor analysis
 * 70) Fisher's linear discriminant
 * 71) Independent component analysis
 * 72) Kernel Linear Discriminant Analysis
 * 73) Kernel principal component analysis
 * 74) Locality preserving projections
 * 75) Non-negative matrix factorization
 * 76) Optimal dimension estimation
 * 77) Principal component analysis/Karhunen–Loève theorem
 * 78) Principal geodesic analysis
 * 79) Probabilistic principal component analysis
 * 80) Rao–Blackwell theorem
 * 81) Sammon projection
 * 82) Singular value decomposition
 * 83) Structure tensor
 * 84) Multi-sensor/Multi-view geometries
 * 85) 3D reconstruction
 * 86) 3D shape from 2D projections
 * 87) 3D reconstruction from multiple images/orthogonal views
 * 88) Slice-based reconstruction
 * 89) Affine and projective stereo
 * 90) Baseline stereo
 * 91) Narrow baseline stereo
 * 92) Wide baseline stereo
 * 93) Binocular stereo algorithms
 * 94) Cooperative stereo algorithms
 * 95) Binocular disparity
 * 96) Subpixel disparity
 * 97) Dense stereo matching approaches
 * 98) Dynamic programming (stereo)
 * 99) Feature matching stereo algorithms
 * 100) Gradient matching stereo algorithms
 * 101) Image rectification
 * 102) Planar rectification
 * 103) Polar rectification
 * 104) Log-polar stereo
 * 105) Multi-scale stereo algorithms
 * 106) Panoramic image stereo algorithms
 * 107) Phase matching stereo algorithms
 * 108) Region matching stereo algorithms
 * 109) Weakly/Uncalibrated stereo approaches
 * 110) Spherical stereo
 * 111) Epipolar geometry/Multi-view geometry
 * 112) Absolute conic
 * 113) Absolute quadric
 * 114) Epipolar geometry definitions
 * 115) Essential matrix
 * 116) Fundamental matrix
 * 117) Grassmannian space/Plücker embedding
 * 118) Homography tensor
 * 119) transfer and novel view synthesis
 * 120) Trifocal tensor
 * 121) Image-based modeling and rendering/Plenoptic modelling
 * 122) Image feature correspondence constraints
 * 123) Active stereo (feature correspondence)
 * 124) Disparity gradient Limit (feature correspondence)
 * 125) Disparity limit (feature correspondence)
 * 126) Epipolar constraint
 * 127) Feature contrast
 * 128) Feature orientation
 * 129) Grey-level similarity (feature correspondence)
 * 130) Lipschitz continuity
 * 131) Ordering (feature correspondence)
 * 132) Surface continuity
 * 133) Surface smoothness
 * 134) Uniqueness (feature correspondence)
 * 135) Viewpoint constraint
 * 136) View consistency constraint
 * 137) Multi-view matching
 * 138) Scene reconstruction/Surface interpolation
 * 139) Adaptive mesh refinement
 * 140) Constrained reconstruction
 * 141) Membrane/Thin plate models
 * 142) Texture synthesis/Texture mapping
 * 143) Triangulation
 * 144) Volumetric reconstruction
 * 145) Visual hull
 * 146) Trinocular (and more) stereo
 * 147) Parameter Estimation
 * 148) Bayesian methods
 * 149) Constrained least squares
 * 150) Linear least squares
 * 151) Optimization
 * 152) Robust techniques
 * 153) Probability and Statistics for Computer Vision
 * 154) Autoregression
 * 155) Bayes estimator
 * 156) Bayesian inference networks
 * 157) Causal models
 * 158) Correlation and dependence
 * 159) Covariance and Mahalanobis distance in Vision
 * 160) Dempster–Shafer theory
 * 161) Distribution mode analysis
 * 162) Normal distribution
 * 163) Heteroscedastic noise and HEIV regression
 * 164) Homoscedastic Noise
 * 165) Hidden Markov models
 * 166) Honest probabilities
 * 167) Statistical hypothesis testing/Analysis of variance
 * 168) Information theory
 * 169) Kalman filters
 * 170) Unscented Kalman filters
 * 171) Kernel canonical correlation
 * 172) Kernel regression
 * 173) Least mean square estimation and estimators/Least-Squares fitting
 * 174) Least median square estimation and estimators
 * 175) Log-normal distribution
 * 176) Logistic regression
 * 177) Maximum likelihood
 * 178) Model/Curve fitting
 * 179) Monte Carlo method
 * 180) Point process
 * 181) Markov chain/Markov chain Monte Carlo methods
 * 182) Markov random field
 * 183) Applications
 * 184) Conditional random fields
 * 185) Multi-level Markov random fields
 * 186) Optimization methods
 * 187) Approximate variational extremum
 * 188) Gibbs sampling
 * 189) Graduated nonconvexity
 * 190) Graph cuts in computer vision
 * 191) Iterated conditional modes
 * 192) "Modern" graph cut
 * 193) Simulated annealing
 * 194) Markov random field theory
 * 195) Mixture models and expectation-maximization (EM)
 * 196) Poisson mixture model
 * 197) Normalization
 * 198) Non-Parametric Methods
 * 199) Non-parametric statistics
 * 200) Kernel density estimation
 * 201) Poisson distribution
 * 202) Density estimation
 * 203) Random number generation
 * 204) Robust estimators
 * 205) Useful distributions
 * 206) Projection geometries and transformations
 * 207) Affine projection model/Affine transformation
 * 208) Anamorphic projection/Catadioptric system
 * 209) Central projection
 * 210) Orthographic projection
 * 211) Homography
 * 212) Hierarchy of geometries
 * 213) Perspective projection
 * 214) Projective plane
 * 215) Projective space
 * 216) Real camera projection
 * 217) Similarity matrix
 * 218) Weak-perspective
 * 219) Properties and invariants of projection
 * 220) absolute points
 * 221) Affine invariants
 * 222) Collineation
 * 223) Conics/Quadrics
 * 224) Coplanarity Invariants
 * 225) Cross-ratio
 * 226) Differential invariants
 * 227) Duality
 * 228) General projective invariants
 * 229) Integral Invariants
 * 230) Laguerre formula
 * 231) Pencils
 * 232) Quasi-Invariants
 * 233) Structural invariants
 * 234) Relational shape descriptions
 * 235) Curves
 * 236) Adjacency/Connectedness
 * 237) Relative Curvature
 * 238) Relative Length
 * 239) Relative Orientation
 * 240) Separation
 * 241) Regions
 * 242) Adjacency/Connectedness
 * 243) Relative area/size
 * 244) Separation
 * 245) Surfaces
 * 246) Adjacency/Connectedness
 * 247) Relative area/size
 * 248) Relative orientation
 * 249) Separation
 * 250) Volumes
 * 251) Adjacency/Connectedness
 * 252) Relative orientation
 * 253) Relative volume/size
 * 254) Separation
 * 255) Shape properties
 * 256) Geometric Morphometrics
 * 257) Kendall's Shape Space
 * 258) Points and Local Invariants
 * 259) Scale-invariant feature transform
 * 260) Curves and Curve Invariants
 * 261) Affine Arc length and Affine curvature
 * 262) Arc length
 * 263) Bending Energy
 * 264) Chord distribution
 * 265) Curvature, Torsion of a curve, Curvature radius
 * 266) Differential geometry, Frenet–Serret formulas
 * 267) Invariant Points: Inflections/Bitangents
 * 268) Image regions and region invariants
 * 269) Angularity ratio
 * 270) Area, Perimeter
 * 271) Boundary properties
 * 272) Center of mass, Centroid
 * 273) Convexity ratio
 * 274) Eccentricity, Circularity ratio, Elongatedness
 * 275) Elongation factor
 * 276) Euler number/Genus
 * 277) Extremal points
 * 278) Feret's diameter, Martin's diameter
 * 279) Fourier descriptors
 * 280) Minimum bounding rectangle
 * 281) Image moments
 * 282) Affine moments
 * 283) Bessel-Fourier moments
 * 284) Binary moments
 * 285) Color moments
 * 286) Eigenmoments
 * 287) Fourier-Mellin moment invariants
 * 288) Gaussian-Hermite moments
 * 289) Grey-level or texture moments
 * 290) Hahn moments
 * 291) Krawtchouk moments
 * 292) Legendre moments
 * 293) Orthogonal Moments: Pseudo-Zernike moments, Legendre moments
 * 294) Racah moments
 * 295) Tchebichef/Chebichev moments
 * 296) Velocity moments
 * 297) Zernike moments
 * 298) Orientation
 * 299) Sphericity ratio
 * 300) Rectangularity
 * 301) Rectilinearity
 * 302) Roundness ratio
 * 303) Topological descriptors
 * 304) Euler characteristic
 * 305) Wadell's circularity shape ratio
 * 306) Differential geometry of surfaces
 * 307) Apparent contour and local geometry
 * 308) Common shape classes and representations
 * 309) Cone representations
 * 310) Cyclide
 * 311) Cylinder representations
 * 312) Ellipsoid/Sphere Representations
 * 313) Thin plate splines
 * 314) Plane representations
 * 315) Polyhedra representations
 * 316) Quadric representations
 * 317) Torus representations
 * 318) Fundamental surface forms
 * 319) Gauge coordinates
 * 320) Hessian
 * 321) Laplace–Beltrami operator
 * 322) Metric determinant
 * 323) Principal curvature and directions and other local shape representations
 * 324) Deviation from flatness
 * 325) Gauss–Bonnet surface description
 * 326) Gaussian curvature
 * 327) Koenderink's shape classification
 * 328) Mean curvature
 * 329) Mean and gaussian curvature shape classification
 * 330) Minimal surface
 * 331) Parabolic points
 * 332) Ridges and Valleys
 * 333) Umbilics
 * 334) Quadratic variation
 * 335) Ricci flow
 * 336) Surface area
 * 337) Surface normals and tangent planes
 * 338) Orientability
 * 339) Symmetry
 * 340) Affine
 * 341) Bilateral
 * 342) Rotational symmetry
 * 343) Skew symmetry
 * 344) Volumes
 * 345) Elongatedness
 * 346) 3D moments and moment invariants
 * 347) Volume
 * 348) Transformations (geometric), registration and pose estimation methods
 * 349) 2D to 2D pose estimation methods
 * 350) Line-based methods
 * 351) 2D to 2D point-based pose estimation methods
 * 352) 2D to 3D pose estimation methods
 * 353) 2D to 3D pose estimation from lines
 * 354) 2D to 3D point-based pose estimation methods
 * 355) 3D to 3D pose estimation methods
 * 356) 3D to 3D line-based pose estimation methods
 * 357) 3D to 3D point-based pose estimation methods
 * 358) Affine transformation estimation
 * 359) Minimal data estimation
 * 360) Least-square estimates
 * 361) Robust estimates
 * 362) Bundle adjustment
 * 363) Euclidean transformation
 * 364) Least-square euclidean transformation estimates
 * 365) Minimal data euclidean transformation estimation
 * 366) Robust euclidean transformation estimates
 * 367) Homography transformation
 * 368) Least-square homography transformation estimates
 * 369) Minimal data estimation
 * 370) Robust homography transformation estimates
 * 371) Kalman filter pose estimation methods
 * 372) Partially constrained pose
 * 373) Incomplete information
 * 374) Intrinsic degrees of freedom
 * 375) Projective transformation estimation
 * 376) Least-square projective transformation estimation
 * 377) Minimal data estimation
 * 378) Robust Estimates
 * 379) Similarity transformation estimation
 * 380) Least square estimates
 * 381) Minimal data estimation
 * 382) Robust estimates