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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 [1] resource.

Vision Geometry and Mathematics

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  1. Basic Representations
    1. Coordinate systems
      1. Cartesian coordinate system
      2. Cylindrical coordinate system
      3. Hexagonal coordinate system
      4. Log-Polar coordinate system
      5. Polar coordinate system
      6. Spherical coordinate system
    2. Digital topology
    3. Dual space
    4. Homogeneous coordinates
    5. Pose/Rotation/Orientation Representations
      1. Axis-angle representation
      2. Clifford algebra
      3. Euler angles
      4. Exponential map
      5. Quaternion/Dual quaternion
      6. Rotation matrix
      7. Pitch/Yaw/Roll
  2. Distance metrics
    1. Affine
    2. Algebraic distance
    3. Bhattacharyya distance
    4. Chi-square test/metric
    5. Curse of dimensionality
    6. Earth mover's distance
    7. Euclidean distance
    8. Fuzzy intersection
    9. Hausdorff distance
    10. Jeffrey-divergence
    11. Kullback–Leibler divergence
    12. Mahalanobis distance
    13. Manhattan/City block distance
    14. Minkowski distance
    15. Procrustes analysis
    16. Procrustes average
    17. Quadratic form
    18. Specific structure similarity
      1. Curve similarity
      2. Region similarity
      3. Volume similarity
  3. Elementary mathematics for Vision
    1. Coordinate systems/Vectors/Matrices/Derivatives/Gradients/Probability
    2. Derivatives in sampled images
  4. Mathematical optimization
    1. Golden section search
    2. Lagrange multipliers/Constraint optimization
    3. Multi-Dimensional Optimization
      1. Derivative Free Search
      2. Global optimization
        1. Ant colony optimization
        2. Downhill simplex
        3. Genetic algorithms
        4. Graduated optimization
        5. Markov random field optimization
        6. Particle swarm optimization
        7. Simulated annealing
      3. Optimization with derivatives
        1. Levenberg–Marquardt
        2. Gradient descent/Quasi-Newton method
    4. Model selection
    5. Variational methods
  5. Linear algebra for computer vision
    1. Eigenfunction
    2. Eigenvalues and eigenvectors
    3. Principal Component and Related Approaches
      1. Dimensionality reduction
      2. Linear discriminant analysis
      3. Factor analysis
      4. Fisher's linear discriminant
      5. Independent component analysis
      6. Kernel Linear Discriminant Analysis
      7. Kernel principal component analysis
      8. Locality preserving projections
      9. Non-negative matrix factorization
      10. Optimal dimension estimation
      11. Principal component analysis/Karhunen–Loève theorem
      12. Principal geodesic analysis
      13. Probabilistic principal component analysis
      14. Rao–Blackwell theorem
    4. Sammon projection
    5. Singular value decomposition
    6. Structure tensor
  6. Multi-sensor/Multi-view geometries
    1. 3D reconstruction
      1. 3D shape from 2D projections
      2. 3D reconstruction from multiple images/orthogonal views
      3. Slice-based reconstruction
    2. Affine and projective stereo
    3. Baseline stereo
      1. Narrow baseline stereo
      2. Wide baseline stereo
    4. Binocular stereo algorithms
      1. Cooperative stereo algorithms
      2. Binocular disparity
        1. Subpixel disparity
      3. Dense stereo matching approaches
      4. Dynamic programming (stereo)
      5. Feature matching stereo algorithms
      6. Gradient matching stereo algorithms
      7. Image rectification
        1. Planar rectification
        2. Polar rectification
      8. Log-polar stereo
      9. Multi-scale stereo algorithms
      10. Panoramic image stereo algorithms
      11. Phase matching stereo algorithms
      12. Region matching stereo algorithms
      13. Weakly/Uncalibrated stereo approaches
      14. Spherical stereo
    5. Epipolar geometry/Multi-view geometry
      1. Absolute conic
      2. Absolute quadric
      3. Epipolar geometry definitions
      4. Essential matrix
      5. Fundamental matrix
      6. Grassmannian space/Plücker embedding
      7. Homography tensor
      8. transfer and novel view synthesis
      9. Trifocal tensor
    6. Image-based modeling and rendering/Plenoptic modelling
    7. Image feature correspondence constraints
      1. Active stereo (feature correspondence)
      2. Disparity gradient Limit (feature correspondence)
      3. Disparity limit (feature correspondence)
      4. Epipolar constraint
      5. Feature contrast
      6. Feature orientation
      7. Grey-level similarity (feature correspondence)
      8. Lipschitz continuity
      9. Ordering (feature correspondence)
      10. Surface continuity
      11. Surface smoothness
      12. Uniqueness (feature correspondence)
      13. Viewpoint constraint
      14. View consistency constraint
    8. Multi-view matching
    9. Scene reconstruction/Surface interpolation
      1. Adaptive mesh refinement
      2. Constrained reconstruction
      3. Membrane/Thin plate models
      4. Texture synthesis/Texture mapping
      5. Triangulation
      6. Volumetric reconstruction
        1. Visual hull
    10. Trinocular (and more) stereo
  7. Parameter Estimation
    1. Bayesian methods
    2. Constrained least squares
    3. Linear least squares
    4. Optimization
    5. Robust techniques
  8. Probability and Statistics for Computer Vision
    1. Autoregression
    2. Bayes estimator
    3. Bayesian inference networks
    4. Causal models
    5. Correlation and dependence
    6. Covariance and Mahalanobis distance in Vision
    7. Dempster–Shafer theory
    8. Distribution mode analysis
    9. Normal distribution
    10. Heteroscedastic noise and HEIV regression
    11. Homoscedastic Noise
    12. Hidden Markov models
    13. Honest probabilities
    14. Statistical hypothesis testing/Analysis of variance
    15. Information theory
    16. Kalman filters
      1. Unscented Kalman filters
    17. Kernel canonical correlation
    18. Kernel regression
    19. Least mean square estimation and estimators/Least-Squares fitting
    20. Least median square estimation and estimators
    21. Log-normal distribution
    22. Logistic regression
    23. Maximum likelihood
    24. Model/Curve fitting
    25. Monte Carlo method
    26. Point process
    27. Markov chain/Markov chain Monte Carlo methods
    28. Markov random field
      1. Applications
      2. Conditional random fields
      3. Multi-level Markov random fields
      4. Optimization methods
        1. Approximate variational extremum
        2. Gibbs sampling
        3. Graduated nonconvexity
        4. Graph cuts in computer vision
        5. Iterated conditional modes
        6. "Modern" graph cut
        7. Simulated annealing
      5. Markov random field theory
    29. Mixture models and expectation-maximization (EM)
      1. Poisson mixture model
    30. Normalization
    31. Non-Parametric Methods
      1. Non-parametric statistics
      2. Kernel density estimation
    32. Poisson distribution
    33. Density estimation
    34. Random number generation
    35. Robust estimators
    36. Useful distributions
  9. Projection geometries and transformations
    1. Affine projection model/Affine transformation
    2. Anamorphic projection/Catadioptric system
    3. Central projection
    4. Orthographic projection
    5. Homography
    6. Hierarchy of geometries
    7. Perspective projection
    8. Projective plane
    9. Projective space
    10. Real camera projection
    11. Similarity matrix
    12. Weak-perspective
  10. Properties and invariants of projection
    1. absolute points
    2. Affine invariants
    3. Collineation
    4. Conics/Quadrics
    5. Coplanarity Invariants
    6. Cross-ratio
    7. Differential invariants
    8. Duality
    9. General projective invariants
    10. Integral Invariants
    11. Laguerre formula
    12. Pencils
    13. Quasi-Invariants
    14. Structural invariants
  11. Relational shape descriptions
    1. Curves
      1. Adjacency/Connectedness
      2. Relative Curvature
      3. Relative Length
      4. Relative Orientation
      5. Separation
    2. Regions
      1. Adjacency/Connectedness
      2. Relative area/size
      3. Separation
    3. Surfaces
      1. Adjacency/Connectedness
      2. Relative area/size
      3. Relative orientation
      4. Separation
    4. Volumes
      1. Adjacency/Connectedness
      2. Relative orientation
      3. Relative volume/size
      4. Separation
  12. Shape properties
    1. Geometric Morphometrics
    2. Kendall's Shape Space
    3. Points and Local Invariants
      1. Scale-invariant feature transform
    4. Curves and Curve Invariants
      1. Affine Arc length and Affine curvature
      2. Arc length
      3. Bending Energy
      4. Chord distribution
      5. Curvature, Torsion of a curve, Curvature radius
      6. Differential geometry, Frenet–Serret formulas
      7. Invariant Points: Inflections/Bitangents
    5. Image regions and region invariants
      1. Angularity ratio
      2. Area, Perimeter
      3. Boundary properties
      4. Center of mass, Centroid
      5. Convexity ratio
      6. Eccentricity, Circularity ratio, Elongatedness
      7. Elongation factor
      8. Euler number/Genus
      9. Extremal points
      10. Feret's diameter, Martin's diameter
      11. Fourier descriptors
      12. Minimum bounding rectangle
      13. Image moments
        1. Affine moments
        2. Bessel-Fourier moments
        3. Binary moments
        4. Color moments
        5. Eigenmoments
        6. Fourier-Mellin moment invariants
        7. Gaussian-Hermite moments
        8. Grey-level or texture moments
        9. Hahn moments
        10. Krawtchouk moments
        11. Legendre moments
        12. Orthogonal Moments: Pseudo-Zernike moments, Legendre moments
        13. Racah moments
        14. Tchebichef/Chebichev moments
        15. Velocity moments
        16. Zernike moments
      14. Orientation
      15. Sphericity ratio
      16. Rectangularity
      17. Rectilinearity
      18. Roundness ratio
      19. Topological descriptors
        1. Euler characteristic
      20. Wadell's circularity shape ratio
    6. Differential geometry of surfaces
      1. Apparent contour and local geometry
      2. Common shape classes and representations
        1. Cone representations
        2. Cyclide
        3. Cylinder representations
        4. Ellipsoid/Sphere Representations
        5. Thin plate splines
        6. Plane representations
        7. Polyhedra representations
        8. Quadric representations
        9. Torus representations
      3. Fundamental surface forms
      4. Gauge coordinates
      5. Hessian
      6. Laplace–Beltrami operator
      7. Metric determinant
      8. Principal curvature and directions and other local shape representations
        1. Deviation from flatness
        2. Gauss–Bonnet surface description
        3. Gaussian curvature
        4. Koenderink's shape classification
        5. Mean curvature
        6. Mean and gaussian curvature shape classification
        7. Minimal surface
        8. Parabolic points
        9. Ridges and Valleys
        10. Umbilics
      9. Quadratic variation
      10. Ricci flow
      11. Surface area
      12. Surface normals and tangent planes
      13. Orientability
    7. Symmetry
      1. Affine
      2. Bilateral
      3. Rotational symmetry
      4. Skew symmetry
    8. Volumes
      1. Elongatedness
      2. 3D moments and moment invariants
      3. Volume
  13. Transformations (geometric), registration and pose estimation methods
    1. 2D to 2D pose estimation methods
      1. Line-based methods
      2. 2D to 2D point-based pose estimation methods
    2. 2D to 3D pose estimation methods
      1. 2D to 3D pose estimation from lines
      2. 2D to 3D point-based pose estimation methods
    3. 3D to 3D pose estimation methods
      1. 3D to 3D line-based pose estimation methods
      2. 3D to 3D point-based pose estimation methods
    4. Affine transformation estimation
      1. Minimal data estimation
      2. Least-square estimates
      3. Robust estimates
    5. Bundle adjustment
    6. Euclidean transformation
      1. Least-square euclidean transformation estimates
      2. Minimal data euclidean transformation estimation
      3. Robust euclidean transformation estimates
    7. Homography transformation
      1. Least-square homography transformation estimates
      2. Minimal data estimation
      3. Robust homography transformation estimates
    8. Kalman filter pose estimation methods
    9. Partially constrained pose
      1. Incomplete information
      2. Intrinsic degrees of freedom
    10. Projective transformation estimation
      1. Least-square projective transformation estimation
      2. Minimal data estimation
      3. Robust Estimates
    11. Similarity transformation estimation
      1. Least square estimates
      2. Minimal data estimation
      3. Robust estimates


References

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  1. ^ R. B. Fisher, "CVonline: an overview", Int. Assoc. of Pat. Recog. Newsletter, 27(2), April 2005. [1]
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