User:Papadim.G/Computer Vision Geometry Summary

Computer Vision Geometry Summary shows an organisation of the geometric and mathematical topics central to computer vision and image processing. This was originally proposed in the [CVonline] resource [cite: URL...].

Vision Geometry and Mathematics

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
   6. Useful distributions
8. 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
9. Properties and invariants of projection
   1. absolute points
   2. Affine invariants
   3. Collineation

External links

• example.com