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

External links

• example.com