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Geometry and mathematics
A part of the
CVonline
computer vision resource summarizing the geometric and mathematical methods commonly encountered in computer vision and image processing.
Basic Representations
Coordinate systems
Cartesian coordinate system
Cylindrical coordinate system
Hexagonal coordinate system (see external links)
Log-Polar coordinate system
Polar coordinate system
Spherical coordinate system
Digital topology
Dual space
Homogeneous coordinates
Pose
/
Rotation
/
Orientation
Representations
Axis-angle representation
Clifford algebra
Euler angles
Exponential map
Quaternion
/
Dual quaternion
Rotation matrix
Pitch/Yaw/Roll
Distance metrics
Affine distance
Algebraic distance
Bregman divergence
Bhattacharyya distance
Chi-square test/metric
Curse of dimensionality
Earth mover's distance
Euclidean distance
Fu
zz
y i
ntersection
Hausdorff distance
Jeff
rey divergence
Jensen-Shannon Divergence
Jaccard index
Kullback–Leibler divergence
Mahalanobis distance
Manhattan/City block distance
Minkowski distance
Procrustes analysis
Quadratic form
Specific
structural similarity
Curve similarity
Region similarity
Volume similarity
Elementary mathematics for Vision
Coordinate systems
/
Vectors
/
Matrices
/
Derivatives
/
Gradients
/
Probability
Derivatives in sampled images
Mathematical optimization
Golden section search
Lagrange multipliers
/
Constraint optimization
Multi-dimensional optimization
Random optimization
Global optimization
Ant colony optimization
Downhill simplex
Genetic algorithms
Graduated optimization
Markov random field
optimization
Particle swarm optimization
Simulated annealing
Optimization with derivatives
Levenberg–Marquardt
Gradient descent
Quasi-Newton method
Model selection
Variational methods
Linear al
geb
ra
for computer vision
Eigenfunction
Eigenvalues and eigenvectors
Principal component
and Related Approaches
Dimensionality reduction
Linear discriminant analysis
Factor analysis
Fisher's linear discriminant
Independent component analysis
Kernel linear discriminant analysis
Kernel principal component analysis
Locality
pr
eserving projections
Non-negative matrix factorization
Optimal dimension estimation
Sufficient dimension reduction
Principal component analysis
/
Karhunen–Loève theorem
Principal geodesic analysis
Probabilistic principal component analysis
Rao–Blackwell theorem
Sammon projection
Singular value decomposition
Structure tensor
Multi-sensor/Multi-view geometries
3D reconstruction
3D shape from 2D projections
3D reconstruction from multiple images
Slice-based reconstruction
Projective reconstruction
Baseline stereo
Narrow baseline stereo
Wide baseline stereo
Binocular stereo algorithms
Cooperative stereo algorithms
Binocular disparity
Subpixel disparity
Dense stereo matching approaches
Dynamic programming (stereo)
Feature matching stereo algorithms
Gradient matching stereo algorithms
Image rectification
Planar rectification
Polar rectification
Log-polar stereo
Multiresolution analysis
Panoramic image stereo algorithms
Phase matching stereo algorithms
Region matching stereo algorithms
Weakly/Uncalibrated stereo approaches
Spherical stereo
Epipolar geometry/Multi-view geometry
Absolute conic
Absolute quadric
Essential matrix
Fundamental matrix
Grassmannian space
/
Plücker embedding
Homography tensor
Transfer and novel view synthesis
Trifocal tensor
Image-based modeling and rendering
Plenoptic modeling
Image feature correspondence
Active stereo
Disparity gradient limit (feature correspondence)
Epipolar constraint
Feature contrast
Feature orientation
Grey-level similarity (feature correspondence)
Lipschitz continuity
Surface continuity
Surface smoothness
View consistency constraint
Scene reconstruction/Surface interpolation
Adaptive mesh refinement
Constrained reconstruction
Thin plate models
Texture synthesis
/
Texture mapping
Triangulation
Volumetric reconstruction
Visual hull
Trinocular (and more) stereo
Parameter Estimation
Bayesian methods
Constrained least squares
Linear least squares
Optimization
Robust techniques
Probability and Statistics for Computer Vision
Autoregression
Bayes estimator
Bayesian inference networks
Causal models
Correlation and dependence
Covariance
and
Mahalanobis distance
in Vision
Dempster–Shafer theory
Multimodal distribution
Normal distribution
Heteroscedastic noise
Homoscedastic
n
oise
Hidden Markov models
Probability axioms
Statistical hypothesis testing
/
Analysis of variance
Information theory
Kalman filters
Unscented Kalman filters
Canonical correlation
Kernel regression
Least mean squares estimation
Least median square estimation and estimators
Log-normal distribution
Logistic regression
Maximum likelihood
Model/Curve fitting
Monte Carlo method
Point process
Markov chain
/
Markov chain Monte Carlo
methods
Markov random field
Applications
Conditional random fields
Multi-level Markov random fields
Optimization methods
Gibbs sampling
Graduated optimization
Graph cuts in computer vision
Iterated conditional modes
Simulated annealing
Mixture models
and
expectation-maximization (EM)
Gaussian mixture model
Categorical mixture model
Normalization
Non-parametric statistics
Non-parametric regression
Kernel density estimation
Poisson distribution
Density estimation
Random number generation
Robust estimators
Projective geometry
/
Projective transformations
Affine projection model
/
Affine transformation
Anamorphic projection
/
Catadioptric system
Central cylindrical projection
Orthographic projection
Map projection
Homography
Hierarchy of geometries
Perspective projection
Projective plane
Projective space
Real camera projection
Similarity matrix
Weak-perspective
Tomasi-Kanade factorization
Projective invariants/cross-ratio
Absolute points (points at infinity)
Affine invariants
Affine geometry of curves
Collineation
Conics
/
Quadrics
Coplanarity
Differential invariants
Duality
Integral invariants
Laguerre formula
Pencils
Quasi-invariants
Structural invariants
Cartan's equivalence method
Relational shape descriptions
Curves
Adjacency/Connectedness
Relative curvature
Relative length
Relative
orientation
Separation
Regions
Adjacency/Connectedness
Relative area/size
Separation
Surfaces
Adjacency/Connectedness
Rel
ative area/size
Relative orientation
Separation
Volumes
Adjacency/Connectedness
Relative orientation
Relative volume/size
Separation
Shape properties
Geometric Morphometrics
Kendall´s Shape
Space
Points and local invariants
Scale-invariant feature transform
Curves
and Curve Invariants
Affine curvature
Arc length
Bending energy
Chord distribution
Curvature
,
Torsion of a curve
,
Radius of curvature
Differential geometry
,
Frenet–Serret formulas
Invariant Points:
Inflections
/
Bitangents
Image regions and region invariants
Compactness measure of a shape
Area
Perimeter
Center of mass
,
Centroid
Eccentricity
,
Elongatedness
Euler number/Genus
Extremal points
Feret's diameter
Fourier descriptors
Minimum bounding rectangle
Image moments
Affine moments
Bessel-Fourier
moments
Binary moments
Color moments
Central moments
Eigenmoments
Fourier-Mellin
moment invariants
Gaussian-Hermite
moments
Texture moments
Hahn moments
Krawtchouk
moments
Legendre moments
Orthogonal moments
Racah moments
Chebyshev moments
Zernike and velocity moments
Orientation
Sphericity
Rectangularity
Rectilinearity
Roundness
Topological invariants
Euler characteristic
Differential geometry of surfaces
Parametric surfaces
Common shape classes and representations
Cone representations
Cyclide
Cylinder representations
Ellipsoid
/
Sphere Representations
Thin plate splines
Plane representations
Polyhedra representations
Quadric representations
Torus representations
Fundamental surface
forms
First fundamental form
Second fundamental form
Gauge coordinates
Hessian
Laplace–Beltrami operator
Metric derivative
Principal curvature
and
directions
and other local shape representations
Deviation from flatness
Gauss–Bonnet surface description
Gaussian curvature
Koenderink's shape classification
Mean curvature
Minimal surface
Parabolic points
Ridges
Umbilics
Quadratic variation
Ricci flow
Surface area
Surface normals
and
tangent planes
Orientability
Symmetry
Affine symmet
ry
Bilateral symmetry
Rotational symmetry
Skew symmetry
Volumes
Elongatedness
3D moments and moment invariants
Volume
Transformations (geometric), registration and pose estimation methods
Poste estimation
2D to 2D pose estimation
Methods
2D to 3D pose estimation
Methods
3D to 3D pose estimation
Methods
Affine transformation
Minimal data estimation
Bundle adjustment
Euclidean transformation
Least-square euclidean transformation estimates
Minimal data euclidean transformation estimation
Robust euclidean transformation estimates
Homographic transformation
Least-square homography transformation estimates
Robust homography transformation estimates
Kalman filter pose estimation methods
Partially constrained pose
Incomplete information
Intrinsic degrees of freedom
Projective transformation
Direct linear transformation
Robust estimates
Similarity transformation
Articulated body pose estimation
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