Algorithms

This page is devoted to algorithms that I am currently working with, or have worked with in the past. Documenting these algorithms is a laborious task, so many of the sections are not yet linked to an algorithm page. I will be adding to the list as frequently as possible.

Additionally the algorithm pages are exported from MS Word and have some formatting scripts imbedded in them. You do NOT need to allow ActiveX to view the pages in-full, so please disregard the ActiveX warnings in MS Explorer. I apologize for the inconvenience.

The underlined sections are the right are links to algorithm pages and the 'Click to Open PDF' links on the right open sections of my algorithms document (very incomplete).

SECTION 1 - MATHEMATICS

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(Approx 20% Complete)

1.1 Algebra
Vector Algebra

1.2 Trigonometry
Trigonometric Identities

1.3 Calculus
Derivative Rules

1.4 Linear Algebra
1.4.1 Matrix Operations
Gauss-Jordan Elimination
Matrix Inverse
Singular Value Decomposition

1.4.2 Eigenvalues & Eigenvectors
Solution of 2x2
Solution of 3x3

SECTION 2 - GEOMETRY

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(Approx 50% Complete)

2.1 Parametric Geometry

2.1.1 Curvalinear Geometry
Parametric Line
Parametric Circle
Parametric Ellipse
Parametric Spiral
Parametric Helix
Parametric 3D Spiral
Bezier Curves

2.1.2 Surface Geometry
Parametric Plane
Parametric Cylinder (Surface)
Parametric Sphere (Surface)
Parametric Ellipsoid (Surface)
Parametric Cone (Surface)
Parametric Torus (Surface)

2.1.3 Volumetric Geometry
Parametric Cylinder (Volume)
Parametric Sphere (Volume)
Parametric Ellipsoid (Volume)
Parametric Cone (Volume)
Parametric Torus (Volume)

2.1.4 Operations
Intersection of Two Parametric Lines
Intersection of Parametric Line and Sphere

2.2 Coordinate Transforms
Rotation & Translation Matrices
Orthographic Projection Matrix
Perspective Projection Matrix

2.3 Projective Geometry

2.3.1 Definitions
Homogeneous Coordinate Space
Homogeneous Point Equations
Homogeneous (Plücker) Line Equations
Homogeneous Plane Equations
Vectors and Unit Vectors

2.3.2 Plücker Line Algorithms
Are Parallel / Are Collinear
Calculate Angle Between
Calculate Closest Point
Calculate Normal Distance
Calculate Normal Line
Calculate Skew Distance
Calculate Principal Point
Create from Two Points
Create from Point and Vector
Is Parallel to Plane
Translation
Rotation
Intesection of Two Lines
Intersection with Plane
Intersection with Sphere

2.3.2 Homogeneous Plane Algorithms
Are Parallel / Are Coplanar
Calculate Angle Between
Calculate Coplanarity
Distance from Point to Plane
Calculate Principal Point of Plane
Create from Point and Vector
Create from Three Points
Intersection with Vector
Intersection of Two Planes
Intersection with Line
Intersection with Sphere
Rotation
Translation

2.4 Polygon Routines
Point Inside Polygon
Concave Hull Polygon
Convex Hull Polygon
Boolean Polygon Operations

2.5 Point Sorting and Bounding Algorithms
2D/3D Vector Point Sorting
Directional Bounding Box
Minimal Bounding Box

SECTION 3 - INTERPOLATION AND REGRESSION

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(Approx 80% Complete)

3.1 General Curve Fitting
Exact Polynomial Curve Fit
Exact Polynomial Surface Fit

3.2 Interpolation
Linear Interpolation
Polynomial Interpolation
Spline Interpolation
Bilinear Interpolation
Irregular Bilinear Interpolation
Bicubic Interpolation
Triangular Interpolation

3.3 Least Squares Regression
Least Squares Regression
Linear Least Squares Regression
Polynomial Regression
Parametric Linear Regression
Planar/Bilinear Regression
Bi-polynomial Regression
Weighed Least Squares Regression

3.4 Eigenvalue/Eigenvector Regression
2D Ellipse Eigensolution Regression
Planar Eigensolution Regression

SECTION 4 - STATISTICS

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(Approx 0% Complete)

4.1 Correlation
Normalized Cross Correlation (NCC)
Sum of Absolute Differences (SAD)
Sum of Squared Differences (SSD)
Rank Correlation
Census Correlation

4.2 Data Classifiers
2D Gaussian
Multivariate Gaussian (Mahalanobis Distance)

SECTION 5 - IMAGE PROCESSING

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(Approx 30% Complete)

5.1 Resampling
Image Interpolation Comparison
Bilinear Interpolation
Bicubic Interpolation

5.2 Convolution
Robert's Cross Edge Detector
Sobel Edge Detector
Canny Edge Detector
Gaussian Smoothing

5.3 Morphological Operators

5.3.1 Binary Morphology
Erosion
Dilation
Opening
Closing
Thinning
Thickening
Hit or Miss Transform
Skeletonization
Pruning
Perimeter Detection

5.3.2 Grayscale Morphology
Erosion
Dilation
Opening
Closing

5.3.3 Grayscale Morphological Filters
Midrange
Pseudomedian

5.4 Image Segmentation
Watershed
Binary Labeling
Grayscale Labeling

5.5 Image Enhancement Techniques
Dynamic Range Adjustment
Unsharp Masking
Thresholding

5.6 Hough Transforms

5.7 Texture Growth

5.8 Other Algorithms
Logical Operators
Hough Image Transform

SECTION 6 - PHOTOGRAMMETRY

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(Approx 40% Complete)

6.1 Geodesy
Geodetic Coordinate Systems and Datums
Geocentric Coordinate Systems
Topographic Coordinate Systems
Geodetic-to-Geocentric Transform
Geocentric-to-Geodetic Transform
Geocentric-to-Topographic Transform
Topographic-to-Geocentric Transform

6.2 Mensuration
Rational Polynomial Coefficients (RPC)
Geodetic-to-Image Transform
Single Image, Image-to- Geodetic Transform
Multiple Image, Image-to- Geodetic Transform

6.3 Satellite Image Geometry
Line-of-Sight Vector (LOS)
Azimuth and Elevation
Ground Sample Distance

6.4 Rectification Methods
Georectification
Epipolar Rectification

6.5 Disparity Mapping