Algorithms

This part of the website is devoted to documenting the algorithms that I've worked on or researched over the years. Each of the images below link to an overview of the algorithms in that section and a PDF file with the algorithm mathematics and explanations.

This is a work-in-progress and is still largely incomplete. Sections that have not been completed are marked with a red [TBD]. I have not even proof read much of this documentation, so please forgive any misspellings, bad grammar, or mathematical blunders.

I am working to complete this in my spare time and hope to have it completed over the next few weeks.

Click to Open PDF (Approx 20% Complete)		SECTION 1 MATHEMATICS Linear Algebra Gauss-Jordan Elimination Matrix Inverse Eigenvalues & Eigenvectors Singular Value Decomposition Trigonometry Singular Value Decomposition Calculus Derivative Rules

Click to open PDF (Approx 50% Complete)		SECTION 2 GEOMETRY Parametric Geometry Parametric Line Parametric Circle Parametric Aligned Ellipse Parametric Rotated Ellipse Coordinate Transforms Rotation & Translation Matrices Orthographic Projection Matrix Perspective Projection Matrix Projective Geometry and Homogeneous Coordinates Homogeneous Coordinate Space Homogeneous Point Equations Homogeneous (Plücker) Line Equations Homogeneous Plane Equations Vectors and Unit Vectors Geometric Intersections Geometric Projections Polygon Routines Point Inside Polygon Non-Self-Intersecting Concave Hull Polygon Convex Hull Polygon Boolean Polygon Operations Point Sorting and Bounding Algorithms 2D/3D Vector Point Sorting Directional Bounding Box Minimal Bounding Box

Click to open PDF (Approx 80% Complete)		SECTION 3 - DATA PREDICTION AND FILLING General Curve Fitting Polynomial Curve Fit Polynomial Surface Fit Interpolation Linear Interpolation Polynomial Interpolation Spline Interpolation Bilinear Interpolation Irregular Bilinear Interpolation Bicubic Interpolation Triangular Interpolation Regression and Least Squares Minimization Least Squares Minimization Linear Regression Polynomial Regression Parametric Linear Regression Bilinear Regression (a.k.a Multilinear Regression) Bi-polynomial Regression

Click to Open PDF (Approx 0% Complete)		SECTION 4 STATISTICS Correlation Normalized Cross Correlation (NCC) Sum of Absolute Differences (SAD) Sum of Squared Differences (SSD) Rank Correlation Census Correlation Data Classifiers 2D Gaussian Multivariate Gaussian (Mahalanobis Distance)

Click to Open PDF (Approx 30% Complete)		SECTION 5 IMAGE PROCESSING Resampling Image Interpolation Comparison Convolution Robert's Cross Edge Detector Sobel Edge Detector Canny Edge Detector Gaussian Smoothing Morphological Operators Erosion Dilation Opening Closing Thinning Thickening Hit or Miss Transform Skeletonization Pruning Perimeter Detection Image Enhancement Techniques Contrast Stretching (a.k.a. Dynamic Range Adjustment) Unsharp Masking Thresholding Hough Transforms Texture Growth

Click to Open PDF (Approx 40% Complete)		SECTION 6 PHOTOGRAMMETRY 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 Mensuration Rational Polynomial Coefficients (RPC) Geodetic-to-Image Transform Single Image, Image-to- Geodetic Transform Multiple Image, Image-to- Geodetic Transform Satellite Image Geometry Line-of-Sight Vector (LOS) Azimuth and Elevation Ground Sample Distance Rectification Methods Georectification Epipolar Rectification Disparity Mapping