Theory of Moments

A computer program has been written for the purpose of building up experience with some concepts in Pattern Recognition. The classical theory of moments has played a predominant role in the development of the code. This is exemplified by the Delphi unit ogenblik.pas, which is entirely devoted to it. As an application of the theory, a technique has been developed for the rendering of good old IBM punchcards. This document contains the mathematics of first and second order moments in one and two dimensions.

  1. One-dimensional Moments
  2. Example: Line Segment 1-D
  3. Two-dimensional Moments
  4. Example: Line Segment 2-D
  5. Example: Quarter of a Circle
  6. Least Squares Best Fit
  7. Schwarz inequality
  8. Tensor of Inertia
  9. Triangle Algebra
  10. Triangle Integrals
  11. Boundary Moments
  12. 2-D Gauss function
  13. Ellipses of Inertia
  14. Rendering of Punch Cards

Questions & Answers @ Mathematics Stack Exchange:

  1. When do equations represent the same curve?
  2. Find a smooth function with prescribed moments
  3. Does a sequence of moments determine the function?
  4. What is the chance that a PDF with compact support is concave?