1. Foundations

Spatial Spectroscopy is a methodology for defining, representing, analyzing, and solving computer vision problems that unifies multiscale analysis, differential geometry, and statistical pattern recognition.
This tutorial introduces the foundations of spatial spectroscopy, specifically the historical, mathematical, engineering, and computational foundations of the methodology.
The methodology begins by defining the spatial analog of electromagnetic spectroscopy, showing the central role of the Taylor Series in the underlying mathematics, shows how Fourier analysis can be used to understand both the power of spatial spectroscopy and how conventional methods fail to exploit that power, and the computational simplifications that make Spatial Spectroscopy practical for use in solving real computer vision problems.