Histogram Matching

  • Definition of histogram matching.
  • Why histogram matching is used in practice .
  • Analytic derivation of the matching technique.
  • Algorithmic specification of the discrete version.

Homogenous coordinates

  • How one may convert between (x,y) and (x,y,w) coordinates.
  • How one may write a translation and rotation as a single matrix multiply using homogeneous coordinates.
  • How the variable may be used for uniform scale changes in the coordinates.
  • Composition of multiple Euclidean transformations.

Linear and Logical Image Operations

  • Image masks by AND, OR logical operations
  • Image mask logical NOT is equivalent to image negative
  • Local masks 

Spatial Filtering of Images

  • Convolution 1D -> 2D
  • Convolution and difference equations
  • Convolution and cross-correlation
  • Filtering definition differences : (1) signal processing defines filtering as convolution, (2) G&W defines filtering as cross-correlation. Why? So indexes of the filter and the image agree.
  • Relationship between convolution and cross-correlation.
  • Image averaging filter, non-normalized.
  • The purpose of normalization and how we guarantee valid images as output using a weighted average filter.
  • Introduction to Gaussian blurring, i.e., Gaussian weighted averaging filters.