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
*w*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.