1. The coordinate transformation space
Geometric transformations to change the spatial relationship between pixels in an image. It consists of two basic operations: the coordinates of the gradation conversion and the interpolated spatial transform.
The image coordinate conversion processing is used in the affine transformation, the affine transformation following common theme
These transformations commonly referred rubber membrane transform. Coordinate transformation can be represented by the following formula: (x, y) = T {(v, w)}. Wherein (v, w) are the coordinates of pixels in the original image, (x, y) are coordinates of pixels in the converted image. Common affine transformation general form:
**
This transformation can be a pixel on the image relocated to a new location in order to complete the process, it must also be assigned gray scale value to these new positions.
In fact, there are two basic ways to use (**) formula. The first method is called the forward mapping, the input image pixel by the scan, and directly computing the output image corresponding to the pixel position of the spatial coordinates (x, y) with (**) formula at each position (v, w) composition. Forward mapping algorithm is a problem in the input image two or more pixels can be transformed into the same position of the output image. The second method is called a reverse mapping, position of the scanning output pixels, and in each position (x, y) 
corresponding to the position of the input image is calculated. Then, interpolation gray-scale value.
2. grayscale interpolation
2.1 nearest neighbor interpolation
2.2 bilinear interpolation
2.3 pairs of cubic interpolation
3. Fourier transform
Fourier series Fourier transform Fourier integral To be continued ...
4. The basic properties of the Fourier transform
To be continued ...
