Image Processing

Image processing is the set of operations applied to images (or video frames) to extract useful information or modify the image.

The key difference between image data and regular time-series is that images have a spatial (2D) distribution. Each pixel has two coordinates $I(x,y)$ or $I_{xy}$. As such, operations that modify images must consider the spatial arrangement of pixels; image filters are 2D filters.

Spatial Filtering

Spatial filtering is a fundamental operation in image processing, with the other being frequency domain filtering. A filter modifies each pixel based on its neighborhood; typically a small region around the pixel. Spatial filters are also called masks, kernels and windows.

A spatial filter has two main ingredients:

• A neighborhood of the pixel of the pixel under examination
• A predefined operation $T$ that is performed on the neighborhood

A typical spatial filter would look something like

$$I^{\prime }(x,y)=\sum _{s=-a}^a\sum _{t=-b}^{b}w(s,t)\cdot I(x+s,y+t)$$

where $w(s,t)$ is a filter weight, $(s,t)$ are offsets from the pixel location, and $(a,b)$ define the neighborhood size.

• Correlation and Convolution Filters
• Smoothing Filters
• Edge Detection Filters