Linear Filters

In this set of chapters, we will discuss a wide family of linear filters. These filters lay the foundation for most representations for images and sequences. Even learning-based representations end up learning filters that are similar to those we will discuss here.

This part is composed of the following chapters:

Outline

• Chapter 17  Blur Filters introduces low-pass filters. These are filters used to lower the resolution of an image and are a key building block of many image processing operations such as image upsampling and downsampling.

• Chapter 18  Image Derivatives describes a set of band-pass filters, such as image derivatives, and several applications.

• Chapter 19  Temporal filters extends filtering to the temporal domain, and describes applications of spatiotemporal filters for motion estimation, a topic that will be further extended in Part Understanding Motion.

Notation

We will continue using the same notation as in the previous chapters.

• Images and sequences: We will use the \(\ell\) symbol to denote images and sequences: \(\ell \left[ n, m, t \right]\) or \(\ell \left( x, y, t \right)\).

• Convolution kernels: We will use \(h\), \(g\).

• Derivatives: We will use subindices for partial derivatives, for example \(\ell_x = \partial \ell / \partial x\).