Lowpass, Highpass, Bandreject and Bandpass filters in image processing

Spatial domain and frequency domain filters are commonly classified into four types of filters — low-pass, high-pass, band-reject and band-pass filters. In this article I have notes, code examples and image output for each one of them.

Types of filters

• Lowpass filters: Allow passing only low frequency details, attenuates the high frequency details. Example: Smoothening filters.
• Highpass filters: Allows passing only high frequency details, attenuates the low frequency details. Example: Sharpening mask filters.
• Bandreject filters: Attenuate signal in range of a certain frequency. Allows frequency below a certain threshold and above another threshold to pass.
• Bandpass filters: Only allows signals within a certain band to pass, attenuates the frequencies below a threshold and above another threshold to pass.

Spatial kernels in terms of low-pass kernel — lp(x, y)

Different types of spatial kernels

δ(x, y) is a unit impulse kernel

Processing images with these…