# Define High-Pass Filter in Image Processing

Here we Define High-Pass Filter and its types in Image Processing. Edges and fine detail in images are associated with high frequency components. A high-pass filter can be used to make an image appear sharper.

## Define High-Pass Filter in Image Processing

• These filters emphasize fine details in the image exactly the opposite of the low-pass filter.
• High-pass filtering works in exactly the same way as low-pass filtering; it just uses a different convolution kernel.
• Only pass the high frequencies, drop the low ones.
• High pass frequencies are precisely the reverse of low pass filters, so:  Hhp(u, v) = 1 – Hlp(u, v)

In the example below, notice the minus signs for the adjacent pixels. If there is no change in intensity, nothing happens. But if one pixel is brighter than its immediate neighbors, it gets boosted.

 0 -1/4 0 -1/4 +2 -1/4 0 -1/4 0

Unfortunately, while low-pass filtering smooths out noise, high-pass filtering does just the opposite: it amplifies noise.

You can get away with this if the original image is not too noisy; otherwise the noise will overwhelm the image.

MaxIm DL includes a very useful “range-restricted filter” option; you can high-pass filter only the brightest parts of the image, where the signal-to-noise ratio is highest.

High-pass filtering can also cause small, faint details to be greatly exaggerated.

## Types of High-Pass Filter in Image Processing

1. Ideal High Pass Filter
2. Butter worth High Pass Filters
3. Gaussian High Pass Filters

### 1. Ideal Low Pass Filter

The ideal high pass filter is given as:

where D0 is the cut off distance as before

Example of Ideal High Pass Filter

### 2. Butter worth Low pass Filters

The Butter worth high pass filter is given as:

where n is the order and D0 is the cut off distance as before

Example of Butter worth high pass filter

### 3. Gaussian High Pass Filters

The Gaussian high pass filter is given as:

where D0 is the cut off distance as before

Example of Gaussian High Pass filter

An over-processed image will look grainy and unnatural, and point sources will have dark donuts around them.

So while high-pass filtering can often improve an image by sharpening detail, overdoing it can actually degrade the image quality significantly.