Consider the following image The image is 64x64 pixels and t

Consider the following image. The image is 64x64 pixels and the bbdt stripe has a width of 8 pixels: Make a sketch (or try to explain) what this image will look like if lowpass filtered. State any assumptions you make. Make a sketch (or try to explain) what this image will look like if highpass filtered. State any assumptions you make.

Solution

When a low-pass filter is used, in this case it shall be optical, this does is filter out high frequency signals thus leaving low frequency. But the real picture of any scene consists of infinite points. The sensor makes a sampling of the scene, so that each pixel contains a sample (light-colored) of the image area that suits you.

When sampling is done there is always some loss of information. Also, if the sampling frequency is not high enough known as aliasing effect it occurs.

Aliasing in images is that the resulting image sampling presents interference patterns: instead of showing for example parallel lines appear waves, visual effects and color artifacts that do not exist in the actual image. These elements are \'alias\' or ghosts that are part of the information (incomplete) high frequency of the original image.

The only way to avoid aliasing is causing the sampling frequency is greater than the spatial frequency of the scene (above the double according to the sampling theorem).
What the OLPF filters is just that: eliminate the very high frequency information of the image.

Lowpass filter: attenuates high frequencies and low remains unchanged. The result in the spatial domain is equivalent to a smoothing filter, where high frequencies are filtered correspond to strong intensity changes. Get reduce noise smoothing existing transitions.
Highpass filter: attenuates low frequencies while maintaining invariable high frequencies. Since high frequencies correspond to the images to sudden changes in density, this type of filter is used because, among other advantages, offers improved edge detection in the spatial domain, as these contain lots of these frequencies. Reinforces the contrasts found in the image.

In this case when applying the low-pass filter to the image for it to be a band where an abrupt change of tone colors and presented it gives a great distortion. For the case in which it applies the high-pass filter is not distortion edge will look but low frequency components that will make the gray colors will fade intensify.