Resolution in downscaling

[sandon]

Let say we have NxM pixels and we need to cut it down to 2/3*(NxM)

The correct method to achieve this is to convolute the original image with sinc(k)sinc(l), then used the nearest neighbor technique to on the convoluted image. Where k and l is matched to the frequency content of the lower resolution image.

Nearest neighbor technique is for the downscaled pixel to find the closest pixel at its current position of the original image and take that color.

Question is: What does the convolution of the 2D sinc functions do to the original image to make it appropriate enough to use the nearest neighbor technique to down scaled the image.

Thanks in advance

 

[meBigGuy]

It is an averaging filter which represents a rectangular frequency response (sharp frequency cutoff). Let's simplify and just use a rectangular window (which has a sinc frequency response). It can be thought of as a simple moving average. As you slide through the data you make each pixel more likes its neighbor so then you can toss some out. If you don't filter before you decimate you get aliasing artifacts. Do you understand aliasing artifacts?

 

[Khashishi]

sinc is the Fourier transform of a box. The convolution theorem says that when you take the Fourier transform of the convolution of two signals, it is the same as taking the product of the Fourier transforms of the signals.

The lower resolution image is also lower resolution in frequency space. Nearest neighbor, by itself, will transfer some higher frequency information to lower frequencies. The sinc convolution removes all the high frequency information (which can't be represented in the lower resolution format and will end up as aliasing artifacts).