This link here goes to the documentation for convolution matrices in GIMP (https://bit.ly/2GkcEFs). Just as a reminder, GIMP is raster graphics editor (free and open source!), and their convolution matrix documentation is a nice encapsulation of what values are required, how the transformations are performed, and some examples of filters like sharpening, blurring, edge detection, etc.
ellenluo
Notice that these filters do not sum to 1. Thus, the brightness of the image is not preserved. This can be seen in the images on the following slide.
shivamparikh
It's also kind of neat to realize that with the negatives on one side and positives on the other, the extraction of a gradient is just a linear algebra version of taking the derivative of a certain pixel in a certain direction (d/dx) and (d/dy).
jessicajyeh
I'm curious what is significant about the centered values of +/- 2. Would these filters work similarly if the +/- 2s were replaced with 1s instead?
This link here goes to the documentation for convolution matrices in GIMP (https://bit.ly/2GkcEFs). Just as a reminder, GIMP is raster graphics editor (free and open source!), and their convolution matrix documentation is a nice encapsulation of what values are required, how the transformations are performed, and some examples of filters like sharpening, blurring, edge detection, etc.
Notice that these filters do not sum to 1. Thus, the brightness of the image is not preserved. This can be seen in the images on the following slide.
It's also kind of neat to realize that with the negatives on one side and positives on the other, the extraction of a gradient is just a linear algebra version of taking the derivative of a certain pixel in a certain direction (d/dx) and (d/dy).
I'm curious what is significant about the centered values of +/- 2. Would these filters work similarly if the +/- 2s were replaced with 1s instead?