Can someone explain what Kayvon was pointing out in saying that the Gaussian blur is better? He said something like "there are still ___" in the box blur, but I'm not sure what concrete feature he was distinguishing in the box blur. I can tell that the Gaussian looks "better" overall, but what was it that he was specifically pointing out?
kayvonf
@jmc. If you look closely at the box blurred image on the previous slide you'll still see edges in the image. On this slide the output is a "smoother blur" that more closely resembles the output of an out of focus lens.
Another way to picture what happens is to consider the effect of filtering an image that is all black with a single white pixel in it. If you apply a box filter to this image, you get a grey square. If you apply a gaussian filter, you'll get a 2D blurred that fades out smoothly.
For those that know a bit about about signal processing, this is because a gaussian filter eliminates more of the high-frequency details in the image than a box blur. To eliminate all frequency content above a threshold, you can convolve an input with a sinc filter (yes, the sinc it has negative coefficients). Therefore, convolution with some approximation to the sinc is used to low pass filter an input image.
kayvonf
The slides below have good illustrations of the difference between the output of a box and gaussian filter. Search for the slide titled "Smoothing with box filter revisited".
Can someone explain what Kayvon was pointing out in saying that the Gaussian blur is better? He said something like "there are still ___" in the box blur, but I'm not sure what concrete feature he was distinguishing in the box blur. I can tell that the Gaussian looks "better" overall, but what was it that he was specifically pointing out?
@jmc. If you look closely at the box blurred image on the previous slide you'll still see edges in the image. On this slide the output is a "smoother blur" that more closely resembles the output of an out of focus lens.
Another way to picture what happens is to consider the effect of filtering an image that is all black with a single white pixel in it. If you apply a box filter to this image, you get a grey square. If you apply a gaussian filter, you'll get a 2D blurred that fades out smoothly.
For those that know a bit about about signal processing, this is because a gaussian filter eliminates more of the high-frequency details in the image than a box blur. To eliminate all frequency content above a threshold, you can convolve an input with a sinc filter (yes, the sinc it has negative coefficients). Therefore, convolution with some approximation to the sinc is used to low pass filter an input image.
The slides below have good illustrations of the difference between the output of a box and gaussian filter. Search for the slide titled "Smoothing with box filter revisited".
http://cs.nyu.edu/~fergus/teaching/vision/3_filtering.pdf
Ohh, I see what you mean now. Thanks @kayvonf!