Ideas of what should constitute an 'edge'. 'edges' are difficult to define things, and different applications may have different First of all let's clarify something : edge detectorsĪnd gradients are not the same thing. Okay, so now let's get back to edge detection.

You justīox upsample then convolve with 121, and that's equivalent to upsampling with 1331. To upsample you just do : box upsample, then odd filter.įor example, the 'magic kernel' (aka bilinear filter) can be done using an odd filter of. To downsample you just do : odd filter, then box downsample. Ones, and box downsample means take four pixels are replace them with their average. Box upsample means replicate a pixel with four identical That is from an image to an image of the same size. That means all your library needs is odd filters and box resamplers. (However, it shouldīe noted that an even 'Sinc' is not made by taking an odd 'Sinc' and convolving with box, it changes the , or even width, in which case the center tap is duplicated :Īny even filter can be made from an odd filter by convolution with the box. Filters can be of odd width, in which case they In all cases I'm talking about discrete symmetric filters. The easiest way to write your filters correctly is using only box operations and odd symmetric filters. So the 'magic kernel' is just bilinear upsampling.Ĭostella shows that Lanczos and Bicubic create nasty grid artifacts. The center of P is 1/4 ofĪn original pixel distance to A, and 3/4 of a pixel distance to B, so the 3,1 taps are just a linear filter. If you prefer, each output pixel is made from (3*A + 1*B)/4, where A is the original pixel closer to theīut clever readers will already recongize that this is just a bilinear filter. The filter means you take each original pixel A and add the four values A* into the output. That is, we replace one pixel with four and they cover the same area :Ī 1d box upsample would be convolution with, where the output discrete taps are half the distance apart

The discrete 1d 'magic kernel' for upsampling is (unnormalized). If you look at that page, something is clearly amiss. Did he do it again with hisįirst of all, the edge detector is based on what he calls the magic kernel. He doesn't have an image science background, and in theĬase of Unblock that led him to some ideas that normal research didn't find. Which is a rather interesting and outside-the-norm deblocker. You may recognize Costella's name as the guy who made Unblock So I thought I'd record it for posterity. It's a little bit tricky to figure out what's going on there because his writing is quite obtuse, A friend recently pointed me at John Costella's

Gimp gradient magnitude