7 - Non-Local means - Duration

Описание: As we just saw, local averaging has some very interesting mathematical properties. It's a very simple operation as well and is very useful as we saw a few examples before. But we have also observed that it can blur the information in the image, it can blur the edges. So, how do we solve that? We have a number of different directions to go. One is to basically replace this local averaging by a different local operation and we're going to see that very soon. The other is, we may ask ourself, are we only limited to average in the local neighborhood? Maybe we can do a smarter average. Remember that averaging is like a heat flow. So, shall we basically average between a very hot pixel and a very cold pixel or shall we try only to average between pixels that are similar and try to stop averaging pixels that are very different. And that's, a very interesting concept that can actually be implementing a very, very variety of ways in a very different number of directions. But let's just explain one which is extremely elegant. In part it's elegant because it's very simple and it's actually called non-local means. Instead of looking at averages in the local neighborhood, we're going to look at averages in the whole image. Let's see why we can do that and how we do that. The idea is very simple. Let's just observe this image. We actually see that images have repetition. Sometimes these are called self-similarities. So for example, if we look at this local neighborhood, it's very similar to this local neighborhood, and very similar to this local neighborhood. We also observed that here this local neighborhood is very similar to this local neighborhood, even similar to this. They're far away, but they're very similar, the same here. So, before, we were thinking about averaging only pixels inside here, maybe we should actually average neighborhoods that are similar. Maybe we should average these three, so we can replace this pixel by certain relationship with others, but we should not mix this with these because the local neighborhoods are very different. So, the basic idea of non local means or non local averaging is to try to average, try to enjoy the properties of averaging but not restrict that to a local neighbourhood. So why are we doing that, and how are we doing that? So, the basic idea is that if we assume that these are identical things, identical structures, but maybe with different noise. Let's see the effects of that. Let's assume that we have a certain pixel, lets call it P, that's what we observed. It's the clean pixel plus some noise. But the noise, basically is a random variable, so it's always slightly different. So, we observed the pixel a number of times.