Lecture (video) by Andrew Ng explaining edge detection with convolutions: distinguishes positive vs negative edges (light→dark vs dark→light), shows vertical and horizontal 3x3 filters and example outputs, explains intermediate values on small images, and compares hand-designed filters (simple 3x3, Sobel, Scharr/SHA) to learned filters via backpropagation; previews upcoming topics of padding and stride for convolutions.
You've seen how the convolution operation allows you to implement a vertical edge detector. In this video, you learn the difference between positive and negative edges, that is the difference between light to dark versus dark to light edge transitions. And you also see other types of edge detectors as well as how to have an algorithm learn, rather than have us hand code an edge detector as we've been doing so far. So let's get started. Here's the example you saw from the previous video where you have this image 6x6 that's light on the left and dark on the right. And convolving it with the vertical edge detection filter results in detecting the vertical edge down the middle of the image. What happens if in an image where the colors are flipped, where it is darker on the left and brighter on the right, so the tens are now on the right half of the image and the zeros on the left, if you convolve it with the same edge detection filter, you end up with negative 30s instead of 30 down the middle. And you can plot that as a picture that maybe looks like that. So because the shade of the transitions is reversed, the 30s now get reversed as well. And negative 30s shows that this is a dark to light rather than a light to dark transition. And if you don't care which of these two cases it is, you could take absolute values of this output matrix. But this particular filter does make a difference between the light to dark versus the dark to light edges. Let's see some more examples of edge detection. This 3x3 filter we've seen allows you to detect vertical edges. So maybe it should not surprise you too much that this 3x3 filter will allow you to detect horizontal edges. So as a reminder, a vertical edge according to this filter is a 3x3 region where the pixels are relatively bright on the left part and relatively dark on the right part. So similarly, a horizontal edge would be a353 region where the pixels are relatively bright on top and relatively dark in the bottom row. So here's one example, this is a more complex one where you have here tins in the upper left and lower right hand corners. If you draw this as an image, this be an image which is going to be darker where there's zeros, so I'm going to shade into darker regions and then lighter in the upper left and lower right hand corners. And if you convolve this with a horizontal edge detector, you end up with this. And so just to take a couple examples, this 30 here corresponds to this three by three region, where indeed there are bright pixels on top and darker pixels on the bottoms kind of over here. And so it finds a strong positive edge there. And this negative 30 here corresponds to this region, which is actually brighter on the bottom and darker on top. So that is a negative edge in this example. And again, as a, this is kind of an artifact of the fact that we're working with relatively small images. You know, that this is just a six by six image. But these intermediate values, like this minus 10 for example, just reflects the fact that that filter here, it captures part of the positive edge on the left and part of the negative edge on the right. And so blending those together gives you some intermediate value. But if this is a very large, say a thousand by a thousand image with this type of, you know, checkerboard pattern, then you won't see these transition regions of the tension. The intermediate values would be quite small relative to the size of the image. So in summary, different filters allow you to find vertical and horizontal edges. It turns out that the 3x3 vertical edge detection filter we've used is just one possible choice. And historically in the computer vision literature there was a fair amount of debate about what is the best set of numbers to use. So here's something else you could use which is maybe 1, 2, 1, 0, 00, minus 1, minus 2, minus 1. This is called a Sobel filter. And the advantage of this is it puts a little bit more weight to the central row, the central pixel. And this makes it maybe a little bit more robust. But computer vision researchers would use other assessor numbers as well, like maybe Instead of a 1, 2, 1, it should be 3, 10, 3, right? And then minus 3, minus 10, minus 3. And this is called a SHA filter. And this has yet other slightly different properties. And this is just for vertical edge detection. And if you flip it 90 degrees, you get horizontal edge detection. And with the rise of deep learning, one of the things we learned is that when you really want to detect edges in some complicated image, maybe you don't need to have computer vision researchers handpick these nine numbers. Maybe you can just learn them and treat the nine numbers of this matrix as parameters, which you can then learn using back propagation. And the goal is to learn nine parameters so that when you take the image, the 6 by 6 image, and convolve it with your 3 by 3 filter, that this gives you a good edge detector. And what you see in later videos is that by just treating these nine numbers as parameters, you know, the back prop can choose to learn 11100 -1 -1 if it wants, or learn a Sobel filter or learn a SHA filter, or more likely learn something else that is even better at capturing the statistics of your data than any of these hand coded filters. And rather than just vertical and horizontal edges, maybe it can learn to detect edges that are at 45 degrees or 70 degrees or 73 degrees, or at whatever orientation it chooses. And so by just letting all of these numbers be parameters and learning them automatically from data, we find that neural networks can actually learn low level features, can learn features such as edges even more robustly then computer researchers are generally able to code up these things by hand. But underlying all these computations is still this convolution operation which allows back propagation to learn whatever three by three filter wants and then to apply it throughout the entire image, you know, at this position, at this position, at this position, in order to output whatever feature it's trying to detect, be it vertical edges or horizontal edges or edges at some other angle or even some other filter that we might not even have a name for in English. So the idea that you can treat these nine numbers as parameters be learned has been one of the most powerful ideas in computer vision. And later in this course, later this week, we'll actually talk about the details how of how you actually go about using back propagation to learn these nine numbers. But first, let's talk about some other details, some of the variations on the basic convolution operation. In the next two videos I want to discuss with you how to use padding, as well as different strides for convolutions. And these two will become important pieces of this convolutional building block of convolutional neural networks. So let's go on to the next video.
