 Hello, my name is Sujat. And hi, I am Harshad. So, today we will discuss about sampling in a digital video. So, as you know any video or an image is basically a sample two dimensional signal. And the rate of sampling is decided by the camera or the device which is capturing that image or the video. So, the rate of sampling is important and we have to decide what the rate of sampling should be. So, that the video can be perceived as it is. So, we will first discuss about spatial sampling. As you can see in this we will take the example of this particular video. So, in this video basically in this frame you can see regions of constant intensity and regions where there are lot of variations, we will see the effect of pixel density on this video. So, when I take up this particular region and represented it by a single pixel, we will see what happens. Now, let us increase the number of pixels to 4 and see what happens to this region. Now, again let us increase to the number of pixels to be 9 and then 16. Now, let us move on to region where there are lot of variations. So, in this video we will particularly represent Herschel space with one pixel. So, what we are doing is taking all the pixels over Herschel space and averaging it and then representing the whole image or the whole region using one value. So, let us see what happens when we represent Herschel space with one pixel. So, I hope you are not able to understand what expression Herschel is making. So, we have to increase the number of pixels to see exactly what Herschel is expressing right now. So, let us increase the number of pixels to 4, still it is not quite visible. Now, let us increase it still more to 9, now 16 and then more. Now, you can see Herschel is smiling and he was smiling all the time. So, we have seen the pixel density, how it affects the video. So, where the regions where we have constant intensities, we require less number of pixels and the region where we have lot of variations like Herschel space, we require large number of pixels. So, this is basically, this has a lot of correspondence with Nyquist rate and basically the Nyquist sampling theorem. The one dimensional Nyquist sampling theorem basically says if we have higher frequencies we require higher sampling rate and if we have a low frequency we will require lower sampling rate. So, this same in this video also, so where we have large number of variation within a particular region, we have to have large number of pixels and where we have constant region, we just require 2 or few pixels. Now that we have seen how pixel density affects our video, we will talk about the resolution of cameras. So, you might have heard of cameras having resolutions like 2 megapixel camera, 8 megapixel, 14 megapixel. So, what this number signifies? So, 14 megapixel camera is basically that we are capturing an image using 40 million pixels. As we have seen in this video, the more the number of pixels, the more better the video will be. So, whenever we are shooting an image or a video having very high amount of variations, we would require high resolution cameras. So, that is why resolution of a camera is important for shooting an image or a video. Now that we have seen how pixel density affects the image or a video, we have seen that lower variation image or lower variation region will require less number of pixels and higher variation region will require high number of pixels. I would like you to think how this can be exploited in image and video compression. So, now that we have looked at spatial sampling, we will look into the temporal sampling also. You might have noticed a fast moving wheel rotating in opposite direction. So, that essentially is effect of the sampling in time direction. To understand it, let us have a simple demonstration. We will take a simple sinusoidal wave moving in left direction. So, here we can see that sinusoidal wave is moving in left direction. Now if we down sample it, we get this which is again moving in left direction. Now if we down sample it further, we will obtain a wave like this in which actually we can see alternate sinusoid in one is in phase and one is out of phase. So, this is essentially we are sampling it at Nyquist rate and hence it is happening. Now if we further down sample it, it will appear as if it is moving in opposite direction. This is essentially because of the fact that initially we were sampling it at a much higher rate and hence we were smoothly getting the sine wave, but now since we are sampling it more than half of its time period, it appears as if it is moving in opposite direction. If we further down sample it, it will appear as if it is moving in opposite direction, but very slowly. At one point of down sampling, it will appear stationary. We can understand this from the fact that we are actually sampling it almost equally and its sampling rate is equal to time period of the sine wave. Further down sampling will make this sine wave appear moving in left direction. We will see one practical example of temporal sampling. Here fan is moving in anticlockwise direction. If we down sample it, it will appear as if it is moving in clockwise direction. Further down sampling will make the fan appear rotating clockwise direction with even low speed. So, this is actually known as wagon wheel effect and the main reason behind this is the aliasing which we observed. In this video we have explored spatial and temporal sampling and its effects on a video and we have also touched upon the fact that this can be used in image compression. So, why do we care? Well, this can be very useful for video compression. A scene having large amount of variation must be represented with large number of samples while scene having fewer variations can be represented with less samples. In temporal direction a scene having fast moving objects must be represented with high frame rate while scene having slow moving object can be represented with low frame rate. This is an a very active area of research in video coding domain. Hope this video has helped you appreciate sampling and its implications in a video which incidentally is a three dimensional signal. We will see you in another video, thank you.