1 00:00:01,060 --> 00:00:04,780 ‫In this lecture, we will understand the concept of a filter. 2 00:00:06,740 --> 00:00:14,610 ‫We have been saying till now that a cell in the Convolutional layer gets information from a set of pictures 3 00:00:14,610 --> 00:00:22,010 ‫cells or a set of cells in the previous layer, for example, that red cell in the Convolutional layer 4 00:00:22,010 --> 00:00:27,290 ‫is getting information from these nine cells and this red rectangle. 5 00:00:29,550 --> 00:00:30,810 ‫But what does this mean? 6 00:00:32,190 --> 00:00:35,580 ‫How is it getting the information from all these pixels? 7 00:00:36,960 --> 00:00:39,080 ‫We have 25 pixels here. 8 00:00:40,440 --> 00:00:48,630 ‫And our cell here can have only one value, which should be the representative value for these 25 pixels. 9 00:00:50,340 --> 00:00:56,700 ‫So we need to find a way to convert these 25 values of pixels into one value. 10 00:00:58,550 --> 00:01:07,320 ‫This is done by using a filter. Filter is a matrix of same dimensions as our window of receptive field. 11 00:01:08,730 --> 00:01:11,580 ‫So if the window is five cross five. 12 00:01:12,570 --> 00:01:14,950 ‫Filter is also of dimension five 13 00:01:14,990 --> 00:01:15,460 ‫Cross five. 14 00:01:17,050 --> 00:01:21,790 ‫If it is of three cross three, filter will also be of three cross three dimensions. 15 00:01:24,870 --> 00:01:33,690 ‫No, we have a window of five into five pixels containing pixel value and we have a five in two five 16 00:01:34,560 --> 00:01:36,870 ‫matrix containing some values. 17 00:01:39,000 --> 00:01:43,860 ‫We multiply each pixel value with the corresponding filter value. 18 00:01:45,280 --> 00:01:47,500 ‫And add all of these products up. 19 00:01:49,540 --> 00:01:51,370 ‫So the pixel value here. 20 00:01:53,500 --> 00:02:00,760 ‫Will be multiplied with zero point four the next pixel value will be multiplied with zero point three. 21 00:02:01,120 --> 00:02:01,750 ‫And so on. 22 00:02:02,770 --> 00:02:05,850 ‫And all these products will be added up 23 00:02:07,610 --> 00:02:09,620 ‫This will give us one number. 24 00:02:10,370 --> 00:02:15,230 ‫And this number will represent information in these 25 pixels. 25 00:02:18,190 --> 00:02:23,310 ‫Now the question comes, how do we decide the values in this filter ? 26 00:02:25,290 --> 00:02:27,360 ‫The answer to this is very pleasing. 27 00:02:28,290 --> 00:02:30,330 ‫We do not have to decide these values. 28 00:02:31,600 --> 00:02:34,370 ‫Our network will learn these values also. 29 00:02:35,620 --> 00:02:39,610 ‫So when we are training our model, these values will be self learnt. 30 00:02:43,330 --> 00:02:50,290 ‫Now to demonstrate how filters work and how they are able to extract certain features out. 31 00:02:51,900 --> 00:02:54,990 ‫I have taken a five into five input image. 32 00:02:56,510 --> 00:03:01,670 ‫With zero one type pixel values and a three by three filter. 33 00:03:05,690 --> 00:03:06,680 ‫Look at this filter. 34 00:03:07,810 --> 00:03:10,600 ‫This filter looks like a cross. 35 00:03:11,810 --> 00:03:16,610 ‫That is the diagonal values are one and the other are 0. 36 00:03:18,600 --> 00:03:24,280 ‫If we use this filter with a stride of one, we get this output. 37 00:03:27,570 --> 00:03:30,720 ‫The gif below shows you how we get this output. 38 00:03:33,020 --> 00:03:40,040 ‫How the filter values are multiplied and their product values are added up to get the first value. 39 00:03:40,610 --> 00:03:44,020 ‫Then the next value and then the next and so on. 40 00:03:49,370 --> 00:03:54,800 ‫This final output, which we get after applying the filter is called a feature map. 41 00:03:56,630 --> 00:04:05,110 ‫A feature map, because each filter highlights some feature of the input image, the images on the 42 00:04:05,110 --> 00:04:10,780 ‫right are demonstrating how particular features are highlighted by filters. 43 00:04:12,870 --> 00:04:21,330 ‫For example, if we use a vertical filter, that is the middle column of this matrix is one one one, 44 00:04:22,470 --> 00:04:24,990 ‫and these side columns are zero zero zero. 45 00:04:27,100 --> 00:04:31,150 ‫This type of filter transforms the image to this image. 46 00:04:33,350 --> 00:04:40,580 ‫Notice that vertical white lines are enhanced and the rest of the image is blurred. 47 00:04:42,810 --> 00:04:45,870 ‫Similarly, if we use the horizontal filter. 48 00:04:47,130 --> 00:04:50,230 ‫That is this middle row will be one one, one. 49 00:04:52,800 --> 00:04:56,310 ‫And top and bottom row will consist of zeros. 50 00:04:57,870 --> 00:05:00,060 ‫If we use such horizontal filter. 51 00:05:01,180 --> 00:05:02,260 ‫We set this image. 52 00:05:03,610 --> 00:05:09,460 ‫You can notice that horizontal white lines are highlighted and rest is blurred. 53 00:05:11,980 --> 00:05:13,450 ‫This is what a filter does. 54 00:05:14,760 --> 00:05:20,910 ‫A filter is a set of values which transforms the window by doing sum of products. 55 00:05:22,520 --> 00:05:29,180 ‫What we get after applying a filter is called a feature map, each feature map has some particular 56 00:05:29,180 --> 00:05:30,400 ‫feature highlighted. 57 00:05:33,320 --> 00:05:37,770 ‫So what we will do is we will use many types of filter. 58 00:05:38,810 --> 00:05:44,600 ‫So that each filter creates different feature maps containing different features. 59 00:05:46,340 --> 00:05:51,560 ‫This means our convolutional live is going to be a bundle of feature maps. 60 00:05:52,870 --> 00:05:56,470 ‫And each feature map has some particular highlighted feature. 61 00:05:57,910 --> 00:06:01,870 ‫Important thing to notice here is what happens in the next layer. 62 00:06:03,390 --> 00:06:04,650 ‫So this cell. 63 00:06:05,640 --> 00:06:09,000 ‫In the first feature map of Convolutional layer 2. 64 00:06:10,260 --> 00:06:11,250 ‫What does this see. 65 00:06:12,310 --> 00:06:17,280 ‫Is it only this rectangle on the first feature map of previous layer 66 00:06:18,250 --> 00:06:22,500 ‫Or this rectangle on all feature maps in the previous layer 67 00:06:24,410 --> 00:06:32,210 ‫The answer is that each cell on Convolutional layer two will be getting information of all the feature 68 00:06:32,210 --> 00:06:34,070 ‫maps in the previous layer. 69 00:06:35,610 --> 00:06:43,050 ‫Because only then can these cells combine the different features to find more high level features. 70 00:06:46,050 --> 00:06:47,870 ‫I'll summarize again for clarity. 71 00:06:49,280 --> 00:06:55,130 ‫We apply a filter on the previous layer of data to extract features. 72 00:06:58,100 --> 00:07:01,730 ‫The output after applying filter is called a feature map. 73 00:07:03,490 --> 00:07:08,710 ‫We apply many different types of filters to extract many different types of features. 74 00:07:09,920 --> 00:07:12,710 ‫This gives us a bundle of feature maps. 75 00:07:14,660 --> 00:07:18,480 ‫The first bundle of feature maps is called Convolutional layer One. 76 00:07:21,860 --> 00:07:26,210 ‫Convolutional layer 2 works on these extracted features. 77 00:07:27,530 --> 00:07:30,110 ‫To extract even higher level of features. 78 00:07:33,670 --> 00:07:36,670 ‫Next, we are going to discuss about the input layer. 79 00:07:38,250 --> 00:07:41,690 ‫Input layer also has multiple layers of information. 80 00:07:42,790 --> 00:07:44,390 ‫These layers are called channels. 81 00:07:44,950 --> 00:07:47,290 ‫We talk about channels in the next video.