Everything about CNN convolution

What is convolution?

Suppose we have a grayscale image. It means we have only one layer and we convert the pixel values into 0 and 1 by using a min-max scaler. Here 0 means white color and 1 means black color. Now we know that in the human brain we have a visual cortex which is responsible for various types of image or video-related operations and we also know that there are layers and each layer is doing different types of operations like edge detection, corner detection, etc. We can also say these layers as filters. We will use filters in CNN which also works like the layers of the visual cortex. There are too many filters. Different filters are used for different works.

Let's see how filters actually works in CNN?

Suppose we have a 6x6 Gary image and a 3x3 filter. This filter is used for edge detection. CNN will do some mathematical operation on our image and will find the vertical edge of our image.

Our image layer:

Our filter is:

Now, at first, put the filter first row, and the first column on the image layer first-row and first column, and other rows and columns of the filter will get automatically set to the rows and columns of the image layer in order.

The new image layer matrix after calculations:

How we get this layer?
As we know that we put our filter on the image layer. So at first, we put filter first-row and first-column on image layer first row and first column and other rows and column will automatically get set in order. Now after putting the filter on the image layer we have to multiply each filter cell value with the image layer cell value and then we have to do the summation.

So here = first-row and first-column value of the filter is 1 and image layer is 0, so the result of multiplying is =0.

Then the result of the first-row and the second-column of the filter and image layer is = 0*0=0.

Now the first-row third-column=0*(-1)=0

Then second-row first-column=2*0=0
Then we will calculate second-row second column , then second-row third-column, then third-row first-column, third-row second-column, and third-row third-column and then we will do summation of all the result.

Summation=0+0+0+0+0+0+0+0+0=0

Now we have to put this value on our new layer matrix first-row first-column. Now go to the new layer matrix and you will see that the value of the first-row and first-column is 0. After calculating we have to move the filter to one column right and apply the filter again.

Summation result=0+0+0+0+0+0+(-1)+(-2)+(-1)=-4

.Now we have put this value on the first-row and second-column cell of the new layer. Now go to the first-row and second-column of the new layer matrix and you will see -4 is written. Then we have to move our filter one step right or one column right. It means now our filter first-row and the first-column will be set on the image layer first-row third-column and again we have to do the calculation. After the calculation we have to put the value again to the new image layer then have to move our filter again one step right or one column right. We have to move the filter to one step right until the columns get the end. After the columns get the end, we have to come one step down. It means now we have to put our filter on the second-row first-column then again have to do the calculation and again have to move one step right after calculation.

This process will go on until the total rows and columns end and after each calculation, we have to put values in our new image layer. This way we run our convolution operation.

Now we can see that our new image matrix max value is 0 and min value is -4. After this, we can say that our new image layer matrix is 4x4 but our main image matrix is 6x6. This means that we have lost some information from our image. So we can say that after convolution we lose some information.