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Hello.

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Welcome back.

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The mathematical definition of convolution is defined like this.

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This equation G of X Y appear.

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However in practice it is written like this one down here where the minus infinity to infinity is replaced

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with an subscript two and m subscript 2 what m subscript to represent.

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D have masks with and the N subscript to represent the half the masks height you can think of the mask

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as a filter or a smaller matrix remember the image itself is a matrix and a mask is a smaller matrix

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that we can evolve the image with and the basic mechanism used to understand one convolution can be

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expanded to the 2D domain as well.

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In this case the 2D array a is usually the input image and B is a small mask or matrix is a small matrix

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usually 3 by 3.

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The idea of mirroring and B and shifting it across it can also be adapted to that 2D case however mirror

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iron will now take place in both X and Y dimensions and shift and will be done starting from the top

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left points in the image.

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Moving along each line on to the bottom right pixel in a has been processed let's see one example let's

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say we have an image a represented by this matrix over here and a mask be represented by this three

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by three matrix when we perform a convolution B.

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This is where we get this other matrix here over here we must note that he has been flipped in both

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X and Y dimensions before the sum of the product is calculated as we can see from this image here as

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well as in the calculation to becomes minus 2 1 becomes minus 1.

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And of course flipping so remains the same convolution that masks that's a very common image processing

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technique and depending on the choice of mask coefficient entirely different result can be obtained.

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For example we can achieve results such as blurring sharpening edge detection etc. Now about correlation

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we express one dimensional correlation like this.

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You will realize that the correlation equation is just exactly like the convolution except that over

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here that minus sign is changed to a plus side.

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Similarly we can express to the correlation like this just like we saw in convolution again or that

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he had a minus sign he's changed to plus.

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So in a nutshell correlation is the same as convolution without flip in the mask before the sum of products

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are computed.

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The difference between using correlation and convolution intuiting neighborhood process operations is

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often irrelevant because many popular masks or floaters used an image process and are symmetrical around

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the origin.

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This diagram here shows the convolution process of an image and a candle in a much more generalized

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form.

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Over here we have come forward and a three by four image with a two by two candle.

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And the outputs is produce the output produced is a two by three matrix or image.

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We will see an equation later on for deriving the output size given the size of the image and the size

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of the filter.

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Kanno kind of post the video to see how you know what the calculation is performed here right.

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We can also convert of a single input image with multiple filters.

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Over here we see a single input image confused with Kana 1 the same image confused with filter Cano

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2 and then the same image involved with filter can 0 3.

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We find the output by adding the results from the 3 different filter can no convolutions.

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And then we add out a bias which is 1 when we are working in deep learning.

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We've got to admit bias as we can see demonstrated in this animation you can post the video or slow

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the video down to see how the animation is showing how the calculation is performed.

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We shall take a look at the reason why this animation is moving the way it is moving and why.

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And yeah the reason why it's moving the way it is moving and why he's taken these number of steps.

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When we start talking about what is known as strides

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right.

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So that's all there is in the next lesson we should describe the convolution layer.