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Hello.

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Welcome back.

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In this lesson we should talk about convolution convolution is a widely used mathematical operator that

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processes an image by computing for each pixel and weighted to some of the values of that pixel and

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its neighbors.

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As we can see over here dependent on the choice of weights a wide variety of image processing operations

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can be implemented convolution and correlation are the two fundamental mathematical operations involved

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in lenient neighborhood oriented image processing algorithms.

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The convolution between two discrete one dimensional arrays a of X and b of x is denoted US is not be

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mathematically mathematically it is described by this equation

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right messianic sample.

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In this example which will show how the resort of a one D convolution operation can be obtained step

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by step.

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Let's say we have reached it with the values 0 1 2 3 1 0 and I repeat with it values 1 3 and minus 1.

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Let's see how to perform a convolution B.

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Initially we narrow our way B and align its center or reference value with the leftmost value of a partial

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result of the convolution calculation is 0 times minus one plus zero times three plus one times one.

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And this is equal to one as we can see over here 3 which is the center value of our rate B is aligned

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with zero which is the left most value of a.

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Next we shift a rate B one position to the right.

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The partial result of this convolution calculation becomes 0 times minus one plus one times my net plus

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one times three as we can see over here plus two times one and this gives us five.

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So at this stage of the stage of our calculation the values in the what a convolution B array is going

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to be one in 5.

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Right.

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So this is a is an array inputs everyone P is inputs every 2 we're going to have the third array here

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where we start a result.

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So this is the current state of that array.

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Next we are going to shift b another position to the right and we perform the calculation again the

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calculation becomes 1 times minus 1 two times three three times one and then we just add up the we just

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add up the product of this this and this and then this is what we get we get 8 and we store that in

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a Y resultant array in a what output array.

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So we're going to shift again we're going to shift.

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I repeat again as you can see we've shifted.

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I repeat again we performed the calculation two times minus one plus three times three plus two times

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one.

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This keeps us nine we stop.

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This will give us nine and we're going to store that in a while we're going to store that in a Y resorts

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array let's see I've written eight over here two times minus two times minus one gives us minus two.

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This would give us nine.

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This would give us two.

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So this value here should be nine not eight.

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So there's a typo here.

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Just bear with me.

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So next we would shift again.

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I repeat is going to be shifted to the right again.

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So when we shift it this becomes the position and then we perform the calculation three times minus

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one plus two three times three plus one times one and then this will give us this would give us four

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and then we store this resort over here in a while outputs array and then we shift again and then we

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perform the same computation to minus one this time and then plus one times three.

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As you can see over here and then plus several times one and then we store the resort over here in a

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while outputs array and then we shift again.

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This is the final shift and then we perform the calculation one times minus one which will give us minus

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one plus three times three which will give us zero plus two times one which will give us zero so the

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output is minus 1.

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So this is the end of a war computation.

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So at the end of the competition this is the results we'll find in our output array and this is the

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results of a convolution B.

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Given that the array a contains these these values 0 1 2 3 2 1 0 and then I repeat contains these values

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minus 1 3 and 1.

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This over here should be number 9.

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We detected this type earlier on so right.

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This is how easy it is to perform convolution.

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What I'm going to do is I'm going to attach the code to perform convolution from some of my other courses.

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I have image processing causes that shows how to develop convolution of rhythms for images.

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So I'm going to take some of those videos and put it here.

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For those of you who are interested in seeing how it is done you can take a look at that.

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But it's not required for what we are doing in this new course.

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And I'm going to touch the quote as well.

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Right.

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So that's all there is.

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And then I'll see you in the next lesson.