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Hi and welcome to the section or chapter where we take a look at convolution, how the convolution operation

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works on color images.

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So let's take a look at this.

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Let's go back to our gray scale scenario.

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Remember, we built the edge detector here.

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This is our edge detector, colonel.

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This is our grayscale two dimensional image, and this is a feature of output.

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And you can see it's a fairly simple, straightforward calculation.

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So a lot of times beginners have trouble understanding when there's tree dimensions here, as you can

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see in the slide now, tree components how and we do have tree kernels one for each color.

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I'll tell you why that's important for people are often confused with why is the output two dimensional?

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And the reason the output is still two dimensional here.

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The feature map is because we take the colors here and we sum them up.

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So you can see this.

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A one is not too visible here.

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So you can see it's one plus one plus one gives this tree and we just some each each.

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Think of it like a like a hole that goes through each of these, these color components, and you can

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just some through each cell here so that each other corresponds to the same location.

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It just keeps summing it.

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And that's how you get the output can also that now the output, you know, is still a two by a tree

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by tree, two dimensional image, but not not a three dimensional image.

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That's what important point is here.

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So what are the advantages of having color components as your filters?

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Now, so imagine we're looking for a red, a stop sign.

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But however, imagine this there's a similar sign that screen and a green stop sign.

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The way we detect colors is by having these different color coded notes here.

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So one of these candidates could be corresponding to that red stop sign.

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The other one could be corresponding could be a filter that's meant to detect green signs and blue signs

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and different color combinations.

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So that's why it's quite important to have it each offensive, each color component.

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So this is how we treating volumes work, and we're going to take a look at basically how it works when

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we have multiple filters.

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So you previously so examples where we just had one filter.

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However, in reality, as I said, CNN's tend to have many, many filters that can have hundreds, even

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thousands, although that's a bit excessive.

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Most in most cases, it has like between 64 and 256 filters for most simple classifiers.

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So let's take a look at this.

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This is now with two filters, and you can see we have a five by five by tree image here.

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Remember, this is a color component of each image had a red, green and blue RGV.

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And this here is the pixel.

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So remember, each pixel point does zero by zero top left pixel has three color components associated

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with it.

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That's why it's a five by five by tree grid of volume right now.

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And here we have.

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We're using two filters now instead of one, like, you know, previous examples.

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So it's a tree by tree, by tree by two, because it's two filters now.

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And this allows us now to produce two feature maps instead of one.

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So you can see now the future maps are directly related to the number of future maps is directly related

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to the number of keynotes here.

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So this is how you actually calculate the feature map volume here.

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You can see end by end by see and see which is the in depth.

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So it's five by five by tree.

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This one here is ftf.

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That's a feature or this sort of filter.

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So you have tree by tree and we have tree depth again here.

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And this is what the of the output feature size is going to be.

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It's going to be an minus f plus one, which is tree.

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Similarly, Tree Hill multiplied by an F, which is two, and what is NF and F is a number of filters.

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So that's basically a mathematical way of just showing how these sizes are mapped back to the output

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of the feature map.

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It's not that complicated, it's just way too.

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It just it's just a way to establish some guidelines.

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So when you're actually calculating what your future map should be, you have a formula to work with.

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This is this formula right here at the end of it here.

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So that concludes this chapter on how you operate convolutions on treaty images or color images.

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Next, we'll take a look at kernel size, which is a filter size and depth.

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So stay tuned for that.

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Thank you.