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Welcome to the section and object detection.

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Object detection is one of the most popular computer vision tasks and also a very important one.

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Object detection entails correctly classifying objects which are in an image and also saying exactly

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where these objects are located in the image.

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So if we have this image, we see clearly that we have an airplane, an aeroplane, a person, a person,

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and then we could say a car.

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So this tool is some sort of car.

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Now, an object detector not only classifies these images, but also localizes exactly their positions

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in the image.

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So this airplane, for example, has this bounding box.

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Now, a bounding box basically surrounds us also square or rectangular box which surrounds the object.

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And then for this person, we have this bounding box, for this, this bounding box and this other aeroplane,

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we have this bounding box which is in this other bounding box.

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So unlike a classification problem, where when given this kind of input, we have as an output one

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hard vector, for example, which represents a number of classes we're dealing with.

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So supposing we have five classes, then when given an input, we have to correctly say whether that

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input belongs to one of the five classes.

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Now, with object detection, we not only have this, but we also have the positions in the image.

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So like this, we have this position like this and we have several conventions for this positions.

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One of the most popular conventions is the center convention, where we have the x center, y center

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width and then height.

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Now, what does this mean?

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This means that based on this referential right here, so we could define a referential right here where

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we have this origin.

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Now, recall we used to have y is to working with this kind of referential.

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Now the referential for image data is considered to be this.

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So our origin starts from here.

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We're moving the x direction and then in the Y direction.

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So this is our friends and then this is based from on this point, on this origin that we actually define

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positions.

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So if we have this airplane, let's consider this bigger airplane.

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So we could have this bigger airplane, we could define its bounding box by its center and then its

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width.

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So once we have a center, obviously, and if we're given this width, we can obviously see that it

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is in this bounding box.

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So this is the first convention the center does the X center and the Y center.

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The X center is basically the distance from this to the center.

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So suppose that the center is right here.

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So if our center is here, then the distance from here to this is X center and the distance from up

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to this is Y center.

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So basically that's what we have.

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So if we want to link this up like this, we could see clearly how we obtain X center the distance from

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here the year and then Y center distance from this origin to this, which now gives us the center.

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So that's how we get a center.

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Now we are given the width and then the height, if we give it the width and height, obviously to get

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this points or to get because we have actually four points right here to get all those four points which

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make up the bounding box, we could start from say, this point for this point to obtain the x and Y

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coordinates right here, we simply take this x coordinate and subtract from the width divided by two

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because from this to this is we divided by two on the diagram.

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It doesn't show clearly at this point is at the center.

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But normally this should be at the center.

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So we could rearrange this bounding box now.

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So as we said, to get this, we have this x center minus the width divided by two to obtain this and

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then to get the Y, we have the Y center plus because this is actually the positive direction and then

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this is the negative direction for the X.

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So for y, this is positive.

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This is negative for Y, this is positive for X and then this is negative for x.

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Now, to obtain the Y, as we said, we have this y center plus the width of this, or rather plus the

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height of this divided by two.

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That's how we obtain this.

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Now, to obtain this, since we're going from this, we're going the x center minus the width divided

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by two.

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We obtain the x coordinate here.

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To obtain the y coordinate we have the Y center minus because this is the negative direction.

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So we have the Y center minus the height, divided by two and.

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This is very similar to obtain the x here.

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There's an x coordinate right here.

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We have the x enter year plus the width divided by two to obtain the same x coordinate.

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Right here is the x center plus the width divided by two.

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Obviously these two have the same x coordinates, but different y coordinates To obtain the y coordinate.

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We have this y center minus the height divided by two.

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To obtain the Y coordinate.

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Here we have the Y center plus the height divided by two.

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Either ways, once we have this to coordinate this point here and then this, we could always obtain

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this and this automatically.

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Now another convention is the x mean y, mean x, max y, and max convention where we just given this

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coordinates.

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If we're given this coordinates and then this coordinates, we could obviously obtain all this because

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when one is given this and then given this, we could just get the whole box or the magically.

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So here are the two main conventions we use to actually locate an object in the image.