Hello everyone and welcome back to computer vision lecture series.

This is lecture 6 part 1.

In this lecture we are going to talk about various camera calibration techniques.

So let's begin.

In the beginning we will see what transforms mean, what kind of transforms are possible

and their associated degrees of freedom and then we will try to see how we can model the

real world coordinates to camera coordinates.

Before that, before we move on to the main camera estimation, camera parameter estimation

techniques, we want to ask the basic questions that are possible, right?

So if you have an image of the real world, basically you want to know things like how

tall is this woman in this particular image or how high is your camera or what angle is

the camera at with respect to the wall and which wall is closer.

So if you are able to model the camera parameters or we are able to find the camera parameters

then we will be able to answer all these questions easily.

So the next step would be to basically see how we can model the real world coordinates

into camera, into image coordinates via camera parameter estimation.

Before we go there we want to standardize our method right and we have discussed the

pinhole camera model in the previous lectures.

We are going to continue assuming that we are doing our analysis based on the pinhole

camera model.

Basically where you have this pinhole camera where you have the camera center, this is

the image of the real world image and there is a image plane where you have your image

coordinates and these are the world coordinates and the relationship between them is represented

by this equation where small x is the coordinates of in the image plane of the object and capital

X is the coordinates of the object in the real world.

R and T represent rotation and transformation of the object in the real world so they are

considered extrinsic parameters.

Whereas K is, K relates to the focal length, the shear and other like camera centers and

things like that they are considered intrinsic parameter of the camera.

So this matrix that we are able to generate here is considered as the projection matrix

and our main task will be to estimate this matrix because we already know the world coordinates

and the image coordinates then how do we use that information to find the or estimate the

camera matrix or the projection matrix that is our main task.

In that pursuit we are going to take use of homogeneous coordinates.

We saw how homogeneous coordinates can be helpful and they allow projection to be represented

as a matrix multiplication which makes it makes our lives easier because there are lot

of libraries available in MATLAB, in Python, in tensor and there are lot of tensor libraries

which handle matrix multiplications and analysis with matrices quite well and that is the reason

why we convert the projections to homogeneous coordinates.

In doing so we are also modeling or approximating our camera and we are neglecting certain distortions

like barrel and pincushion distortions that we discussed before but we have to remember

that this can be caused by the different shutter speeds and the sizes of the shutter.

So just keep these things in mind and we go ahead.

So what are transformation, image transformations or parametric global transformations?

It is represented by T and P dash is the transformed image, P is the original image and the transformation

is represented as P prime equals to T of P. These transformations are such that they apply

to the global, they apply globally to all the pixels in the input image.

So let us say if you are stretching this image every pixel is stretched along the y direction

and x direction and that is how this transformation is represented.

The globalness of T is basically that every point in P is affected by this transformation.