Hello everyone and welcome back to Computer Vision lecture series.

This is lecture 9 part 2.

In this lecture we are going to talk more about correspondence problems.

In the last part of this lecture we saw the problem of having smaller baselines in comparison

to having larger baselines.

On the left hand side of this slide you can see the same problem being recreated here.

The problem with having smaller baseline is that we would have larger depth of uncertainty

and because of this we would not be able to localize the correspondence properly and this

would fail in locating the depth of the 3D object.

However by increasing the length of the baseline we can reduce this depth of uncertainty and

try to solve the problem.

However the uncertainty in the point correspondences will increase because the images will have

larger differences between them.

And this problem, so there has to be a compromise between a small baseline and a larger baseline.

And we saw that vergence is one solution to this.

By rotating the camera centers inwards we increase the field of view of our stereo and

essentially reduce the depth of uncertainty as well as the correspondences are reduced.

So if you have seen this area getting smaller in this vergence this is what we want to do

at the end.

But we achieve this by rotating the camera centers towards one another and this will

disrupt our binocular setup where we had made certain assumptions for calculating the triangulation

and finding the point correspondences using stereo and epipolar constraints.

So if we turn the cameras towards one another their optical axis no longer are parallel

neither are the image planes in the same plane.

And because of this however vergence provides us a solution it presents us with another

problems like solving a more complex geometry.

So what is, so we don't have to be worried about more complex geometry there are ways

of rectifying that and that method or the task of rectification of such complex situation

is called stereo image rectification.

What is done here essentially is we assume that no two images or no two cameras can have

consistency or have parallel optical axis similar image planes.

So we let go of this assumptions and therefore we have to also let go of our scan line coherence

assumptions as well.

So how to solve this problem.

One way is that so we will look at what is the way but usually this is the how the 3D

scene is imaged via two cameras.

So this is the image plane on the left when viewed from the left hand side and this is

the image plane on the right when viewed from the right hand side.

And this point on the 3D in the 3D world is recreated in these two different planes in

these two different locations.

And because these cameras are or these camera centers or these eye centers in this case

are not do not have their optical axis parallel their axis would intersect in the real world.

So these are very common cameras which are called worst cameras or everyday cameras if

you want to call them.

And can we use the question is now we already know our binoculars stereo setup.

So can we reformulate this problem into the previous problem in such a way that we can

use the previously established techniques.

And this is a very common practice in computer vision in many as in many other field that

you reformulate or repurpose certain things in such a way that you can reuse the previously

well established methods to solve a newer problem.