# Transforming a point from one coordinate system to another

I am trying to map the position of an object in one image to another. I have four points in one image with corresponding points in another image so as to bound an area say A. Now, if I have points in A from one image, how do I get the coordinate of the points in the second image.

It must be noted that the first image has oblique coordinates while the second one is orthogonal. Also, I do not have any other information such as the angle between the two coordinate systems. I only have four points in both the images that encompass all my required points (in area A) within them.

-

## 1 Answer

It depends on the coordinate systems and how they are related to one another. For example, if they are related by a linear transformation then you need to construct the change of basis matrix.

More work is required for other coordinate systems, e.g. changing from to polar coordinates to Cartesian coordinates. If a point has polar coordinates $(r,\theta)$ then it has Cartesian coordinates $$(x,y) = (r\cos\theta,r\sin\theta).$$

Perhaps you might like to give more information about the coordinate systems you're using. In the meantime, take a look at this chapter on Changes of Coordinates in 2D.

-
+1 The links were useful –  Stat-R Oct 23 '12 at 20:25