Overview / Usage

We started with the projection from the real world coordinate to the camera world and then to image plane. We developed an algorithm to project the 2D image points to 3D world objects provided assuming that know the scale of the world points. We defined an objective function to transform the 2D image points to world points and we find that the objective function is convex. By minimizing the objective function we got the real world coordinate.

Methodology / Approach

Let x is the image coordinates, X is the real world coordinates. We have assumed that the camera center is at (0,0,0). we have also asumed that we know the distance between three real world points. Let's the the distance is d_1, d_2, d_3.

1. Find the camera matrix K by direct linear transform

2. Real world coordinate X=inv(K)x

3. Construct a objective function by the above equation and the known parameters

4. The objective function is convex with respect to the parameters.

5. Minimize the objective function and find the parameters.

6. We construct a equation of a plane and find the coefficient of the plane equation

7. once we get the plane equation, we can get any points in the plane.

Technologies Used

Intel Python