Activity 14: Stereometry

For this activity, we are asked to reconstruct a 3D image of an object using stereometry, wherein the dimensions (such as depth) of the image are determined.

From the object point (x,y,z), an image is reduced to (x,y) with z projected as a function of x and y and the camera object geometry. By preserving the depth of the image, the 3D image can be inspected at different viewing angles.

In the figure below, considering 2 identical cameras positioned such that the lens centers are at a traverse distance b apart, the image planes of each camera are at a distance f from the camera lens. For an object at point P lying at an axial distance z, P appears in the image plane at a traverse distance x1 and x2 from the centers of the left and right cameras respectively.

To determine the internal parameter f, calibration was done to determine the components of matrix A. Using RQ factorization on A(1:3,1:3), the matrix was converted to a diagonal matrix K given by the expression below,

Then, the x,y coordinates of corresponding vertices in the two images were determined. Using the equation below, z was calculated, and the 3D image of the object was reconstructed.