Activity 7. Stereometry

I. Introduction

There are many ways to render the structure and to measure volumes of different 3D objects. One of the commonly utilized way is stereometry.


Stereometry uses two identical cameras, whose lens' centers are separated by some distance b (see Figure 1). The idea is to combine multiple 2D views to get information on the depth of several points on an object, thereby rendering the 3D object. The plane connecting the centers of our lenses is located at a distance z from the object's location, which is what we want to recover. From the point of view of our cameras one and two, this point appears to be located at a transverse distance x1 and x2 with respect to the centers of cameras one and 2. f here indicates the distance of our image plane from the lenses of the camera. This principle is similar to the principle used by our eyes to perceive depths of objects.

Figure 1. Geometry of the setup used.

In our activity, the setup is simplified further. Since we are using only one camera, we just need to displace the camera to a finite transverse distance, where the lens centers of the two cameras are supposed to be placed when using two cameras. From the geometry in Figure 1, we can derive z as follows:
Applying the camera calibration that we have studied in our previous activity, we can reconstruct the 3D structure that we used.


II. Data Gathering

The raw images used are shown below. This is taken from the group of Kaye from their Applied Physics class.


III. 3D Reconstruction

The following is my reconstructed image using Matlab. From a 2D image, it's still not that good.. I'm having problem with the calibration part of the camera used here since I have to calibrate it again before 3D reconstruction.

I give a grade of 7 to myself here since it's still not good. There was an error in the calibration.