Activity 7: Stereometry

Try this!

1. Hold your left thumb near you face, say around two feet, and look at a distant background (any object like a tree or building).

2. Close your left eye only and focus on a distant backdrop with your thumb still placed in front of you.

3. Open your left eye and then close your right eye. Look again at the distant backdrop with thumb still placed in front.

You will notice the difference in the position of your thumb relative to the distant backdrop.

Figure 1. Parallax effect*

This observation is what we call parallax effect. There is an apparent shift in the angle that occurs when a nearby object is seen against a distant backdrop from two different perspectives. The images that we see are essentially 3D objects projected onto a 2D frame. However, multiple 2D views allow the computation of depth information that serves to reconstruct a 3D object. In a way, each of our eyes acts as a single camera and the combined views of the left eye and the right eye can reconstruct 3D objects.

In this activity, we will reconstruct a 3D object captured using a digital camera by employing a technique called stereo imaging inspired by how our eyes perceive depth.

I. Theory

Figure 1 considers two identical cameras positioned such that the centers of the lenses are placed a traverse distance b apart. Let the object point P lie at the axial distance z. It is this z that we wish to recover. The image planes of each camera are at a distance f from the camera lens. In the image plane, P appears at a traverse distance x1 and x2 from the centers of the left and right cameras respectively.

Figure 2. Geometry for stereometry using two views


From similar triangles, we see that



Solving for z we find that




If done for several points on the object, we can reconstruct its 3D shape.


II. Experiment

Our 3D object was a box wrapped with graphing paper, which served as a guide in determining the points to be used for the reconstruction. Eight points were utilized in the experiment. Two shots were taken of the same camera settings with the second shot moved a distance d.


Figure 3. A shot of the 3D object, box, covered with a graphing paper.




Figure 4. A second shot using the same camera settings and displaced by a distance b.

Figure 5. Reconstructed image using the stereometry technique


We were able to successfully reconstruct our 3D object using the stereometry technique. Remember, as long as one have multiple views of a 3D object, one can obtain the surface of the image using a digital camera with a 2D view.

Tips:

1. In taking the pictures, make sure not to rotate the camera and carefully(and accurately) measure the distance, b.

I give myself a grade of 10 for this activity since I was able to render accurately a 3D reconstructed image of the sample images. I easily finished the activity because I already did a similar one during my AP 186 class.

*image taken from: http://http://spot.pcc.edu/.../lecture%201/parallax.jpg

Reference:

1. Maricor Soriano. Applied Physics Lectures: Stereometry. 2009

For teaching concerns please visit: https://sites.google.com/site/alongjas/