Activity 9: Stereometry

Depth perception in human is due to the separation of the human eyes.  Each of the eye receives a signal which seems to be exactly the same with the other eye, but actually both signals report differences in details of objects seen by each of the eye.  One of the differences in the signals received by each eye is what the brain interprets to be the depth of the object .

Stereo imaging technique is one of the methods used in 3D imaging.  This specific imaging technique is inspired by the mechanism on how a human eye can perceive depth [1], Fig. 1.

Figure 1:  Illustration for stereo imaging [2].

Because of this inspiration, just like a human eye, this technique requires 2 imaging devices whose image information will be interpreted to perceive the depth of the object taken in the image.

In our case, because we don't have two identical cameras to be able to capture the object simultaneously, we used only one camera and took two images of the object wherein the second image was taken after the camera was displaced a distance $b = 2.54$ cm along the x-axis from the location where the first image was taken making sure that no rotation in the camera was made, Fig. 2.

Figure 2:  Images of the same Rubik's cube produced before and after translation of the camera.

The object which we used for this activity was a Rubik's cube.  After taking the images, we take the image coordinates of the intersection of the blocks in the visible edges of the Rubik's cube to be used in the reconstruction.

From the previous activity we can derive the focal length of the camera using RQ-factorization but here, we did not perform this intermediate method because the value of the focal length of the camera used was given in the properties of the image which is $f = 4.7$ mm.

Using the equations [2],

we have recovered the real-world coordinates of the points sampled in the images.  The expression in the denominator for the z-real-world coordinate is called the disparity.

We plotted the 3D reconstruction of the Rubik's cube and resulted to the surface plot as shown in Fig. 3.

Figure:  3D reconstruction of the Rubik's cube using stereo imaging technique.

Based on the result of the reconstruction, we have concluded through qualitative comparison that the reconstruction has a high resemblance with the object of interest (i.e. Rubik's cube).


Code:

Sources:
    [1] Dr. Maricor Soriano - Applied Physics 187: Activity 9 Manual
    [2] Introduction to Stereo Imaging - http://www.cs.cf.ac.uk/Dave/Vision_lecture/node11.html