*Stereo imaging* is the method for reconstructing the 3D properties of an object by collecting information from images captured in 2D. This method can have important applications in recording and/or finding elevations and depths in images.

Figure 1 shows the setup of the technique wherein the two cameras (or two views of the same camera) are located at distance *b* from each other. The images of the object are projected at planes *x _{1}* and

*x*, which are both at distance

_{2}*f*from the axis where the center of the camera is located. By similar triangles, we will find that

*x*and

_{1}*x*are given by the equations below.

_{2}Figure 1. Image geometry for stereo imaging (courtesy of Dr. Soriano [1]) |

From the equations above we will find that:

The 3D shape of the object can then be reconstructed by performing this on several points.

**Camera calibration and stereo recording**

We looked at the manual of the camera used in taking the pictures and the focal length *f* of the camera was found to be 6.5mm. The focal length can also be found in the calibration matrix based on the previous activity on creating a geometric model for 3D imaging.

We captured two images of a Rubix cube, aiming to use the corners of the small squares as reference points. It was made sure the the camera is able to view the set of vertices and that they lie along the same *y*-distance from the object. The camera was moved a distance of 4 inches between the two shots.

Figure 2. Images captured from a 3D object (Rubix cube). |

**3D reconstruction**

We gathered as many points we can from the object in *xy* coordinates corresponding the corners of the small squares of the Rubix cube. We then calculated for the *z* value for each point and then plotted the object in a 3D mesh (with an intermediate necessity for interpolation) [3]. Figure 3 displays three different views of the 3D object reconstructed.

Figure 3. The 3D reconstruction of the Rubic’s cube at different views. |

From the reconstruction obtained, it can be found that stereometry was able to recreate an approximate 3D representation of the object. Though the results showed satisfactory output in terms of its surface, the corner of the cube was not fully defined. This can be accounted on the minor inaccuracies in distances during recording and human error in picking the points used in calculations.

Lastly, we would like to thank Dr. Soriano the assistance and for lending us the camera and materials used in this activity.

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**References:**

[1] Soriano, 2010. Stereometry. Applied Physics 187.

[2] Marshall, 1997. Introduction to Stereo Imaging — Theory.

[3] MathWorks. Tri-scattered Interpolation