Act 17: Photometric Stereo

In this activity, we attempt to construct a 3-D image using four pictures of the same synthetic spherical image. These four images are for the four different locations of the point source namely:

V1 = {0.085832, 0.17365, 0.98106}
V2 = {0.085832, -0.17365, 0.98106}
V3 = {0.17365, 0, 0.98481}
V4 = {0.16318, -0.34202, 0.92542}

The image as displayed in Matlab is displayed below:


First, we compute the surface normal of the image, which is given in the following equation

where g is computed from

From the obtained surface normals, nx, ny and nz were used to obtain the partial derivatives of f(u,v) with respect to both x and y using the following equations:

To get f, the equation below was used


The Scilab function cumsum can be done in lieu of integration. The obtained surface normal was then plotted using plot3d, and the reconstruction is shown below.

I will give myself a grade of 10/10 since this activity was accomplished within the period. I would like to thank Earl for the cooperation and Martin for helping us with the final parts of the code.