A13 - Photometric Stereo

Photometric stereo is an algorithm for obtaining local surface orientation by using several images of a surface taken under different illumination conditions with the camera viewpoint held fixed.

The technique assumes that intensity I captured by camera at point (x,y) is directly proportional to brightness of surface at that point. This also assumes that light rays arriving on the surface are parallel. Shape of the surface is estimated from the multiple images and the information about the surface is coded in the shadings obtained from the images.

In this activity, we use Photometric Stereo technique to obtain a 3D reconstruction from 2D images. The input images are shown below.

The intensity at each point is denoted in matrix form as

Knowing the light source directions (V) for each of the input images (I), we use the equation below to solve for g.

From the computed values of g (a 3 row matrix corresponding to the xyz locations), we get a normal vector by dividing each element in a column with the magnitude of that column. After this, a linear integral was used to obtain the z values. Plotting z with a 128x128 plane yields the following 3D reconstruction.

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Rating: 10/10 for the accurate reconstruction of the shape of the input images using the algorithm