ACTIVITY 17 Photometric Stereo

In this activity, we used the technique photometric stereo in constructing the 3D shape of an object. This technique works under the assumption that the source is at infinity and so, the radial waves reaching the surface appear as planar waves. Moreover, it is assumed that the intensity captured by a camera at point (x,y) is directly proportional to the brightness of the surface at that point.

By capturing multiple images with the sources at different locations, one can estimate the shape of the object. The sources can be represented by matrix V in equation 2 where Vn1, Vn2 and Vn3 are the component of the source n in the x-, y- and z- direction, respectively. If we know the intensity of the surface image captured by source n, then we can solve for g as illustrated in equation 3. The surface normals can then be calculated by normalizing g with its length (see equation 4). The surface elevation, z, is a function of x and y. The partial derivatives of this function with respect to x and y are shown in equation 5. Therefore, the surface elevation is given by equation 6.

In this activity, we used four sources and the surface images captured by these sources are shown in Figures 1 to 4. After implementing equations 2 to 6, we were able to generate a 3D shape of the object as shown in Figure 5.

Figure 1.

Figure 2.

Figure 3.

Figure 5.