Activity 17 | Photometric Stereo

Light when shone upon an object gives us an idea on the reflectance of that object that can be used in obtaining information about the object like color. The information stored in an objects reflectance due to a light source is used in many image processing methods which we have explored in the previous activities. Aside from the information that we have been using, we can also obtain the profile or the structure of the object by using images of the object with different light source positions and reconstruct the 3D structure of that object. This is what we call Photometric Stereo.

When light illuminates an object it produces shadows and color gradients all throughout the illuminated surface. And by getting images of the object at different light source locations, we obtain intensity profile of the whole illuminated surface. Different light sources also affect the intensity profile of the captured image of an object. Figure 1 shows the basic idea of Photometric Stereo where the angle in which light hits the surface of the object affects the captured intensity given by Equation 1 for a light source at infinity for that point P.

Figure 1. Photometric Stereo.

Equation 1. Intensity at point P(x,y).

In this activity, we use four images of an object taken with different light source positions and use it to reconstruct the 3D structure of the illuminated area, as shown by Figure 2.

Figure 2. Images of object at different light source positions.

To calculate for the surface normal of the object we need to get the far away point source locations given by V which was already provided, and the intensity I which is simply the images . The equations needed for calculating the surface normal is shown in Figure 2.

Figure 3. Equations needed for solving the surface normal.

After getting the surface normal, we can now compute for the surface elevation of the object at point (u,v) which is given by z = f(u,v) as shown in the equation below.

Figure 4. Surface elevation at point (u,v).

The resulting reconstructed 3D surface is shown below in Figure 5. We can see that the reconstructed surface is not smooth having jagged peaks and grooves. Also there is a concave dip at the areas where a transition in the intensity is located by comparing it to the four object images shown previously. All in all, the semi-spherical shape obtained matches the expected structure of the object from the images. I give myself a grade of 9 in this activity due to the roughness of the reconstructed surface.

Figure 5. Reconstructed 3D surface of object.