..on photometric stereo

We use photometric stereo to extract the 3D shape of an object using only the information from the shadow. We estimate the shape of the object using the shading obtained from different images of different light source location.

Consider a point source of light at infinity.











The intensity I of the image is related to the vector position of the camera given by:








where N is the number of images used. We now solve for g using:




to get the normal vector n, we simply normalize it:





to derive the shape from the normals, we note that the surface elevation f(x,y) is related to the normals by:






Finally, we solve for the surface elevation using:







We apply this technique using four images of a sphere. The resulting 3D rendition is:















Indeed, the resulting shape is a sphere.

I've successfully accomplished the activity. I want to give myself a 10.