Shapes From Shading

Shape From Shading is an application of Photometric Stereo which is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions. It is based on the fact that the amount of light reflected by a surface is dependent on the orientation of the surface in relation to the light source and the observer. By measuring the amount of light reflected into a camera, the space of possible surface orientations is limited. Given enough light sources from different angles, the surface orientation may be constrained to a single orientation or even over-constrained.

A key assumption used here is that the surfaces of the objects are purely Lambertian.

S1

This program will locate the sphere in question, while also computing its center and radius. The sphere image used is sphere0.pgm.

S2

This program will compute the direction of the light source hitting the sphere. This will be computed for sphere sphere1, sphere2, and sphere3. The goal is to use these normals for the actual object.pgm images, which are placed in the same location and under the same lighting conditions.

S3

Now that we have the normals for the directions of the light source, we can compute the normals for all points on the object. However, we will only compute the normal for the points which are visible on all three of the object.pgm images. The result of this program can actually output a visual representation of the object in 3D using something called a needle map as shown below.

S4

In addition to the needle map, we can also compute something called the albedo map. The albedo actually gives us information about the surface of the object at that point. Here's the albedo map of the object:

Program Execution

./s1 <input original image> <input threshold> <output parameters file>

• threshold: 90

./s2 <input parameters file> <image 1> <image 2> <image 3> <output directions file>

Formulas in S2

Sphere:
  x^2 + y^2 + z^2 = r^2
  z = sqrt(r^2 - (x^2 + y^2))
p = dz/dx = -x / sqrt(r^2 - (x^2 + y^2))
q = dz/dy = -y / sqrt(r^2 - (x^2 + y^2))
n = (p,q,1) / sqrt(p^2 + q^2 + 1)

./s3 <input directions> <image 1> <image 2> <image 3> <step> <threshold> <output>

• step: 10
• threshold: 100

./s4 <input directions> <image 1> <image 2> <image 3> <threshold> <output>

• threshold: 85