ProFORMA: Probabilistic Feature-based On-line Rapid Model Acquisition

This is just neat; much better than edge detecting with a webcam to read a dial.

Here's the paper describing the method.

I think the section on probabilistic carving is most interesting:

One fast and efficient method of removing tetrahedra is by looking at visibility of landmarks. Each triangular face of a tetrahedron is tested in turn against all rays from landmarks to cameras in which they were visible as shown in Figure 3(a). Tetrahedra with one or more faces which intersect with rays are removed. Let T_i represent a triangle in the model, j the keyframe number, k the landmark number and R_j,k the ray from the camera centre at keyframe j to landmark k. Let ν represent the set of all rays with indice pairs (j,k) for which landmark k is visible in keyframe j. For each triangle in the model, the probability that it exists given the set of visible rays can be expressed as:

(1)

(2)

In this formulation, P_exist(T_i|ν) takes the value of 0 if any rays intersect the triangle and 1 if no rays intersect the triangle. This yields a very noisy model surface as points slightly below a true surface due to noise cause the true surface to be carved away (Figure 3(c)). Therefore, we design a probabilistic carving algorithm which takes surface noise into account, yielding a far smoother model surface (Figure 3(b) and (d)). Landmarks are taken as observations of a surface triangle corrupted by Gaussian noise along the ray R_j,k , centered at the surface of triangle T_i with variance σ² . Let x = 0 be defined at the intersection of R
_j,k and T_i , and let x be the signed distance along R_j,k , positive towards the camera. Let l_k be the signed distance from
x = 0 to landmark L_k . The null hypothesis is that T_i is a real surface in the model and thus observations exhibit Gaussian noise around this surface. The hypothesis is tested by considering the probability of generating an observation at least as extreme as l_k :

(3)

This leads to a probabilistic reformulation of simple carving:

(4)

(5)

If P_exist(T_i|ν) > 0.1, the null hypothesis that T_i exists is accepted, otherwise it is rejected and the tetrahedron containing T_i is marked for removal.

In their recommendations for future work they mention guiding the user to present novel views or revist views that could be erroneous, this seems like a place where the ideas discussed in the Duelling Bayesians post about maximum entropy sampling could be applied.