Reputation: 79
My problem is: I have a set of 4 points O, A, B, C locating on a surface. Due to distortion of that surface, the points A, B, C are moved to new positions which are A', B', C'. Now I want to find new position of O that minimises the root mean square error (RMSE) of two sets of distances (O'A', O'B', O'C', O'O) and (OA, OB, OC, OO). Does anyone know which algorithm can solve my problem?
Upvotes: 3
Views: 118
Reputation:
It is equivalent to minimize the sum of squared errors, which is expressed by
(O'A'-OA)² + (O'B'-OB)² + (O'C'-OC)²
This expression is nonlinear in the unknowns and you'll need to resort to a sophisticated algorithm such as Levenberg-Marquardt. In addition there will be several extrema in the function and you'll need to find the global minimum.
A slightly easier approach is to use the squared distances instead of the distances, leading to a purely polynomial expression of the fourth degree.
(O'A'²-OA²)² + (O'B'²-OB²)² + (O'C'²-OC²)²
Upvotes: 2