Structure from motion-a critical analysis of methods

Abstruct-There are a multitude of equations, methods, formulations and solutions in the literature for solving the structure from motion problem. It is shown how such methods can be mathematically related by certain changes, some of these changes preserve the essential qualities of the original system, while other changes do not. Existing methods for structure from motion are classified and analyzed and mathematical relationships between them are shown. Their behavior on the same synthetic data is evaluated, examining the effect of noise, initial estimates, and the amount of motion. The missing necessary polynomial constraint on the singular values of Tsai and Huang's essential parameter matrix is shown, and derive related linear methods for less general SFM problems, and their necessary polynomial constraints. The experiments show that for data where the constraints are satisfied, linear methods work correctly and quickly, where they are not applicable, polynomial methods may work but are slower.