A novel method of three-dimensional reconstruction based on the double algebra

The double algebra is a system for computations involving subspace of a general finite dimensional vector space and an effective tool for computation of linear invariants of geometric configurations. We address an implicit method of 3D reconstruction based on the double algebra. The invariant of double algebra's form has a simple and explicit expression, which can be computed directly from coordinates of image points and fundamental matrix. The steps to choose the basis of projective coordinates are also presented in order to get an accurate result. Experiments with both synthetic data and real images show that our method is more precise and robust to noise.