Algebraic framework for fusing geometric constraints of vision and range sensor data

In this paper we propose a new framework for fusing multiple geometric sensor outputs to reconstruct 3-Dimensional target shapes. The proposed framework is of an application of Wu's mechanical theorem proving method in algebraic geometry. First we list up three groups of equations on the constraints. Next, we classify all the groups of equations into two sets, a set of hypotheses and a conjecture. Then, we apply Wu's method to prove that the hypotheses follow the conjecture and obtain pseudo-divided remainders of the conjectures, which represent new relations of geometric measures such as angles or lengths between 3-D space and their projected data on the sensors. Here, as an example, a typical case is considered where an image sensor and a range sensor are used together to reconstruct and recognize 3-D object shapes. By this method we obtained new geometrical relations for seven cases of geometrical models.