An algebraic framework for using geometric constraints of vision and range sensor data

Proposes 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 the author lists three groups of equations on the constraints. Next, the author classifies all the groups of equations into two sets, a set of hypotheses and a conjecture. Then, the author applies 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. 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 the author obtained new geometrical relations for seven cases of geometrical models