Abstract
This paper presents a vector field matrix [2] derivation on a recursive algorithm of six degrees of freedom contour matching through single-eye imagery. We have already reported an algorithm in which the position and orientation of an object is determined by matching the reference pattern to the edge pattern on the image. However, in that algorithm, the vector field matrix was given intuitively. Here we actually derived the vector field matrix.
First, a mathematical model of the potential field is formulated by the stochastic evolution equality in Hilbert space. The existence and uniqueness properties of the solution to the potential field equations are studied. Second, we consider the cost function and derive a pattern matching algorithm suitable for computers within the framework of the gradient method. Third, we derive the vector field matrix for mathematical security of the algorithm. Finally, a representative time result of the experiments is shown, to support the theoretical aspects developed here.
