A novel algorithm for extracting the boundaries of two planar curves' morphologic summation

Abstract

In this paper, the morphologic summation of two curves is studied and its parametric equation is obtained. Because the morphologic summation is usually a region that not convenient to analyze and to use, we turn to research its boundaries and found a super set of the boundaries by solving the Jacobi determinant equation. In our method, the super set consists of several sub-curves and the corresponding parametric equation of each sub-curve can be obtained. As the super set includes the real boundaries and the pseudo boundaries, we propose a method of removing the pseudo boundaries real. To avoid the complicated computation, based on the geometric meanings of the boundaries, an approximate algorithm is also applied. Experimental results show that the approximate boundaries are very close to the real boundaries and the computational cost is low. © Springer-Verlag Berlin Heidelberg 2006.