# A Novel Algorithm for Extracting the Boundaries of Two Planar Curves’ Morphologic Summation

• WenYu Liu
• HaiRong Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3942)

## 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.

## Keywords

Path Planning Boundary Curve Parametric Equation Approximate Algorithm Planar Curf
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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