COMPUTATION OF THE HAUSDORFF DISTANCE BETWEEN TWO ELLIPSES

We are interested in the problem of finding the Hausdorff distance between two objects in ${\mathbb{R}}^2$, or in ${\mathbb{R}}^3$. In this paper, we develop an algorithm for computing the Hausdorff distance between two ellipses in ${\mathbb{R}}^3$. Our algorithm is mainly based on computing the distance between a point $u{\in}{\mathbb{R}}^3$ and a standard ellipse $E_s$, equipped with a pruning technique. This algorithm requires O(log M) operations, compared with O(M) operations for a direct method, to achieve a comparable accuracy. We give an example,and observe that the computational cost needed by our algorithm is only O(log M).