Next: Using Distance Transform to Up: Matching Method for Defect Previous: Matching Method for Defect

## The Hausdorff Distance

The basis of our methodology is the median Hausdorff distance which is a similarity measure between two arbitrary point sets. The classical Hausdorff distance between two (finite) sets of points, and , is defined as

 (1)

Here, , the directed distance from to , will be small when every point of is near some point of . This distance is too fragile for practical tasks: for example, a single point in that is far from anything in will cause to be large. A natural way to take care of this problem is to replace equation 1 with

 (2)

where denotes the -th quantile value of over the set , for some value of between zero and one. When we get the modified median Hausdorff distance which we use in our method.

Let be a point set representing the reference shape, the measured point set. As already mentioned, we assume that is complete, dense and precise, while may be incomplete, sparse and noisy. is obtained either analytically, or as the result of a careful, high-resolution, off-line measurement.

Next: Using Distance Transform to Up: Matching Method for Defect Previous: Matching Method for Defect
Dmitry Chetverikov
1998-11-16