Beyond the Hausdorff Metric in Digital Topology
This work is incremental, offering improved comparison methods for digital images in fields like computer vision and image processing.
The paper addresses the limitation of the Hausdorff metric in digital topology by proposing alternative measures for comparing digital images that ensure geometric and topological similarity, and suggests combining these with the Hausdorff metric to create a more comprehensive metric.
Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar geometric or topological property. Such measures may be combined with the Hausdorff metric to yield a metric in which close images are similar with respect to multiple properties.