Multiscale medial axis

 

Coggins and Pizer were motivated by the desire to analyze images over a continuum of spatial scales. The classic approaches, which relied solely on edge and region information, were unable to handle many simple problems in image understanding. For example, how would you extract all the letter n's in Figure ?

  
Figure: An example of object recognition at different scales. The number of ``n'''s recognized in this figure depends on the resolution of the segmentation algorithm (see text).

Although the correct answer is 12, a simple classification algorithm would report either 11 or 0, depending on its scale of operation. If the scale of the algorithm was the same as the scale of the smaller letter n's, it would probably report 11. If the algorithm was operating on the scale of the larger character, it would probably report zero because it would not find any edges or contiguous regions that resemble the letter n.

This led Coggins to the following conclusions:

• Edges can be misleading because they often contain too much noise and yield information of poor quality.
• Regions can be misleading because they often appear to be discontiguous.
• The human vision system seems to preserve features and their related ambiguities at various spatial resolutions; competing hypotheses about an image can be preserved and resolved at the level of cognition rather than at the level of perception.

As a result, Coggins reasoned that it is important to be able to interpret features on a continuous spatial-resolution scale.