From: drjohnruss@aol.com (DrJohnRuss)
Subject: Re: Circle erosion
Date: 22 Dec 1999 00:00:00 GMT
Message-ID: <19991222071417.02076.00000789@ng-fv1.aol.com>
References: <3860AA99.12B068D4@club-internet.fr>
Organization: AOL http://www.aol.com
Newsgroups: sci.image.processing
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>Christophe Jacquelin cjacquel@club-internet.fr wrote
>
>When I do 10 erosions on a circular region, the result is a diamond shaped
region.
>
>Can anyone send me informations to obtain a circular eroded region.

Classical erosion that removes pixels based on nearest neighbor comparisons
always produces distortion in shapes when applied more than a few times,
because one pixel removed in the diagonal direction corresponds to a distance
of 1.414 (square root of 2, the diagonal of a square) pixels compared to
removing one in a vertical or horizontal direction.

The solution,which is both faster and isotropic in its results, is to use the
Euclidean distance map. this is a two step operation but both steps are very
quick. The EDM assigns a value to every pixel within the feature a number (grey
scale value) that is the distance to the nearest background point. the fast
(Danielsson)algorithm for this has been around since 1961. Then you just
threshold to get any desired distance of erosion.

This method is used in The Image Processing Tool Kit. You can get more info at
http://members.aol.com/ImagProcTK/