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Shouldn't medial axis and topological skeleton be merged? 132.68.248.87 (talk) 16:52, 10 July 2008 (UTC)
I have edited this page to include a reference to Harry Blum. I thought this was important as it is standard in the introductions of most papers on medial axis transforms. I have also attempted to generalize the first paragraph, as it was initially biased towards the medial axis of 2d objects.
Some of the original text remains incorrect. For example, the second paragraph assumes the curve is G1 continuous, although this is not stated. At tangent discontinuities the normal is not defined, but a disc which is maximal for inclusion within the object can touch the boundary at such a point. -- Dr J. G. Lambourne —Preceding unsigned comment added by Jglambourne (talk • contribs) 12:01, 13 June 2009 (UTC)
"The medial axis of an object is the set of all points having more than one closest point on the object's boundary." I could not think of any way to parse that opening sentence so that it made any sense.Norlesh (talk) 18:50, 26 October 2013 (UTC)
- Do you have a proposal for how to simplify the wording? Given an object X with boundary B, some of the points in the plane have a unique nearest point on B, while for some others there are multiple equally close points on B. The medial axis is the collection of points whose nearest point on B is not unique. —David Eppstein (talk) 19:54, 26 October 2013 (UTC)
"The medial axis of an object is the set of all points having more than one closest point on the object's boundary." Set of all points having more than one closest point on the object's boundary? Is that set a subset of something?
Because if it's not, then the whole definition is senseless.
I see the pictures that indicate that this medial axis creates points, so they are not a subset of anything, but then if you create points (and add them to the set of object's boundary points) then no matter where you would create this point - it would always have two nearest points on the object's boundary - because there are no other points to compare them with!
I think that what you meant is that this is a set of points that lie in the middle of any circle that can be placed within the object, with restriction that two points of this circle lie on the boundary of the object. — Preceding unsigned comment added by Kogi123 (talk • contribs) 11:18, 29 November 2013 (UTC)
- I think the input to the question "what is the medial axis?" is unclear in this page. In the first paragraph we just talk about an "object". The second paragraph mentions a planar curve S (which is very concrete) but then suggests that the medial axis is contained in the S. This is not correct: what is intended here is that the medial axis is contained in the bounded component of the plane which is bounded by S. Most generally, the medial axis definition doesn't really need the "object" to be defined, just the "boundary": e.g., we can take all points in the plane that have more than one closest point to a given curve. But I think it is most common in the literature to start with a "full dimensional" set and talk about a medial axis with respect to that set. Then medial axis points are generally expected to belong to the set. Does anyone know any examples of "medial axis" where the full-dimensional set is not defined (only the d-1 dimensional "boundary") or the components of the "medial axis" which are outside the original set are used? RuppertsAlgorithm (talk) 12:24, 29 November 2013 (UTC)