Planar Pixelations, Shape Reconstruction
نویسنده
چکیده
Given a PL (piecewise linear) set S in the plane R we consider the set Pε(S) consisting of all pixels of size ε that touch S. This pixelation Pε(S) resembles the original set, but may not well approximate various important invariants of the original set such as Betti numbers, perimeter, curvature measures. We describe an algorithm that associates to the pixelation Pε(S) a PL-set Pε(S) which approximates S in a very strong sense.
منابع مشابه
Pixelations of planar semialgebraic sets and shape recognition
We describe an algorithm that associates to each positive real number r and each finite collection Cr of planar pixels of size r a planar piecewise linear set Sr with the following additional property: if Cr is the collection of pixels of size r that touch a given compact semialgebraic set S, then the normal cycle of Sr converges to the normal cycle of S in the sense of currents. In particular,...
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