Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods

Abstract Let I :Ω→ℜ be a given bounded image function, where Ω is an open and bounded domain which belongs to ℜn. Let us consider n=2 for the purpose of illustration. Also, let S={xi}i∈Ω be a finite set of given points. We would like to find a contour Γ⊂Ω, such that Γ is an object boundary interpolating the points from S. We combine the ideas of the geodesic active contour (cf. Caselles et al. [7,8]) and of interpolation of points (cf. Zhao et al. [40]) in a level set approach developed by Osher and Sethian [33]. We present modelling of the proposed method, both theoretical results (viscosity solution) and numerical results are given.

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