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

Abstract

Let I : → be a given bounded image function, where is an open and bounded domain which belongs to n . Let us consider n = 2 for the purpose of illustration. Also, let S = {x i } i ∈ be a finite set of given points. We would like to find a contour ⊂ , such that 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.

Segmentation of Brain MR Images Using a Charged Fluid Model

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“…Recently, Xu et al [17] proposed a level-set-based segmentation method that uses an adaptive triangular mesh to achieve higher resolution at the interface. Gout et al [18] proposed a segmentation approach that combines the idea of the geodesic active contour and interpolation of points in the Osher-Sethian level set framework to find a boundary contour from a finite set of given points.…”

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“…Figure 11͑a͒ shows that there is one CFM initialized in a free plane. The four fluid elements having equal charge 14 Experimental results in segmenting an object with sharp corners and cusps using ␤ = −1.2 in a 256ϫ 256 phantom image. Note that the object has a wide intensity distribution that is similar to the background.…”

“…This approach introduces another term into the partial differential equation to balance the speed functions such that the propagating interface can more flexibly evolve toward the desired position. Recently, Gout et al 14 proposed a segmentation approach that combines the idea of the geodesic active contour and interpolation of points in the Osher-Sethian level set framework to find a boundary contour from a finite set of given points. Guyader et al 15 used the Osher-Sethian level set to evolve an explicit function, while minimizing the energy.…”

Circular contour retrieval in real-world conditions by higher order statistics and an alternating-least squares algorithm

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