Several geometric active contour models have been proposed for segmentation in computer vision and image analysis. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) under constraints from image forces so that it clings to features of interest in an intensity image. Recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented. However, it is still unclear how to apply these techniques to images of narrow elongated structures, such as blood vessels, where intensity contrast may be low and reliable region statistics cannot be computed. To address this problem we derive the gradient
ows which maximize the rate of increase of
ux of an appropriate vector eld through a curve (in 2D) or a surface (in 3D). The key idea is to exploit the direction of the vector eld along with its magnitude. The calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions. We illustrate its advantages with several level-set based segmentations of 2D and 3D angiography images of blood vessels.
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