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Green Image
Issue No. 03 - May/June (2006 vol. 12)
ISSN: 1077-2626
pp: 289-300
<p><b>Abstract</b>—In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete <it>Hodge</it> Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the <it>Green Function Method (GFM)</it> can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.</p>
Hodge decomposition, Green Function Method, normalized cut, vector field segmentation, streamline, contour, approximation.

I. Shen, W. Chen and H. Li, "Segmentation of Discrete Vector Fields," in IEEE Transactions on Visualization & Computer Graphics, vol. 12, no. , pp. 289-300, 2006.
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