Siddiqi K, Lauzière Y B, Tannenbaum A, Zucker S W
Dept. of Comput. Sci. and Electr. Eng., Yale Univ., New Haven, CT 06520, USA.
IEEE Trans Image Process. 1998;7(3):433-43. doi: 10.1109/83.661193.
A number of active contour models have been proposed that unify the curve evolution framework with classical energy minimization techniques for segmentation, such as snakes. The essential idea is to evolve a curve (in two dimensions) or a surface (in three dimensions) under constraints from image forces so that it clings to features of interest in an intensity image. The evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional, tailored to features such as edges. However, because the flow may be slow to converge in practice, a constant (hyperbolic) term is added to keep the curve/surface moving in the desired direction. We derive a modification of this term based on the gradient flow derived from a weighted area functional, with image dependent weighting factor. When combined with the earlier modified length gradient flow, we obtain a partial differential equation (PDE) that offers a number of advantages, as illustrated by several examples of shape segmentation on medical images. In many cases the weighted area flow may be used on its own, with significant computational savings.
已经提出了许多主动轮廓模型，这些模型将曲线演化框架与用于分割的经典能量最小化技术（如蛇形模型）统一起来。其基本思想是在图像力的约束下演化曲线（二维）或曲面（三维），使其紧贴强度图像中的感兴趣特征。演化方程已从第一原理推导为梯度流，该梯度流使针对边缘等特征量身定制的修改后的长度泛函最小化。然而，由于在实际中流可能收敛缓慢，因此添加一个常数（双曲）项以保持曲线/曲面沿所需方向移动。我们基于从加权面积泛函导出的梯度流（具有与图像相关的加权因子）对该项进行了修改。当与早期修改后的长度梯度流相结合时，我们得到一个偏微分方程（PDE），该方程具有许多优点，如医学图像形状分割的几个示例所示。在许多情况下，加权面积流可以单独使用，从而显著节省计算量。
