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Adaptive level set evolution starting with a constant function

机译：从常数函数开始的自适应水平集演化

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摘要

In this paper, we propose a novel level set evolution model in a partial differential equation (PDE) formulation. According to the governing PDE, the evolution of level set function is controlled by two forces, an adaptive driving force and a total variation (TV)-based regularizing force that smoothes the level set function. Due to the adaptive driving force, the evolving level set function can adaptively move up or down in accordance with image information as the evolution proceeds forward in time. As a result, the level set function can be simply initialized to a constant function rather than the widely-used signed distance function or piecewise constant function in existing level set evolution models. Our model completely eliminates the needs of initial contours as well as re-initialization, and so avoids the problems resulted from contours initialization and re-initialization. In addition, the evolution PDE can be solved numerically via a simple explicit finite difference scheme with a significantly larger time step. The proposed model is fast enough for near real-time segmentation applications while still retaining enough accuracy; in general, only a few iterations are needed to obtain segmentation results accurately.
机译：在本文中，我们提出了一种新的偏微分方程（PDE）公式中的水平集演化模型。根据控制PDE，水平设置功能的演化由两个力控制，自适应驱动力和使水平设置功能平滑的基于总变化（TV）的正则化力。由于自适应驱动力，随着时间的发展，演进水平设置功能可以根据图像信息自适应地向上或向下移动。结果，可以简单地将水平集函数初始化为常数函数，而不是现有的水平集演化模型中广泛使用的有符号距离函数或分段常数函数。我们的模型完全消除了对初始轮廓和重新初始化的需求，从而避免了轮廓初始化和重新初始化带来的问题。此外，可以通过简单的显式有限差分方案以较大的时间步长来求解演化PDE。所提出的模型足够快用于近实时分割应用，同时仍保持足够的精度。通常，只需要几次迭代就可以准确地获得分割结果。

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