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Curve/Surface Representation and Evolution Using Vector Level Sets with Application to the Shape-Based Segmentation Problem

机译:矢量水平集的曲线/曲面表示和演化及其在基于形状的分割问题中的应用

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In this paper, we revisit the implicit front representation and evolution using the vector level set function (VLSF) proposed in [1]. Unlike conventional scalar level sets, this function is designed to have a vector form. The distance from any point to the nearest point on the front has components (projections) in the coordinate directions included in the vector function. This kind of representation is used to evolve closed planar curves and 3D surfaces as well. Maintaining the VLSF property as the distance projections through evolution will be considered together with a detailed derivation of the vector partial differential equation (PDE) for such evolution. A shape-based segmentation framework will be demonstrated as an application of the given implicit representation. The proposed level set function system will be used to represent shapes to give a dissimilarity measure in a variational object registration process. This kind of formulation permits us to better control the process of shape registration, which is an important part in the shape-based segmentation framework. The method depends on a set of training shapes used to build a parametric shape model. The color is taken into consideration besides the shape prior information. The shape model is fitted to the image volume by registration through an energy minimization problem. The approach overcomes the conventional methods problems like point correspondences and weighing coefficients tuning of the evolution (PDEs). It is also suitable for multidimensional data and computationally efficient. Results in 2D and 3D of real and synthetic data will demonstrate the efficiency of the framework.
机译:在本文中,我们使用[1]中提出的向量水平集函数(VLSF)重新审视隐式前沿表示和演化。与常规标量级别集不同,此函数设计为具有矢量形式。从任何点到最前面的最近点的距离在矢量函数中包含的坐标方向上都有分量(投影)。这种表示形式也用于生成封闭的平面曲线和3D曲面。将考虑将VLSF属性保持为通过演化的距离投影,并结合针对这种演化的矢量偏微分方程(PDE)的详细推导。基于形状的分割框架将被演示为给定隐式表示的应用。拟议的水平集功能系统将用于表示形状,以在变体对象注册过程中提供相异度度量。这种表达方式使我们可以更好地控制形状配准的过程,这是基于形状的分割框架的重要组成部分。该方法取决于用于构建参数形状模型的一组训练形状。除了形状先验信息外,还要考虑颜色。通过能量最小化问题的配准,将形状模型拟合到图像体积。该方法克服了常规方法的问题,例如点对应和演化的权重系数调整(PDE)。它还适用于多维数据并且计算效率高。真实和合成数据的2D和3D结果将证明该框架的效率。

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