Center for Interactive Digital Media Technologies, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China.
IEEE Trans Image Process. 2012 Dec;21(12):4735-45. doi: 10.1109/TIP.2012.2210724. Epub 2012 Jul 30.
Geometric flows have been successfully used for surface modeling and designing, largely because they are inherently good at controlling geometric shape evolution. Variational image segmentation approaches, on the other hand, detect objects of interest by deforming certain given shapes. This motivates us to revisit the minimal partition problem for segmentation of images, and propose a new geometric flow-based formulation and solution to it. Our model intends to derive a mapping that will evolve given contours or piecewise-constant regions toward objects in the image. The mapping is approximated by B-spline basis functions, and the positions of the control points are to be determined. Starting with the energy functional based on intensity averaging, we derive a Euler-Lagrange equation and then a geometric evolution equation. The linearized system of equations is efficiently solved via a special matrix-vector multiplication technique. Furthermore, we extend the piecewise-constant model to a piecewise-smooth model which effectively handles images with intensity inhomogeneity.
几何流已成功用于曲面建模和设计，主要是因为它们在控制几何形状演化方面具有固有优势。另一方面，变分图像分割方法通过变形某些给定的形状来检测感兴趣的对象。这促使我们重新审视图像分割的最小划分问题，并提出了一种新的基于几何流的公式和解决方案。我们的模型旨在导出一种映射，该映射将给定的轮廓或分段常数区域朝着图像中的对象进行演化。映射由 B 样条基函数逼近，并且控制点的位置有待确定。从基于强度平均的能量泛函出发，我们推导出欧拉-拉格朗日方程，然后推导出几何演化方程。通过特殊的矩阵-向量乘法技术有效地求解线性化系统方程。此外，我们将分段常数模型扩展到分段平滑模型，该模型有效地处理具有强度不均匀性的图像。
