Unal Gozde, Krim Hamid, Yezzi Anthony
Dept. of Electr. and Comput. Eng., North Carolina State Univ., Raleigh, NC 27695, USA.
IEEE Trans Image Process. 2002;11(12):1405-16. doi: 10.1109/TIP.2002.804568.
In previous years, curve evolution, applied to a single contour or to the level sets of an image via partial differential equations, has emerged as an important tool in image processing and computer vision. Curve evolution techniques have been utilized in problems such as image smoothing, segmentation, and shape analysis. We give a local stochastic interpretation of the basic curve smoothing equation, the so called geometric heat equation, and show that this evolution amounts to a tangential diffusion movement of the particles along the contour. Moreover, assuming that a priori information about the shapes of objects in an image is known, we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise. We also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features, in contrast to the original geometric heat flow which tends to circularize any closed curve.
在过去几年中，通过偏微分方程应用于单个轮廓或图像水平集的曲线演化，已成为图像处理和计算机视觉中的一种重要工具。曲线演化技术已被用于图像平滑、分割和形状分析等问题。我们对基本的曲线平滑方程，即所谓的几何热方程，给出了一种局部随机解释，并表明这种演化相当于粒子沿轮廓的切向扩散运动。此外，假设已知图像中物体形状的先验信息，我们提出了几何热方程的修正形式，旨在在去除噪声的同时保留这些形状中的某些特征。我们还展示了与原始几何热流倾向于将任何封闭曲线圆化不同，这些新的流如何应用于平滑有噪声的曲线而不破坏其较大尺度特征。
