Felsberg Michael, Forssén Per-Erik, Scharr Hanno
Computer Vision Laboratory, Department of Electrical Engineering, Linköping University, S-58183 Linköping, Sweden.
IEEE Trans Pattern Anal Mach Intell. 2006 Feb;28(2):209-22. doi: 10.1109/TPAMI.2006.29.
In this paper, we present a new and efficient method to implement robust smoothing of low-level signal features: B-spline channel smoothing. This method consists of three steps: encoding of the signal features into channels, averaging of the channels, and decoding of the channels. We show that linear smoothing of channels is equivalent to robust smoothing of the signal features if we make use of quadratic B-splines to generate the channels. The linear decoding from B-spline channels allows the derivation of a robust error norm, which is very similar to Tukey's biweight error norm. We compare channel smoothing with three other robust smoothing techniques: nonlinear diffusion, bilateral filtering, and mean-shift filtering, both theoretically and on a 2D orientation-data smoothing task. Channel smoothing is found to be superior in four respects: It has a lower computational complexity, it is easy to implement, it chooses the global minimum error instead of the nearest local minimum, and it can also be used on nonlinear spaces, such as orientation space.
在本文中，我们提出了一种新的高效方法来实现低级信号特征的鲁棒平滑：B样条通道平滑。该方法包括三个步骤：将信号特征编码到通道中、通道平均以及通道解码。我们表明，如果使用二次B样条来生成通道，那么通道的线性平滑等同于信号特征的鲁棒平滑。从B样条通道进行的线性解码允许导出一种鲁棒误差范数，它与图基双权误差范数非常相似。我们在理论上以及在二维方向数据平滑任务中，将通道平滑与其他三种鲁棒平滑技术进行比较：非线性扩散、双边滤波和均值漂移滤波。发现通道平滑在四个方面具有优势：它具有较低的计算复杂度，易于实现，它选择全局最小误差而不是最近的局部最小误差，并且它还可以用于非线性空间，如方向空间。
