二维经验小波变换的Demons配准方法
Demons registration for 2D empirical wavelet transforms
AI总结：
本文针对二维经验小波变换中谐波模式支撑形状复杂导致映射计算困难的问题，提出利用Demons配准算法高效计算经验小波系数，实现了数值稳健的小波变换，并成功应用于扫描隧道显微镜图像的纹理分割。
摘要：
经验小波变换是一种完全自适应的时-尺度表示方法，在过去十年中被广泛应用。受经验模态分解的启发，它由基于谐波模式支撑的滤波器组构成。近年来，该方法已被推广为利用映射从任意生成函数构建滤波器组。在实际应用中，二维谐波模式支撑可能具有低约束形状，导致计算映射及相关小波滤波器时出现数值困难。本工作旨在提出一种高效的数值方案，利用Demons配准算法计算经验小波系数。结果表明，所提方法能够给出数值上稳健的小波变换。本文还展示了该方法在扫描隧道显微镜图像纹理分割中的应用。
英文摘要：
The empirical wavelet transform is a fully adaptive time-scale representation that has been widely used in the last decade. Inspired by the empirical mode decomposition, it consists of filter banks based on harmonic mode supports. Recently, it has been generalized to build the filter banks from any generating function using mappings. In practice, the harmonic mode supports can have low constrained shape in 2D, leading to numerical difficulties to compute the mappings and therefore the related wavelet filters. This work aims to propose an efficient numerical scheme to compute empirical wavelet coefficients using the demons registration algorithm. Results show that the proposed approach gives a numerically robust wavelet transform. An application to texture segmentation of scanning tunnelling microscope images is also presented.
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