用德蒙斯配准法解决2D经验小波变换的数值难题
Demons registration for 2D empirical wavelet transforms
- 引入德蒙斯配准算法计算2D经验小波变换的映射关系
- 在扫描隧道显微镜图像纹理分割任务中表现稳定可靠
- 适合处理形状不规则的2D谐波模式分解问题
经验小波变换是一种完全自适应的时间-尺度表示方法，近十年来广泛应用。受经验模态分解启发，其基于谐波模式支撑构建滤波器组。近期，该方法被推广为通过任意生成函数和映射构建滤波器组。然而，在2D情况下，谐波模式支撑形状约束较弱，导致映射计算出现数值困难，进而影响小波滤波器构造。本文提出一种基于德蒙斯配准算法的高效数值方案，用于计算经验小波系数。实验结果表明，所提方法具有良好的数值稳定性。此外，还展示了该方法在扫描隧道显微镜（STM）图像纹理分割中的应用。
原文摘要 · Abstract (English)
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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