提出可任意划分频域的二维经验小波变换方法
The Empirical Watershed Wavelet
- 基于尺度空间与分水岭算法自适应分割频谱
- 支持任意形状频域分区，突破传统限制
- 适用于纹理分割与图像去卷积，效果更优
经验小波变换是一种基于数据驱动频域划分的自适应多分辨率分析工具。然而，现有二维扩展受限于检测到的分区形状。本文提供理论支持，使二维经验小波滤波器可基于任意频域划分构建。我们提出一种算法，通过尺度空间表示估计主导谐波模式位置，并结合分水岭变换确定不同支撑区域边界，从而实现期望的频域划分。该过程定义了经验分水岭小波变换。我们在合成图像上进行可视化验证，并在无监督纹理分割和图像去卷积任务中展示了该方法的有效性与优势。
原文摘要 · Abstract (English)
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the detected partitioning. In this paper, we provide theoretical results that permits us to build 2D empirical wavelet filters based on an arbitrary partitioning of the frequency domain. We also propose an algorithm to detect such partitioning from an image spectrum by combining a scale-space representation to estimate the position of dominant harmonic modes and a watershed transform to find the boundaries of the different supports making the expected partition. This whole process allows us to define the empirical watershed wavelet transform. We illustrate the effectiveness and the advantages of such adaptive transform, first visually on toy images, and next on both unsupervised texture segmentation and image deconvolution applications.
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