The Empirical Watershed Wavelet
arXiv:2410.19187 · doi:10.3390/jimaging6120140
Abstract
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.
References in corpus (5)
- Empirical wavelet transform
- 2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited
- Review of wavelet-based unsupervised texture segmentation, advantage of adaptive wavelets
- Empirical curvelet based Fully Convolutional Network for supervised texture image segmentation
- Continuous empirical wavelets systems