The Empirical Watershed Wavelet

• URL: http://arxiv.org/abs/2410.19187v1
• Date: Thu, 24 Oct 2024 22:36:43 GMT
• Title: The Empirical Watershed Wavelet
• Authors: Basile Hurat, Zariluz Alvarado, Jerome Gilles,
• Abstract summary: 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.
• Score: 0.0
• License:
• 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.

Related papers

• 2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited [0.0]
  We present several extensions of this approach to 2D signals (images) We prove that such constructions lead to different adaptive frames which show some promising properties for image analysis and processing.
  arXiv  Detail & Related papers  (2024-10-31T00:52:59Z)
• Wavelet Burst Accumulation for turbulence mitigation [0.0]
  We investigate the extension of the recently proposed weighted Fourier burst accumulation (FBA) method into the wavelet domain. The purpose of the method is to reconstruct a clean and sharp image from a sequence of blurred frames.
  arXiv  Detail & Related papers  (2024-10-30T08:31:48Z)
• F2former: When Fractional Fourier Meets Deep Wiener Deconvolution and Selective Frequency Transformer for Image Deblurring [8.296475046681696]
  We propose a novel approach based on the Fractional Fourier Transform (FRFT), a unified spatial-frequency representation. We show that the performance of our proposed method is superior to other state-of-the-art (SOTA) approaches.
  arXiv  Detail & Related papers  (2024-09-03T17:05:12Z)
• Misalignment-Robust Frequency Distribution Loss for Image Transformation [51.0462138717502]
  This paper aims to address a common challenge in deep learning-based image transformation methods, such as image enhancement and super-resolution. We introduce a novel and simple Frequency Distribution Loss (FDL) for computing distribution distance within the frequency domain. Our method is empirically proven effective as a training constraint due to the thoughtful utilization of global information in the frequency domain.
  arXiv  Detail & Related papers  (2024-02-28T09:27:41Z)
• Exploring Invariance in Images through One-way Wave Equations [96.90549064390608]
  In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. We demonstrate it using an intuitive encoder-decoder framework where each image is encoded into its corresponding initial condition.
  arXiv  Detail & Related papers  (2023-10-19T17:59:37Z)
• Unified Frequency-Assisted Transformer Framework for Detecting and Grounding Multi-Modal Manipulation [109.1912721224697]
  We present the Unified Frequency-Assisted transFormer framework, named UFAFormer, to address the DGM4 problem. By leveraging the discrete wavelet transform, we decompose images into several frequency sub-bands, capturing rich face forgery artifacts. Our proposed frequency encoder, incorporating intra-band and inter-band self-attentions, explicitly aggregates forgery features within and across diverse sub-bands.
  arXiv  Detail & Related papers  (2023-09-18T11:06:42Z)
• Deep Fourier Up-Sampling [100.59885545206744]
  Up-sampling in the Fourier domain is more challenging as it does not follow such a local property. We propose a theoretically sound Deep Fourier Up-Sampling (FourierUp) to solve these issues.
  arXiv  Detail & Related papers  (2022-10-11T06:17:31Z)
• Style Spectroscope: Improve Interpretability and Controllability through Fourier Analysis [42.59845771101823]
  Universal style transfer (UST) infuses styles from arbitrary reference images into content images. Existing methods are unable to explain experimental observations. We present an equivalent form of the framework in the frequency domain.
  arXiv  Detail & Related papers  (2022-08-12T07:15:33Z)
• aiWave: Volumetric Image Compression with 3-D Trained Affine Wavelet-like Transform [43.984890290691695]
  Most commonly used volumetric image compression methods are based on wavelet transform, such as JP3D. In this paper, we first design a 3-D trained wavelet-like transform to enable signal-dependent and non-separable transform. Then, an affine wavelet basis is introduced to capture the various local correlations in different regions of volumetric images.
  arXiv  Detail & Related papers  (2022-03-11T10:02:01Z)
• A Fourier-based Framework for Domain Generalization [82.54650565298418]
  Domain generalization aims at tackling this problem by learning transferable knowledge from multiple source domains in order to generalize to unseen target domains. This paper introduces a novel Fourier-based perspective for domain generalization. Experiments on three benchmarks have demonstrated that the proposed method is able to achieve state-of-the-arts performance for domain generalization.
  arXiv  Detail & Related papers  (2021-05-24T06:50:30Z)
• Transforming Spectrum and Prosody for Emotional Voice Conversion with Non-Parallel Training Data [91.92456020841438]
  Many studies require parallel speech data between different emotional patterns, which is not practical in real life. We propose a CycleGAN network to find an optimal pseudo pair from non-parallel training data. We also study the use of continuous wavelet transform (CWT) to decompose F0 into ten temporal scales, that describes speech prosody at different time resolution.
  arXiv  Detail & Related papers  (2020-02-01T12:36:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.