pith. sign in

arxiv: 1907.03591 · v1 · pith:773VK2WSnew · submitted 2019-07-05 · 📡 eess.IV · cs.LG· stat.ML

Feature-Based Image Clustering and Segmentation Using Wavelets

Junyu Chen , Eric C. Frey This is my paper

Pith reviewed 2026-05-25 02:24 UTC · model grok-4.3

classification 📡 eess.IV cs.LGstat.ML
keywords wavelet transformimage segmentationk-means clusteringfuzzy c-meansactive contour without edgesfeature-based clusteringfrequency sub-bandsrobust segmentation
0
0 comments X

The pith

Adding wavelet sub-band features to standard clustering algorithms lets segmentation results vary with frequency emphasis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Pixel intensity alone often leads to noisy or context-poor segmentations in standard methods. The authors modify K-means, fuzzy c-means, and active contour without edges to use wavelet sub-band features instead. They add a weighting parameter to balance low-frequency contributions. These changes allow the algorithms to converge on results that differ according to the selected frequency bands. The goal is to create more robust versions of familiar tools by borrowing wavelet properties for denoising and multi-scale analysis.

Core claim

The conventional K-means, Fuzzy c-means (FCM), and Active contour without edges (ACWE) algorithms were modified to adapt Wavelet features, leading to robust clustering/segmentation algorithms. A weighting parameter to control the weight of low-frequency sub-band information was also introduced. The new algorithms showed the capability to converge to different segmentation results based on the frequency information derived from the Wavelet sub-bands.

What carries the argument

Modified K-means, FCM, and ACWE that replace or augment intensity-based distances with wavelet sub-band features, controlled by a weighting parameter on low-frequency content.

If this is right

  • Segmentation results become less sensitive to noise in raw pixel intensities.
  • Spatial context information from the wavelet decomposition enters the clustering process.
  • The same image can produce different segmentations by changing which frequency sub-bands are emphasized.
  • The original convergence behavior of K-means, FCM, and ACWE is retained after the modifications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Frequency emphasis could let users target structures at particular scales without changing the base algorithm.
  • The weighting parameter might be learned or adapted per image rather than set manually.
  • The same wavelet-feature idea could be tested on other intensity-based methods beyond the three examined here.

Load-bearing premise

That adding wavelet sub-band features will produce meaningful improvements in robustness to noise and spatial context without breaking the convergence or stability properties of the original methods.

What would settle it

Direct tests on noisy benchmark images where the wavelet-modified algorithms show no improvement in segmentation accuracy metrics or stability compared with the unmodified versions.

read the original abstract

Pixel intensity is a widely used feature for clustering and segmentation algorithms, the resulting segmentation using only intensity values might suffer from noises and lack of spatial context information. Wavelet transform is often used for image denoising and classification. We proposed a novel method to incorporate Wavelet features in segmentation and clustering algorithms. The conventional K-means, Fuzzy c-means (FCM), and Active contour without edges (ACWE) algorithms were modified to adapt Wavelet features, leading to robust clustering/segmentation algorithms. A weighting parameter to control the weight of low-frequency sub-band information was also introduced. The new algorithms showed the capability to converge to different segmentation results based on the frequency information derived from the Wavelet sub-bands.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The paper proposes modifications to the standard K-means, Fuzzy C-Means (FCM), and Active Contour Without Edges (ACWE) algorithms that incorporate wavelet sub-band features in place of or in addition to pixel intensity. A weighting parameter is introduced to control the contribution of low-frequency sub-band information. The central claim is that these augmented algorithms remain convergent while producing segmentation results that depend on the frequency content extracted from the wavelet decomposition.

Significance. A rigorously validated method for embedding wavelet coefficients into these classical algorithms while preserving their convergence guarantees would be of practical interest for noise-robust segmentation. The manuscript, however, supplies neither the modified objective functions nor any convergence analysis, so the significance cannot be assessed from the given text.

major comments (3)
  1. [Abstract] Abstract: the assertion that the modified algorithms 'showed the capability to converge' to frequency-dependent results is unsupported; no modified objective function, membership-update rule, or level-set evolution equation is supplied for any of the three algorithms.
  2. [Abstract / Method description] No section derives or verifies that the wavelet-coefficient statistics preserve the contractivity or monotonic energy descent of the original K-means, FCM, or ACWE iterations; for ACWE this is particularly critical because the region integrals are replaced by wavelet-coefficient statistics whose Lipschitz or convexity properties are not examined.
  3. [Abstract] The weighting parameter for the low-frequency sub-band is introduced without any analysis of how its value affects stability or of the range over which convergence is retained.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments highlighting the need for explicit derivations and analysis. We agree that the current version lacks these details and will revise the manuscript to include them, strengthening the presentation of the proposed modifications.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the modified algorithms 'showed the capability to converge' to frequency-dependent results is unsupported; no modified objective function, membership-update rule, or level-set evolution equation is supplied for any of the three algorithms.

    Authors: We acknowledge that the manuscript does not supply the explicit modified objective functions, membership-update rules, or level-set evolution equations. In the revision we will add a new section that derives these for the wavelet-augmented K-means, FCM, and ACWE algorithms, thereby supporting the convergence claim with the necessary mathematical detail. revision: yes

  2. Referee: [Abstract / Method description] No section derives or verifies that the wavelet-coefficient statistics preserve the contractivity or monotonic energy descent of the original K-means, FCM, or ACWE iterations; for ACWE this is particularly critical because the region integrals are replaced by wavelet-coefficient statistics whose Lipschitz or convexity properties are not examined.

    Authors: The referee correctly notes the absence of any derivation or verification that wavelet-coefficient statistics preserve the original convergence properties. We will include in the revised manuscript a dedicated analysis addressing contractivity and monotonic energy descent for all three algorithms, with specific examination of the Lipschitz/convexity properties of the wavelet-based region integrals in the ACWE case. revision: yes

  3. Referee: [Abstract] The weighting parameter for the low-frequency sub-band is introduced without any analysis of how its value affects stability or of the range over which convergence is retained.

    Authors: We agree that no analysis of the weighting parameter's influence on stability or the admissible range for convergence is provided. The revision will add both theoretical discussion and empirical evaluation of the parameter's effect on algorithmic stability, including bounds on values that preserve convergence. revision: yes

Circularity Check

0 steps flagged

No circularity; paper offers empirical algorithmic adaptations without any derivation chain or self-referential equations.

full rationale

The manuscript describes modifications to K-means, FCM, and ACWE by adding wavelet sub-band features plus an explicit weighting parameter, then reports that the resulting procedures converge to frequency-dependent segmentations. No objective functions, update rules, or convergence proofs appear in the provided text; the weighting parameter is introduced directly rather than fitted in a hidden loop. Because the work contains no load-bearing derivation that could reduce to its own inputs by construction, self-citation, or renaming, the circularity score is zero.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that wavelet sub-bands supply useful spatial and frequency context beyond raw intensity, plus one explicit free parameter for weighting low-frequency content. No new entities are postulated.

free parameters (1)
  • weighting parameter for low-frequency sub-band
    Introduced to control the relative influence of low-frequency wavelet information in the modified algorithms.
axioms (1)
  • domain assumption Wavelet transforms extract frequency sub-band information that can serve as robust features for clustering and segmentation
    Invoked as the justification for replacing or augmenting pixel intensity with wavelet features.

pith-pipeline@v0.9.0 · 5643 in / 1229 out tokens · 22092 ms · 2026-05-25T02:24:22.542294+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages · 1 internal anchor

  1. [1]

    INTRODUCTION Many real images are often corrupted by noise in their ac- quisition, such as biomedical images like Single-photon emission computed tomography (SPECT) images, and the image itself often contains both smooth and textured regions. Wavelet decomposition is a heavily used tool in image pro- cessing and classification; it enables the decomposition...

    work page

  2. [2]

    Feature-Based Image Clustering and Segmentation Using Wavelets

    IMAGE CLUSTERING AND SEGMENTA TION IN W A VELET DOMAIN 2.1. Wavelet Decomposition The wavelet transform represents the singularity content of an image at multiple scales [8]. In our wavelet decomposition scheme, as shown in Fig. 2, the transform is applied on the entire image and the first Wavelet tree was extracted and then vectorized. The vectorized Wave...

    work page internal anchor Pith review Pith/arXiv arXiv 1907

  3. [3]

    4; the proposed ACWE-W algorithm was tested on the simulated Quantitative Bone SPECT image using the NURBS-based XCAT phantom [16], an example slice is shown in Fig

    RESULTS The proposed K-means and FCM algorithms were tested on binarized minefield image, as shown in Fig. 4; the proposed ACWE-W algorithm was tested on the simulated Quantitative Bone SPECT image using the NURBS-based XCAT phantom [16], an example slice is shown in Fig. 5 (a). In Fig. 5 (b), the green curve indicates the rectangular region of interest th...

    work page 2022

  4. [4]

    CONCLUSION Image clustering and segmentation algorithms often concen- trate only on local pixel intensities, although many algorithms have been proposed to incorporate spatial context [4][5][6], the modified clustering/segmentation algorithms could still be sensitive to noises. In this paper, we proposed to apply clus- tering/segmentation algorithms in the...

    work page

  5. [5]

    ACKNOWLEDGMENT The authors would like to thank Shuwen Wei who provided expertise that greatly assisted this work

    work page

  6. [6]

    Wavelet feature selection for image classification,

    K. Huang and S. Aviyente, “Wavelet feature selection for image classification,” IEEE Transactions on Image Processing, vol. 17, no. 9, pp. 1709–1720, Sept 2008

    work page 2008

  7. [7]

    Adaptive wavelet thresholding for image denoising and compression,

    S.G. Chang, Bin Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Transactions on Image Processing , vol. 9, no. 9, pp. 1532–1546, 2000

    work page 2000

  8. [8]

    Image Denois- ing Via Sparse and Redundant Representations Over Learned Dictionaries,

    Michael Elad and Michal Aharon, “Image Denois- ing Via Sparse and Redundant Representations Over Learned Dictionaries,” IEEE Transactions on Image Processing, vol. 15, no. 12, pp. 3736–3745, dec 2006

    work page 2006

  9. [9]

    Spatial Models for Fuzzy Clustering,

    Dzung L. Pham, “Spatial Models for Fuzzy Clustering,” Computer Vision and Image Understanding, vol. 84, no. 2, pp. 285–297, nov 2001

    work page 2001

  10. [10]

    A clustering algorithm for liver lesion segmentation of diffusion-weighted MR images,

    Abhinav K. Jha, Jeffrey J. Rodriguez, Renu M. Stephen, and Alison T. Stopeck, “A clustering algorithm for liver lesion segmentation of diffusion-weighted MR images,” in 2010 IEEE Southwest Symposium on Image Analysis & Interpretation (SSIAI). may 2010, pp. 93–96, IEEE

    work page 2010

  11. [11]

    A robust fuzzy local in- formation c-means clustering algorithm,

    S. Krinidis and V . Chatzis, “A robust fuzzy local in- formation c-means clustering algorithm,” IEEE Trans- actions on Image Processing , vol. 19, no. 5, pp. 1328– 1337, May 2010

    work page 2010

  12. [12]

    A robust automatic clus- tering scheme for image segmentation using wavelets,

    R. Porter and N. Canagarajah, “A robust automatic clus- tering scheme for image segmentation using wavelets,” IEEE Transactions on Image Processing , vol. 5, no. 4, pp. 662–665, April 1996

    work page 1996

  13. [13]

    Multiscale image seg- mentation using wavelet-domain hidden Markov mod- els,

    H. Choi and R.G. Baraniuk, “Multiscale image seg- mentation using wavelet-domain hidden Markov mod- els,” IEEE Transactions on Image Processing , vol. 10, no. 9, pp. 1309–1321, 2001

    work page 2001

  14. [14]

    Julius T Tou and Rafael C Gonzlez, Pattern recogni- tion principles, Appl. Math. Comput. Addison-Wesley, Amsterdam, 1974

    work page 1974

  15. [15]

    Bankman, Ed., Handbook of Medical Imaging, Academic Press, Inc., Orlando, FL, USA, 2000

    Isaac N. Bankman, Ed., Handbook of Medical Imaging, Academic Press, Inc., Orlando, FL, USA, 2000

    work page 2000

  16. [16]

    Fcm: The fuzzy c-means clustering algorithm,

    James C. Bezdek, Robert Ehrlich, and William Full, “Fcm: The fuzzy c-means clustering algorithm,” Com- puters & Geosciences , vol. 10, no. 2, pp. 191 – 203, 1984

    work page 1984

  17. [17]

    Active contours without edges,

    T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Transactions on Image Processing , vol. 10, no. 2, pp. 266–277, Feb 2001

    work page 2001

  18. [18]

    Image seg- mentation based on active contours without edges,

    A. Morar, F. Moldoveanu, and E. Grller, “Image seg- mentation based on active contours without edges,” in 2012 IEEE 8th International Conference on Intelligent Computer Communication and Processing , Aug 2012, pp. 213–220

    work page 2012

  19. [19]

    Fronts propagat- ing with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations,

    Stanley Osher and James A Sethian, “Fronts propagat- ing with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations,” Journal of Computa- tional Physics, vol. 79, no. 1, pp. 12 – 49, 1988

    work page 1988

  20. [20]

    Level set methods,

    R. S. MacKay, “Level set methods,” Journal of Fluid Mechanics, vol. 345, pp. 412413, 1997

    work page 1997

  21. [21]

    Incorporating CT Prior Information in the Robust Fuzzy C-means Algo- rithm for QSPECT Image Segmentation,

    J. Chen, A. K. Jha, and E. C. Frey, “Incorporating CT Prior Information in the Robust Fuzzy C-means Algo- rithm for QSPECT Image Segmentation,” in 2019 SPIE Medical Imaging, 2019

    work page 2019