pith. sign in

arxiv: 1907.06988 · v1 · pith:JO57AXZInew · submitted 2019-07-16 · 📊 stat.ME · stat.AP

Detecting anomalies in fibre systems using 3-dimensional image data

Denis Dresvyanskiy , Tatiana Karaseva , Vitalii Makogin , Sergei Mitrofanov , Claudia Redenbach , Evgeny Spodarev This is my paper

Pith reviewed 2026-05-24 20:52 UTC · model grok-4.3

classification 📊 stat.ME stat.AP
keywords anomaly detectionfibre materials3D imagingSAEM algorithmchange point detectiondirectional distributionrandom fieldsfibre reinforced polymers
0
0 comments X

The pith

A spatial SAEM modification and change point tests on random fields detect anomalies in fibre directional distributions from 3D images.

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

The paper develops a method to find anomalies in fibre orientations within 3D images of materials such as reinforced polymers. Images are split into scanning windows, and local fibre directions yield attributes including coordinate-wise means and entropy. These attributes drive clustering of windows into normal or anomalous groups via a new spatial version of the SAEM algorithm. A change point technique for random fields then supplies exact tail bounds to test whether identified anomalies reach statistical significance. Validation occurs first on simulated data before application to a real fibre-reinforced polymer image.

Core claim

The proposed methodology, including a new spatial modification of the SAEM algorithm and a change point technique for random fields, enables detection and significance testing of anomalies in the directional distribution of fibres observed in 3D images.

What carries the argument

Spatial modification of the Stochastic Approximation Expectation-Maximization (SAEM) algorithm for clustering scanning windows, paired with change point detection on random fields to bound tail probabilities of test statistics.

Load-bearing premise

Anomalies produce shifts in local directional distributions that the chosen attributes (coordinate-wise means and entropy) inside scanning windows capture reliably.

What would settle it

Apply the full pipeline to simulated 3D fibre images containing known planted anomalies and check whether detection rates and significance levels match the model's predicted performance.

Figures

Figures reproduced from arXiv: 1907.06988 by Claudia Redenbach, Denis Dresvyanskiy, Evgeny Spodarev, Sergei Mitrofanov, Tatiana Karaseva, Vitalii Makogin.

Figure 19
Figure 19. Figure 19 [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
read the original abstract

We consider the problem of detecting anomalies in the directional distribution of fibre materials observed in 3D images. We divide the image into a set of scanning windows and classify them into two clusters: homogeneous material and anomaly. Based on a sample of estimated local fibre directions, for each scanning window we compute several classification attributes, namely the coordinate wise means of local fibre directions, the entropy of the directional distribution, and a combination of them. We also propose a new spatial modification of the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. Besides the clustering we also consider testing the significance of anomalies. To this end, we apply a change point technique for random fields and derive the exact inequalities for tail probabilities of a test statistics. The proposed methodology is first validated on simulated images. Finally, it is applied to a 3D image of a fibre reinforced polymer.

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 / 2 minor

Summary. The paper proposes a method for detecting anomalies in the directional distribution of fibres observed in 3D images. Images are partitioned into scanning windows; for each window, attributes consisting of coordinate-wise means of estimated local fibre directions, entropy of the directional distribution, and their combination are computed from samples of directions. These attributes are used to cluster windows into homogeneous material versus anomaly via a newly proposed spatial modification of the SAEM algorithm. Significance of detected anomalies is assessed via a change-point technique for random fields, for which exact tail-probability inequalities are derived for the test statistic. The approach is validated on simulated images and demonstrated on a real 3D image of fibre-reinforced polymer.

Significance. If the central claims hold, the work supplies a statistically rigorous pipeline that combines attribute-based clustering with change-point analysis on random fields and supplies explicit tail bounds, which is a concrete strength for applications in materials science. The derivation of exact inequalities for the test statistic provides a non-asymptotic guarantee that could be useful beyond the fibre setting.

major comments (3)
  1. [Abstract / validation on simulated images] Abstract and validation section: the claim that the methodology 'enables detection and significance testing' rests on validation on simulated images, yet no quantitative performance metrics (e.g., detection rates, false-positive rates, ROC curves), comparisons with alternative clustering or change-point methods, or error analysis are reported. This leaves the practical utility of the chosen attributes and the spatial SAEM modification without empirical grounding.
  2. [Validation on simulated images] Anomaly simulation design (validation section): the construction of anomalies in the simulated images is not described in sufficient detail to verify that shifts in coordinate-wise means and entropy are the relevant signatures. If anomalies instead alter higher moments, spatial correlations, or induce multimodality while leaving the low-order attributes nearly unchanged, both the SAEM clustering step and the subsequent change-point test will have low power; the current validation therefore does not address the weakest assumption identified in the approach.
  3. [Methodology / spatial SAEM] Spatial modification of SAEM (methodology section): the paper introduces a 'new spatial modification' of SAEM, but the precise manner in which spatial dependence is incorporated into the stochastic approximation or expectation steps, together with any convergence analysis, is not provided. Without these details the novelty and correctness of the clustering procedure cannot be assessed, which is load-bearing for the clustering-based anomaly detection claim.
minor comments (2)
  1. [Abstract] The abstract would be strengthened by a brief statement of the quantitative outcomes obtained on the simulated data.
  2. [Introduction / attribute definition] Notation for the directional distribution and the precise definition of the entropy attribute should be introduced earlier and used consistently.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and will revise the manuscript to strengthen the validation and methodological descriptions.

read point-by-point responses

  1. Referee: [Abstract / validation on simulated images] Abstract and validation section: the claim that the methodology 'enables detection and significance testing' rests on validation on simulated images, yet no quantitative performance metrics (e.g., detection rates, false-positive rates, ROC curves), comparisons with alternative clustering or change-point methods, or error analysis are reported. This leaves the practical utility of the chosen attributes and the spatial SAEM modification without empirical grounding.

    Authors: We agree that quantitative performance metrics and comparisons would strengthen the empirical validation. In the revised manuscript we will add detection rates, false-positive rates, ROC curves on the simulated images, and direct comparisons against standard k-means clustering as well as alternative change-point methods, together with a brief error analysis. revision: yes

  2. Referee: [Validation on simulated images] Anomaly simulation design (validation section): the construction of anomalies in the simulated images is not described in sufficient detail to verify that shifts in coordinate-wise means and entropy are the relevant signatures. If anomalies instead alter higher moments, spatial correlations, or induce multimodality while leaving the low-order attributes nearly unchanged, both the SAEM clustering step and the subsequent change-point test will have low power; the current validation therefore does not address the weakest assumption identified in the approach.

    Authors: We will expand the validation section with a precise description of the anomaly construction, explicitly showing how the simulated anomalies are generated to produce the targeted shifts in coordinate-wise directional means and entropy while leaving higher-order features largely unchanged. This will confirm that the simulation directly probes the attributes used by the method. revision: yes

  3. Referee: [Methodology / spatial SAEM] Spatial modification of SAEM (methodology section): the paper introduces a 'new spatial modification' of SAEM, but the precise manner in which spatial dependence is incorporated into the stochastic approximation or expectation steps, together with any convergence analysis, is not provided. Without these details the novelty and correctness of the clustering procedure cannot be assessed, which is load-bearing for the clustering-based anomaly detection claim.

    Authors: We will add a dedicated subsection detailing the exact modifications made to the stochastic approximation and expectation steps to incorporate spatial dependence, together with a convergence analysis of the resulting algorithm. These additions will clarify the novelty and support the correctness of the spatial SAEM procedure. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard methods to derived attributes

full rationale

The paper divides 3D images into scanning windows, computes attributes (coordinate-wise means of local fibre directions and entropy of directional distribution), applies a spatial SAEM modification for clustering into homogeneous vs. anomaly classes, and uses change-point techniques on random fields with derived tail-probability inequalities for significance testing. These steps rely on standard statistical procedures applied to image-derived features without self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations. Validation occurs on simulated images and a real fibre-reinforced polymer dataset, keeping the chain self-contained and externally falsifiable. No quoted equations or citations reduce the central claims to tautologies by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters or invented entities; the method rests on standard assumptions of directional statistics and clustering.

axioms (1)
  • domain assumption Local fibre directional distributions within scanning windows can be summarized sufficiently by coordinate-wise means and entropy for the purpose of distinguishing homogeneous from anomalous regions.
    These quantities are explicitly listed as the classification attributes used for clustering.

pith-pipeline@v0.9.0 · 5696 in / 1144 out tokens · 64723 ms · 2026-05-24T20:52:20.992917+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

53 extracted references · 53 canonical work pages · 1 internal anchor

  1. [1]

    Alonso-Ruiz and E

    P. Alonso-Ruiz and E. Spodarev. Entropy-based inhomogeneity detection in fiber mate- rials. Methodology and Computing in Applied Probability , Nov. 2017. https://doi.org/ Detecting anomalies in fibre systems using 3-dimensional image data 31 1st layer 5th layer Fig. 17 Spatial SAEM clustering according to entropy 1st layer 5th layer Fig. 18 Spatial SAEM clu...

    work page doi:10.1007/s11009-017-9603-2 2017

  2. [2]

    Alonso-Ruiz and E

    P. Alonso-Ruiz and E. Spodarev. Estimation of entropy for Poisson marked point pro- cesses. Adv. in Appl. Probab. , 49(1):258–278, 2017

    work page 2017

  3. [3]

    Andr¨ a, M

    H. Andr¨ a, M. Gurka, M. Kabel, S. Nissle, C. Redenbach, K. Schladitz, and O. Wirjadi. Geometric and mechanical modeling of fiber-reinforced composites. In Proceedings of the 2nd International Congress on 3D Materials Science , pages 35–40. Springer, 2014

    work page 2014

  4. [4]

    Basseville and I

    M. Basseville and I. Nikiforov. Detection of abrupt changes: theory and application . Pren- tice Hall Information and System Sciences Series. Prentice Hall, Inc., Englewood Cliffs, NJ, 1993

    work page 1993

  5. [5]

    Beirlant, E

    J. Beirlant, E. J. Dudewicz, L. Gy¨ orfi, and E. C. van der Meulen. Nonparametric entropy estimation: an overview. Int. J. Math. Stat. Sci. , 6(1):17–39, 1997

    work page 1997

  6. [6]

    B. E. Brodsky and B. S. Darkhovsky. Nonparametric methods in change-point problems , volume 243 of Mathematics and its Applications . Kluwer Academic Publishers Group, Dordrecht, 1993

    work page 1993

  7. [7]

    B. E. Brodsky and B. S. Darkhovsky. Problems and methods of probabilistic diagnostics. Avtomat. i Telemekh., 60(8):3–50, 1999

    work page 1999

  8. [8]

    B. E. Brodsky and B. S. Darkhovsky. Non-parametric statistical diagnosis, volume 509 of Mathematics and its Applications . Kluwer Academic Publishers, Dordrecht, 2000. Prob- lems and methods

    work page 2000

  9. [9]

    B. Bucchia. Testing for epidemic changes in the mean of a multiparameter stochastic process. J. Statist. Plann. Inference , 150:124–141, 2014

    work page 2014

  10. [10]

    Bucchia and C

    B. Bucchia and C. Heuser. Long-run variance estimation for spatial data under change- point alternatives. J. Statist. Plann. Inference , 165:104–126, 2015. 32 Denis Dresvyanskiy et al. 1st layer 5th layer Fig. 19 Spatial SAEM clustering according to a combination of entropy and MLD

    work page 2015

  11. [11]

    Bucchia and M

    B. Bucchia and M. Wendler. Change-point detection and bootstrap for Hilbert space valued random fields. Journal of Multivariate Analysis , 155:344 – 368, 2017

    work page 2017

  12. [12]

    Bulinski and D

    A. Bulinski and D. Dimitrov. Statistical estimation of the Shannon entropy. Acta. Math. Sin.-English Ser., 2018. https://doi.org/10.1007/s10114-018-7440-z

    work page doi:10.1007/s10114-018-7440-z 2018

  13. [13]

    Cao and K

    J. Cao and K. J. Worsley. The detection of local shape changes via the geometry of Hotelling’s T 2 fields. Ann. Statist., 27(3):925–942, 1999

    work page 1999

  14. [14]

    Carlstein, H.-G

    E. Carlstein, H.-G. M¨ uller, and D. Siegmund, editors. Change-point problems, volume 23 of Institute of Mathematical Statistics Lecture Notes—Monograph Series . Institute of Mathematical Statistics, Hayward, CA, 1994. Papers from the AMS-IMS-SIAM Summer Research Conference held at Mt. Holyoke College, South Hadley, MA, July 11–16, 1992

    work page 1994

  15. [15]

    Celeux and J

    G. Celeux and J. Diebolt. A stochastic approximation type EM algorithm for the mixture problem. Stochastics Stochastics Rep., 41(1-2):119–134, 1992

    work page 1992

  16. [16]

    A. Chambaz. Detecting abrupt changes in random fields. ESAIM Probab. Statist., 6:189– 209, 2002. New directions in time series analysis (Luminy, 2001)

    work page 2002

  17. [17]

    Chen and A

    J. Chen and A. K. Gupta. Parametric statistical change point analysis . Birkh¨ auser/Springer, New York, second edition, 2012. With applications to genetics, medicine, and finance

    work page 2012

  18. [18]

    S. N. Chiu, D. Stoyan, W. S. Kendall, and J. Mecke. Stochastic geometry and its appli- cations. Wiley Series in Probability and Statistics. John Wiley & Sons, Ltd., Chichester, third edition, 2013

    work page 2013

  19. [19]

    Cs¨ org¨ o and L

    M. Cs¨ org¨ o and L. Horv´ ath.Limit theorems in change-point analysis . Wiley Series in Probability and Statistics. John Wiley & Sons, Ltd., Chichester, 1997

    work page 1997

  20. [20]

    R. L. Dobrushin. A simplified method of experimentally evaluating the entropy of a stationary sequence. Theory of Probability & Its Applications , 3(4):428–430, 1958

    work page 1958

  21. [21]

    Dresvyanskiy, T

    D. Dresvyanskiy, T. Karaseva, S. Mitrofanov, C. Redenbach, S. Schwaar, V. Makogin, and E. Spodarev. Application of clustering methods to anomaly detection in fibrous media. arXiv preprint arXiv:1810.12401 [stat.AP], 2018

    work page arXiv 2018

  22. [22]

    Adaptive Nonparametric Clustering

    K. Efimov, L. Adamyan, and V. Spokoiny. Adaptive nonparametric clustering. arXiv preprint arXiv:1709.09102, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  23. [23]

    B. S. Everitt, S. Landau, M. Leese, and D. Stahl. Cluster analysis . Wiley Series in Probability and Statistics. John Wiley & Sons, Ltd., Chichester, fifth edition, 2011

    work page 2011

  24. [24]

    Falconer

    K. Falconer. Fractal geometry. John Wiley & Sons, Inc., Hoboken, NJ, second edition,

    work page

  25. [25]

    Mathematical foundations and applications

    work page

  26. [26]

    Franke, C

    J. Franke, C. Redenbach, and N. Zhang. On a mixture model for directional data on the sphere. Scand. J. Stat. , 43(1):139–155, 2016

    work page 2016

  27. [27]

    MAVI – modular algorithms for volume images

    Fraunhofer ITWM, Department of Image Processing. MAVI – modular algorithms for volume images. http://www.mavi-3d.de, 2005

    work page 2005

  28. [28]

    A. K. Gorshenin, V. Y. Korolev, and A. M. Tursunbaev. Median modifications of the EM- algorithm for separation of mixtures of probability distributions and their applications to the decomposition of volatility of financial indexes. J. Math. Sci. (N.Y.) , 227(2):176–195, 2017. Detecting anomalies in fibre systems using 3-dimensional image data 33

    work page 2017

  29. [29]

    Hahubia and R

    T. Hahubia and R. Mnatsakanov. On the mode-change problem for random measures. Georgian Math. J., 3(4):343–362, 1996

    work page 1996

  30. [30]

    Heinrich

    L. Heinrich. Some bounds of cumulants of m-dependent random fields. Math. Nachr. , 149:303–317, 1990

    work page 1990

  31. [31]

    Hennig, M

    C. Hennig, M. Meila, F. Murtagh, and R. Rocci, editors. Handbook of cluster analy- sis. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press, Boca Raton, FL, 2016

    work page 2016

  32. [32]

    Jaruˇ skov´ a and V

    D. Jaruˇ skov´ a and V. I. Piterbarg. Log-likelihood ratio test for detecting transient change. Statist. Probab. Lett., 81(5):552–559, 2011

    work page 2011

  33. [33]

    E. I. Kaplan. On the change-point problem for random fields. Teor. Veroyatnost. i Primenen., 35(2):353–358, 1990

    work page 1990

  34. [34]

    E. I. Kaplan. Convergence of estimates for partitions in the change point problem for random fields. Teor. ¯Imov¯ ır. ta Mat. Statist., 47:34–39, 1992

    work page 1992

  35. [35]

    V. Y. Korolev. EM-algorithm, its modifications and their use in the problem of decom- posing the mixtures of probability distributions . IPIRAS, Moscow, 2007

    work page 2007

  36. [36]

    L. F. Kozachenko and N. N. Leonenko. A statistical estimate for the entropy of a random vector. Problemy Peredachi Informatsii, 23(2):9–16, 1987

    work page 1987

  37. [37]

    T. L. Lai. Saddlepoint approximations and boundary crossing probabilities for random fields and their applications. In Third International Congress of Chinese Mathematicians. Part 1, 2 , volume 2 of AMS/IP Stud. Adv. Math., 42, pt. 1 , pages 29–39. Amer. Math. Soc., Providence, RI, 2008

    work page 2008

  38. [38]

    Laurent, C

    B. Laurent, C. Marteau, and C. Maugis-Rabusseau. Multidimensional two-component Gaussian mixtures detection. Ann. Inst. Henri Poincar´ e Probab. Stat., 54(2):842–865, 2018

    work page 2018

  39. [39]

    W. D. Miller. Quasi-Heyting algebras: A new class of lattices, and a foundation for nonclassical model theory with possible computational applications . ProQuest LLC, Ann Arbor, MI, 1993. Thesis (Ph.D.)–Kansas State University

    work page 1993

  40. [40]

    H. G. M¨ uller and K.-S. Song. Cube splitting in multidimensional edge estimation. In Change-point problems (South Hadley, MA, 1992) , volume 23 of IMS Lecture Notes Monogr. Ser., pages 210–223. Inst. Math. Statist., Hayward, CA, 1994

    work page 1992

  41. [41]

    Ninomiya

    Y. Ninomiya. Construction of conservative test for change-point problem in two- dimensional random fields. J. Multivariate Anal. , 89(2):219–242, 2004

    work page 2004

  42. [42]

    E. S. Page. Continuous inspection schemes. Biometrika, 41:100–115, 1954

    work page 1954

  43. [43]

    M. D. Penrose and J. E. Yukich. Limit theory for point processes in manifolds. Ann. Appl. Probab., 23(6):2161–2211, 2013

    work page 2013

  44. [44]

    Redenbach and I

    C. Redenbach and I. Vecchio. Statistical analysis and stochastic modelling of fibre com- posites. Composites Science and Technology, 71:107–112, 2011

    work page 2011

  45. [45]

    C. A. Rogers. Hausdorff measures. Cambridge University Press, 1998

    work page 1998

  46. [46]

    Sen and M

    A. Sen and M. S. Srivastava. On tests for detecting change in mean. Ann. Statist. , 3:98–108, 1975

    work page 1975

  47. [47]

    Sharipov, J

    O. Sharipov, J. Tewes, and M. Wendler. Sequential block bootstrap in a Hilbert space with application to change point analysis. Canad. J. Statist. , 44(3):300–322, 2016

    work page 2016

  48. [48]

    Siegmund and B

    D. Siegmund and B. Yakir. Detecting the emergence of a signal in a noisy image. Stat. Interface, 1(1):3–12, 2008

    work page 2008

  49. [49]

    D. O. Siegmund and K. J. Worsley. Testing for a signal with unknown location and scale in a stationary Gaussian random field. Ann. Statist., 23(2):608–639, 1995

    work page 1995

  50. [50]

    S. T. Wierzcho´ n and M. A. K l opotek.Modern algorithms of cluster analysis , volume 34 of Studies in Big Data . Springer, Cham, 2018

    work page 2018

  51. [51]

    Wirjadi, M

    O. Wirjadi, M. Godehardt, K. Schladitz, B. Wagner, A. Rack, M. Gurka, S. Nissle, and A. Noll. Characterization of multilayer structures of fiber reinforced polymer employ- ing synchrotron and laboratory X-ray CT. International Journal of Materials Research , 105(7):645654, 2014

    work page 2014

  52. [52]

    Wirjadi, K

    O. Wirjadi, K. Schladitz, P. Easwaran, and J. Ohser. Estimating fibre direction distri- butions of reinforced composites from tomographic images. Image Analysis & Stereology, 35(3):167–179, 2016

    work page 2016

  53. [53]

    Y. Wu. Inference for change-point and post-change means after a CUSUM test , volume 180 of Lecture Notes in Statistics . Springer, New York, 2005

    work page 2005