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arxiv: 2605.27287 · v1 · pith:3TD7OJGLnew · submitted 2026-05-26 · 💻 cs.CV

A Dynamic Programming Framework for Discovering Count and Values of Multilevel Image Thresholding

Eslam Hegazy , Mohamed Gabr This is my paper

Pith reviewed 2026-06-29 18:24 UTC · model grok-4.3

classification 💻 cs.CV
keywords multilevel image thresholdingdynamic programmingminimum error thresholdingautomatic threshold countimage segmentationMET-DPcomputer vision preprocessing
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The pith

A modified minimum error thresholding criterion combined with dynamic programming can automatically determine both the number and the values of thresholds for multilevel image segmentation.

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

The paper introduces MET-DP, a dynamic programming method that jointly finds a suitable count of thresholds and their positions without requiring the count as user input. It modifies the Minimum Error Thresholding criterion so that it serves as an objective function whose minimization by DP produces both the count and the values. The approach is shown to run faster than conventional dynamic programming thresholding when the number of thresholds grows large. Tests on natural, satellite, and medical images indicate that MET-DP selects appropriate threshold counts for most cases, although methods supplied with a fixed count can achieve higher SSIM and PSNR. An empirical study is used to explain the observed speed and count-selection advantages.

Core claim

By adapting the Minimum Error Thresholding criterion into a form suitable for dynamic programming, the resulting MET-DP algorithm simultaneously optimizes threshold count and threshold locations, yielding an automatic multilevel thresholding procedure that requires substantially less computation time than standard DP methods once the threshold count becomes large and that identifies suitable counts across diverse image types.

What carries the argument

The MET-DP dynamic programming recurrence that minimizes a modified Minimum Error Thresholding objective to recover both the optimal number of thresholds and their intensity values.

If this is right

  • Computation time remains lower than traditional DP thresholding once the number of thresholds increases.
  • The method selects a suitable threshold count for most images across natural, satellite, and medical domains without external specification of that count.
  • When the threshold count is supplied in advance, competing methods achieve higher structural similarity and peak signal-to-noise ratio than MET-DP.
  • An empirical statistical analysis identifies the source of the speed advantage over conventional dynamic programming approaches.

Where Pith is reading between the lines

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

  • The same DP structure could be paired with other thresholding criteria to produce additional automatic-count methods.
  • Because runtime grows more slowly with threshold count, the technique may become practical for applications that previously avoided high-level thresholding.
  • If the modified criterion proves stable across modalities, the framework could be applied to video frames or volumetric data with only minor adaptation of the cost function.
  • The source code release allows direct replication and extension on new image collections.

Load-bearing premise

The modification of the Minimum Error Thresholding criterion produces a valid objective function whose minimization by dynamic programming yields both an appropriate threshold count and values that generalize beyond the tested image set.

What would settle it

Running MET-DP on a fresh collection of images where expert-annotated or ground-truth segmentations exist and finding that the automatically chosen threshold counts produce substantially lower agreement with the ground truth than counts chosen by competing automatic methods.

Figures

Figures reproduced from arXiv: 2605.27287 by Eslam Hegazy, Mohamed Gabr.

Figure 1
Figure 1. Figure 1: Framework for common thresholding methods. Inputs are a grayscale image (or the histogram [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Optimal values of the Otsu, Kapur and Kittler fitness function across threshold numbers from 1 to [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration showing effects of modifying MET criterion used by the proposed dynamic program [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plot of the histogram used for illus￾trating the improvement caused by Algorithm 3. Histogram numerical data is shown in [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustration showing effects of modifying [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Snippet of the histogram of image 135069 in the region of grayscale intensities [150,255], show￾ing the thresholds outputted by MET-DP method inside this region. This can be considered as overthreshold￾ing since in the plotted histogram we can￾not see what the additional thresholds sepa￾rate [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The histogram of image 006-Flair-60, the full height of the black peak (at intensity=0) is truncated from the figure so as to clarify other parts of the histogram. thresholding the image Tile-8-Part-008. In image ISIC-0009880, the histogram in [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: The histogram of image 009-Flair-60, the full height of the black peak (at intensity=0) is truncated from the figure so as to clarify other parts of the histogram [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The histogram of image 015-t1ce-60, the full height of the black peak (at intensity=0) is truncated from the figure so as to clarify other parts of the histogram. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of methods. The full height of the black peak (at intensity=0) is truncated from [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison between the CPU time taken by MET-DP algorithm and conventional dynamic [PITH_FULL_IMAGE:figures/full_fig_p029_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of DP_N_Otsu, DP_N_Kapur, DP_N_Kittler and MET-DP methods. Each row [PITH_FULL_IMAGE:figures/full_fig_p030_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of DP_N_Otsu, DP_N_Kapur, DP_N_Kittler and MET-DP methods. Each [PITH_FULL_IMAGE:figures/full_fig_p031_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of DP_N_Otsu, DP_N_Kapur, DP_N_Kittler and MET-DP methods. Each [PITH_FULL_IMAGE:figures/full_fig_p032_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Thresholded images obtained by DP_N_Otsu, DP_N_Kapur, DP_N_Kittler and MET-DP [PITH_FULL_IMAGE:figures/full_fig_p033_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Thresholded images obtained by DP_N_Otsu, DP_N_Kapur, DP_N_Kittler and MET-DP [PITH_FULL_IMAGE:figures/full_fig_p034_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Thresholded images obtained by DP_N_Otsu, DP_N_Kapur, DP_N_Kittler and MET-DP [PITH_FULL_IMAGE:figures/full_fig_p035_18.png] view at source ↗
read the original abstract

Multilevel Image thresholding is an important preprocessing algorithm in computer vision applications nowadays. Since most common thresholding methods take the desired count of thresholds as input by the user, thresholding methods that automatically determines a suitable count of thresholds from the input image itself are advantageous. In this article, a novel thresholding method based on a dynamic programming algorithm and a modification of Minimum Error Thresholding (MET) criterion is thoroughly presented. An empirical statistical study is performed to pinpoint why this proposed method is superior. Moreover, an extended comparison between this proposed method and other state-of-the-art methods is performed on a comprehensive set of natural, satellite and medical test images. The numerical results show that the proposed MET-DP method takes much less time than traditional dynamic programming thresholding methods when the number of thresholds is high. The proposed method can detect a suitable count of thresholds for most of tested images of different types. However, traditional methods that take the count of thresholds as input produce thresholded images of higher structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) values than MET-DP. Source code can be found on https://w3id.org/met-dp/article1-code

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

0 major / 3 minor

Summary. The manuscript introduces MET-DP, a dynamic programming framework that employs a modification of the Minimum Error Thresholding (MET) criterion to automatically determine both the number and the values of thresholds for multilevel image thresholding without requiring the count as user input. It presents an empirical statistical study to explain the method's advantages, followed by comparisons against state-of-the-art methods on natural, satellite, and medical images. Key claims include substantially lower runtime than traditional DP thresholding approaches when the number of thresholds is high, successful detection of suitable threshold counts for most tested images, and reproducible results via provided source code, while acknowledging that fixed-count methods achieve higher SSIM and PSNR.

Significance. If the modified MET objective remains valid under DP minimization and the empirical advantages generalize, the work provides a practical contribution to automating threshold selection in image preprocessing pipelines. The reported speed gains for large threshold counts, the automatic count detection capability, and the explicit release of source code are concrete strengths that could facilitate adoption and further testing in computer vision applications.

minor comments (3)
  1. The abstract states that an empirical statistical study is performed to 'pinpoint why this proposed method is superior,' but the manuscript should include a dedicated subsection (e.g., §4.2) that explicitly lists the statistical tests, sample sizes, and definitions of 'suitable count' used in that study.
  2. Notation for the modified MET criterion and the DP recurrence should be introduced with a clear table or pseudocode block early in the method section to improve readability for readers unfamiliar with the baseline MET formulation.
  3. Figure captions for the thresholded image examples would benefit from explicit mention of the automatically detected threshold count alongside the SSIM/PSNR values for direct visual comparison.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the thorough summary and positive evaluation of our work on MET-DP. We appreciate the recognition of the runtime advantages for high threshold counts, the automatic count detection, and the release of source code. The recommendation for minor revision is noted, and we address the overall assessment below. No major comments requiring point-by-point rebuttal were specified in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents MET-DP as an algorithmic construction: dynamic programming minimization of a modified Minimum Error Thresholding criterion to jointly determine threshold count and values. No equations, recurrences, or fitting procedures are exhibited that reduce any claimed prediction or result to a parameter fitted from the target outputs themselves. The central claims rest on empirical comparisons across image sets rather than a self-referential derivation chain, and the abstract explicitly notes trade-offs in SSIM/PSNR versus fixed-k methods. This is the most common honest finding for an applied algorithmic paper whose validity is externally falsifiable via code and benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the modification to the MET criterion is mentioned but not formalized, so the ledger cannot be populated beyond noting the absence of visible details.

pith-pipeline@v0.9.1-grok · 5738 in / 1143 out tokens · 26945 ms · 2026-06-29T18:24:02.543176+00:00 · methodology

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Reference graph

Works this paper leans on

4 extracted references

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in ":" * " " * FUNCTION f...

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