Image thresholding

Overview

Thresholding turns a pixel value into a class by comparing it with one or more cut points. The two sources on this page use it for different tasks, and the variants differ in what the cut points are chosen to optimise.

• Multilevel thresholding picks k grey-level cut points t1 < ... < t_k on the range 0 to L-1. The cut points divide the image into k+1 classes 2609.12756 §1 2609.12756 eq. 22. They are chosen by maximising a criterion over the grey-level histogram, here Otsu or Kapur entropy 2609.12756 eq. 22. No labels are needed. Adding thresholds makes exhaustive search grow exponentially, so the paper uses meta-heuristics to search for the cut points 2609.12756 §1.
• Single-threshold classification of a colour index computes one value per pixel from its RGB channels, then labels the pixel by comparing that value with one cut 2609.40212 §2.2.1. The cut is chosen to maximise the Matthews correlation coefficient (MCC) against hand-labelled pixels 2609.40212 §2.2.1 2609.40212 eq. 7. This variant is supervised.

Two source cards list this concept. Each variant rests on one of them, and the two papers do not share a dataset or task, so their numbers are not compared.

Variants

Metaheuristic search over cut points (MAAPO)

The search is an artificial protozoa optimizer (APO) extended with two parts: a membrane-style split and merge of the population, and a roulette-wheel fitness-distance rule that picks the guiding solution 2609.12756 §3. The membrane part is controlled by a volume diversity metric, mVOL 2609.12756 §3.1 2609.12756 eq. 15. The paper applies this search to segmentation with the Otsu and Kapur objectives and reports results against APO and other optimizers 2609.12756 §5.3. Card: MAAPO: an innovative membrane algorithm based on artificial protozoa optimizer for multilevel threshold image segmentation.

The base APO is not a thresholding method. It is a general search, and it is the baseline the paper compares against 2609.12756 §2.1 tab. 11 tab. 12.

Single threshold on a vegetation index (Excess Blue)

The paper classifies each pixel of UAV orthomosaics as urbanized or non-urbanized using one index and one threshold 2609.40212 §2.2.1. The steps are:

1. Standardise the RGB channels to the range 0 to 1, and compute the chromatic coordinates r, g and b 2609.40212 tab. 1 note.
2. Compute the index for each pixel. Excess Blue is 1.4b − g 2609.40212 tab. 1.
3. Label pixels by one cut. For Excess Blue, a value above the threshold means urbanized 2609.40212 §3.1 fig. 6.

The paper tests 16 indices and clusters them by the absolute Pearson correlation between their values. It keeps one index per cluster, the one with the best MCC, and six remain 2609.40212 §3.1 eq. 8 fig. 5. For each kept index the threshold maximising MCC on the training site is taken tab. 2. On the second site, Excess Blue reaches MCC 0.61 and accuracy 0.87, the best index there by MCC 2609.40212 tab. 2. Its optimised threshold is 0.108. Thresholds per acquisition series move between 0.100 and 0.131, and the single value 0.108 lowers MCC by at most 0.04 2609.40212 §3.1 fig. 7. Card: Recognition of Urbanized Areas in UAV-Derived Very-High-Resolution Visible-Light Imagery.

The same paper compares this variant with pixel classifiers on RGB patches (a linear network, an MLP and a CNN). Those networks are not thresholds, so they are covered only in "When to use which".

When to use which

The table covers constraints that the two sources address. It does not cover other methods.

Implementation sketch

The common core of the multilevel variant is a search over candidate cut points, scored by the histogram criterion. The paper's search loop itself is in 2609.12756 alg. 1. The rounding rule from a continuous candidate to grey levels is not stated in the paper, so the sketch leaves it open.

# Histogram of the grey channel, L bins  [arxiv:2609.12756 §5.3]
hist = grey_histogram(image, L)
# Candidate: k real values; to be mapped to grey levels  [arxiv:2609.12756 eq. 22]
t = to_grey_levels(candidate)  # rounding and de-duplication: not stated
# Objective to maximise: Otsu or Kapur entropy  [arxiv:2609.12756 eq. 22]
fitness = objective(hist, t)
# Search loop: any metaheuristic; MAAPO's is in [arxiv:2609.12756 alg. 1]
best = search(fitness, k, lower=0, upper=L - 1)

For colour images, the paper segments each RGB band separately and then combines the three results. The combining rule is not defined 2609.12756 §5.3.

The single-threshold variant has a different core: one index per pixel, then a search over one cut value scored by MCC on labelled pixels.

# Excess Blue per pixel from 0-1 RGB  [arxiv:2609.40212 tab. 1]
def excess_blue(rgb):
    total = rgb[..., 0] + rgb[..., 1] + rgb[..., 2]
    b = rgb[..., 2] / total   # chromatic coordinates r, g, b
    g = rgb[..., 1] / total
    return 1.4 * b - g
# Choose the cut that maximises MCC on labelled training pixels  [§2.2.1]
# Candidate grid and step are not stated in the paper
best_t = argmax_t mcc(excess_blue(train_rgb) > t, train_labels)
# Label a pixel urbanized when its index is above the cut  [§3.1]
urbanized = excess_blue(image_rgb) > best_t

Contradictions

None known. The two sources cover different tasks and datasets, so their numbers do not bear on each other. Both name Otsu, but for different uses: the MAAPO paper uses it as a multilevel objective, and the UAV paper reports single-threshold Otsu on indices as a baseline that performs much worse than the MCC-optimised cut 2609.40212 tab. 4. This is a difference of setting, not a disagreement.

Pitfalls

• Best of 20 runs. The segmentation numbers are the best of 20 runs, not means 2609.12756 §5.3. CEC2017 results are means over 51 runs 2609.12756 tab. 6.
• Margins are small. On CEC2017, MAAPO's Friedman rank (3.35) is within 0.02 of MAQUATRE's (3.37) 2609.12756 §4.5. These results are author-reported.
• SSIM constant. C2 is printed as 8.5225 2609.12756 §5.2. The paper does not explain it; check it before reuse.
• Metric scope. The paper does not say whether PSNR, SSIM and FSIM are computed per band or on the whole image 2609.12756 §5.3.
• Selection rules. The paper does not state which best solution the distance term uses, or whether the roulette rule uses fixed or time-varying weights 2609.12756 §3.2.
• Dimensions. Only 4 to 7 thresholds per band were tested. Other counts are not shown 2609.12756 §5.3.
• Code. No official code was located and checked. See the card for the search.
• Threshold search not described. For the Excess Blue variant, the grid, step size, search range and strict or non-strict comparison are not stated 2609.40212 §2.2.1.
• Labels and sampling. Labels were made by hand on 54 sample squares per dataset. The paper calls the sampling both a uniform grid and a random sample, and gives no estimate of label error 2609.40212 §2.1.1 2609.40212 §2.1.2.
• Accuracy is misleading here. About 87% of JERZ pixels are non-urbanized, so accuracy alone rewards labelling everything non-urbanized. For AB, accuracy 0.86 comes with MCC 0.23 on JERZ 2609.40212 §2.3 2609.40212 tab. 2.
• Two sites only. Results come from one site each, with one UAV per site. The paper says generalisation needs larger datasets 2609.40212 §4.
• Shadows. Excess Blue and the networks both misclassify shadows, and bare soil and dead matter in shadow are read as vegetation 2609.40212 §4 fig. 9. Excess Blue calls dark pixels urbanized, while the networks call them non-urbanized 2609.40212 §4. The brightness rule the paper proposes was not tested 2609.40212 §4.

Papers

• MAAPO: an innovative membrane algorithm based on artificial protozoa optimizer for multilevel threshold image segmentation: adds membrane-style splitting and merging and a roulette fitness-distance selection rule to APO, and reports results on multilevel thresholding with Otsu and Kapur objectives (author-reported).
• Recognition of Urbanized Areas in UAV-Derived Very-High-Resolution Visible-Light Imagery: compares 16 colour indices with one threshold each, and linear, MLP and CNN pixel classifiers, for urbanized areas in UAV RGB imagery; Excess Blue is the best index, and the networks reach higher accuracy (author-reported).