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REVIEW 5 major objections 3 minor 50 references

Complexity in Complexity: Understanding Visual Complexity Through Structure, Color, and Surprise

T0 review · 5 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper argues that visual complexity predictions improve when structural regularity, color diversity, and semantic surprise are added to segmentation and class counts, and that the combined interpretable model stays competitive with a…

desk verdict A useful, well-documented empirical challenge to the simple two-feature account of visual complexity, but the headline gains are selected maxima rather than unbiased estimates because the evaluation uses the same labels for feature and hyperparameter choices. read the letter →

arxiv 2501.15890 v3 pith:YGJI5E7G submitted 2025-01-27 cs.CV cs.AI

Karahan Sar{i}taş , Peter Dayan , Tingke Shen , Surabhi S Nath This is my paper · ORCID
classification cs.CVcs.AI
keywords visualcomplexityMulti-ScaleSobelGradientUniqueColorcolorfulnesssurpriselargelanguagemodelsimagesegmentationSVGdataset
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a recent interpretable baseline—predicting perceived complexity from the square roots of segment and semantic-class counts—under-explains human judgments on several image domains. To fill the gap, it introduces two pixel-level features and one semantic feature: Multi-Scale Sobel Gradient (MSG), Multi-Scale Unique Color (MUC), and LLM-generated surprise scores, plus a new dataset of surprising images with human complexity ratings. The paper reports that each feature adds variance on datasets where the baseline fails, and that the combined model remains competitive with a supervised deep network while preserving interpretability. A sympathetic reader should care because this challenges the idea that visual complexity is simply object and segment numerosity, and it offers transparent features usable wherever complexity estimates must be explainable.

What carries the argument

The argument is carried by three features stacked onto the two-feature segment-and-class baseline. MSG (Multi-Scale Sobel Gradient) applies the Sobel operator at four scales over RGB channels and averages the gradient magnitudes; symmetric patches cancel, so MSG acts as a local symmetry detector and quantifies structural regularity. MUC (Multi-Scale Unique Color) quantizes each RGB channel to a lower bit precision, counts unique color triples after flattening, and repeats this at four spatial scales with fixed weights; it measures color diversity at multiple resolutions. Surprise is a 0–100 rating elicited from an LLM with zero-shot chain-of-thought prompting, yielding both a number and a natural-language explanation. A linear model with the square-root segment and class counts augmented by these features is evaluated by cross-validated Spearman correlation, with permutation tests used to decide which feature wins on which dataset.

What would settle it

Run the same regressions on the Savoias Art and Suprematism subsets with MUC computed at a fixed bit precision chosen before seeing the complexity labels (for example, 7 bits for every dataset) and check whether the reported +0.08 and +0.05 correlation gains over the segment-and-class baseline survive; if they vanish, the part of the central claim that MUC adds genuine predictive value would fail.

Watch

Extended reading notes

Core claim

The central claim is that a two-feature account of visual complexity—regressing perceived complexity on the square roots of the number of image segments and semantic classes—fails precisely where segment and class counts are uninformative, and that three additional explainable features repair the account. Multi-Scale Sobel Gradient (MSG), a multi-resolution gradient statistic over RGB channels, captures local asymmetry and texture regularity; Multi-Scale Unique Color (MUC), a per-channel bit-quantized count of unique colors at four spatial scales, captures color diversity; and an LLM-generated surprise score captures whole-image semantic novelty. On the datasets where the baseline struggles, these features add variance: MSG raises the reported Spearman correlation on VISC from 0.56 to 0.68 and on the architecture subset of IC9600 from 0.66 to 0.76; MUC raises the Savoias Art subset from 0.73 to 0.81 and the Suprematism subset from 0.89 to 0.94; MSG plus MUC lifts the Interior Design subset from 0.61 to 0.87 and the Abstract subset from 0.66 to 0.83; and surprise raises the new SVG dataset from 0.78 to 0.83. The paper concludes that the combined interpretable model is competitive with a supervised deep network while requiring no training, and that visual complexity perception is genuinely multi-factorial.

Load-bearing premise

The load-bearing premise is that selecting the MUC bit precision per dataset after looking at the human complexity ratings does not inflate the reported correlations; if that in-sample tuning is effectively overfitting, the gains attributed to MUC would be smaller than claimed.

Editorial extensions

If this is right

  • If the central claim holds, the two-feature segmentation model is not a complete account; models of perceived complexity should include structural regularity and color diversity as separate explanatory variables.
  • The gains concentrate where segment and class counts fail, so complexity models may need to be dataset- or domain-aware rather than universal across image categories.
  • LLM-generated surprise is a viable interpretable semantic feature: it adds unique variance on the SVG dataset and matches a supervised model's correlation, and the accompanying natural-language explanations make the prediction auditable.
  • An interpretable combination of these features can approach supervised accuracy without being trained on a complexity dataset, which would help applications requiring transparent complexity estimates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the LLM-generated explanations could be parsed into object-level surprise (unusual subject, unusual activity, unusual object-context pairing), turning the holistic score into a decomposition testable against the scene-graph annotations inherited from Visual Genome.
  • Beyond the paper: coupling the paper's reported weak surprise–memorability correlations with a paired memory experiment—surprising vs. ordinary images matched on segment and class counts—would test whether surprise is a common cause of both complexity and memorability.
  • Beyond the paper: because MSG and MUC each help most where images are regular or color-dominant, applying the same two features to GUI or information-visualization complexity could reveal domain-specific weights, a practical extension of the paper's dataset-aware finding.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 3 minor

Summary. The paper extends the interpretable two-feature complexity model of Shen et al. (2024) with three additional features: Multi-Scale Sobel Gradient (MSG), Multi-Scale Unique Color (MUC), and LLM-generated surprise scores. It evaluates these features on existing complexity benchmarks and introduces a new dataset, Surprising Visual Genome (SVG), with 200 images, human pairwise complexity ratings, and human surprise ratings. The authors report that adding their features improves mean Spearman correlations over the segmentation/class-count baseline on selected datasets, and that the final combined model is competitive with a supervised CNN while remaining interpretable.

Significance. If the quantitative claims survive a label-independent evaluation protocol, the paper makes a useful contribution: it identifies concrete structural, chromatic, and semantic dimensions beyond segment/class counts; introduces the SVG dataset with human ratings; validates LLM surprise scores against human surprise judgments (ρ = 0.73); and provides code, data, and detailed permutation-based ablations. The interpretability goal is well served by the algorithmic definitions and qualitative examples. The main weakness is that several feature-selection decisions use the evaluation labels, so the reported effect sizes are optimistic and need re-estimation under a fixed protocol.

major comments (5)
  1. [Datasets; Table 1] The headline results are based on post-hoc dataset selection. The Datasets section states: 'We select image subsets to demonstrate the effectiveness of our new features to explain complexity - VISC and IC9600 architecture subset for MSG, Savoias Art and Suprematism subsets for MUC, and Savoias Interior Design and IC9600 Abstract for the combination of MSG and MUC.' Because these subsets were chosen after observing which datasets benefit, the increments in Table 1 (e.g., +0.13 on VISC, +0.10 on IC9 Architecture, +0.26 on Sav. Interior Design) are selected maxima, not expected gains for a randomly chosen dataset. The central claim that the two-feature model is insufficient should be supported by per-feature results on the complete set of datasets (Appendix Table 2 reports only the final model), or by a fixed, pre-specified dataset selection rule with multiple-comparison correction.
  2. [Multi-Scale Unique Color; Multi-Scale Sobel Gradient; Appendix] Several hyperparameters are tuned against the same ground-truth labels used for evaluation. The MUC section reports 'we report results using the best bit precision for each dataset in terms of correlation to complexity,' so the MUC gains (e.g., +0.08 on Sav. Art, +0.05 on Sav. Suprematism) are maxima over b in {3,...,8}. In addition, the color-versus-grayscale choice for MSG is based on permutation tests against complexity on the same datasets, the MSG/MUC scale weights are selected from the ablations in Appendix Table 4, and the square-root transform was retained because it 'achieved slightly better results' than log. None of these choices is nested inside the 3-fold cross-validation, so the reported Spearman correlations are optimistically biased. A fixed-protocol rerun (e.g., fixed b, or selection inside training folds only) is needed before the magnitudes of the improvements can be interpreted.
  3. [Appendix: Ablations on LLMs for Surprise Scores] The choice of Gemini-1.5-Flash as the surprise scorer is also made on the basis of the evaluation labels: Appendix Table 3 compares three LLMs by the Spearman correlation of the resulting surprise features with SVG ground-truth complexity, and Gemini is selected because it performs best. The reported +0.05 surprise improvement on SVG is therefore not an unbiased estimate for a fixed, pre-specified LLM. Please report the SVG result for a pre-specified LLM or select the LLM on a held-out portion of the data, and provide a confidence interval or permutation test for the +0.05 increment.
  4. [Results; Table 1] No uncertainty quantification is provided for the headline correlation coefficients or increments. With dataset sizes as small as 200 (SVG) and 49 (RSIVL), differences of 0.03-0.05 in Spearman correlation may be within sampling noise. Please report bootstrap or permutation-based confidence intervals for the Table 1 increments, or at least significance tests for each increment.
  5. [Appendix Figure 7] The instruction text in Figure 7, which is supposed to describe the visual complexity experiment, says 'simply click on the image you judge to be more surprising.' If participants actually saw these instructions, the SVG complexity ratings are contaminated by surprise, which would make the surprise-feature result partly circular. Please clarify whether this is a typographical error in the figure and confirm the exact wording shown to participants.
minor comments (3)
  1. [SVG: A Dataset of Surprising Images] The text says 'A histogram of these scores shows clear separation' but no histogram appears in the main text; please add the figure or move it to the appendix with a reference.
  2. [Table 1 caption] The table caption does not define the '↑' notation used in the rows for 'Baseline + visual features'; please define it and state what test, if any, supports the arrowed increments.
  3. [Figure 4] The figure caption does not mention the red highlighting used for surprise-related words; please add a note explaining the highlighting.

Circularity Check

4 steps flagged · score 6.0 of 10

Per-dataset tuning of MUC bit precision and MSG/MUC scales, plus LLM selection, uses the target complexity labels; the printed SVG instructions ask for 'more surprising' images, making part of the surprise claim self-referential.

  1. self definitional [Appendix, Figure 7: Initial instructions provided to participants at the beginning of the visual complexity experiment]
    "you will be shown pairs of images and asked to judge which one appears more visually complex to you. ... For each pair, simply click on the image you judge to be more surprising. There are no right or wrong answers - we are interested in your perception of surprise."

    The appendix presents these as the instructions for the visual complexity experiment. Taken literally, participants were told to click the more surprising image and that the study concerns 'perception of surprise.' The paper then reports that LLM surprise scores explain residual variance in those ratings (Figure 3, rho = 0.48) and improve SVG prediction from 0.78 to 0.83. If those instructions were used, the 'complexity' target is itself a surprisal judgment, so the surprise feature and target are the same construct by construction. The Methods text says 'more visually complex,' creating an inconsistency; if the figure is a typo, this becomes an evaluation error, but as printed the SVG surprise claim is self-definitional.

  2. fitted input called prediction [Multi-Scale Unique Color section, discussion of Algorithm 3]
    "In the rest of this paper we report results using the best bit precision for each dataset in terms of correlation to complexity (this was typically 7–8 bits)."

    The MUC bit precision b controls color quantization before counting unique colors. Selecting b per dataset by maximizing its Spearman correlation with the complexity labels on that same dataset means the reported correlations, such as Sav. Art 0.73 to 0.81 and Sav. Suprematism 0.89 to 0.94 in Table 1, are selected maxima over b in {3,...,8}, not unbiased estimates of MUC's contribution. The cross-validated regression only fixes the regression weights; the feature definition itself is chosen using the full labeled dataset, leaking target information into the feature values. The claim that MUC adds variance beyond segment and class counts is therefore partly forced by the label-based selection.

2 more flagged steps
  1. fitted input called prediction [Appendix, Further Details on MSG and MUC, Table 4 and surrounding text]
    "Our baseline used scales [1,2,4,8] with weights [0.4,0.3,0.2,0.1] (baseline). We compared this against three alternatives... Based on our ablation study, we selected the baseline weight and scale configuration for MSG and MUC algorithms to conduct subsequent experiments."

    The scale and weight definitions of MSG and MUC are selected by comparing their correlations with visual complexity across the same 16 datasets later used for the reported evaluations. Since these feature definitions were chosen using the target labels, the performance numbers in Table 1, such as MSG+MUC gains of +0.26 on Sav. Int. and +0.17 on IC9 Abstract, reflect an in-sample choice of feature representation rather than a fixed, label-independent protocol. This inflates the apparent advantage of MSG/MUC over the two-feature baseline and makes the reported effect sizes optimistic.

  2. fitted input called prediction [Appendix, Ablations on LLMs for Surprise Scores, Table 3 discussion]
    "Based on these findings, we ultimately selected GEMINI-1.5-FLASH-produced surprise scores for our final model—a choice that offered the additional practical advantage of free access within certain usage limits."

    GEMINI-1.5-FLASH was chosen after comparing LLM surprise scores against ground-truth perceived complexity on the SVG dataset (Table 3: ChatGPT-4O 0.81, GEMINI-1.5-FLASH 0.83). The final model then reports the GEMINI-based 0.83 on the same SVG labels, so the +0.05 over the baseline is partly a selected maximum over LLM choices. The independent human-surprise validation (rho = 0.73) gives the feature genuine content, but the specific complexity gain reported for SVG remains optimistically selected.

full rationale

This is an empirical feature-evaluation paper rather than a mathematical derivation, so most of it is not circular: MSG and MUC are deterministic image statistics, the surprise scores are partially validated against independent human surprise ratings (rho = 0.73), and the Shen et al. (2024) baseline is an external prior model rather than an input to the new features. However, several feature choices are selected using the same complexity labels that are later used as the evaluation target. The MUC bit precision is explicitly chosen per dataset 'in terms of correlation to complexity'; the MSG/MUC scale-weight configuration is chosen after ablations comparing correlations with complexity on the same 16 datasets; and GEMINI-1.5-FLASH was selected as the surprise scorer after comparing its complexity correlation on SVG. Each of these choices makes the reported Spearman gains partly selected maxima, so the headline increments, such as +0.08 on Sav. Art, +0.05 on Sav. Suprematism, and +0.05 on SVG, are optimistic. In addition, the appendix Figure 7, if taken literally, tells participants to click the 'more surprising' image and says the study is about 'perception of surprise,' conflicting with the Methods text; under that literal reading, the SVG surprise-complexity correlation is self-definitional. The dataset subsets shown in Table 1 (VISC, IC9600 Architecture, Sav. Art, Sav. Suprematism, Sav. Int., IC9 Abstract) are also selected after the fact to demonstrate the new features. The underlying features still have independent content, and the broad conclusion that complexity is multifaceted may survive, but the quantitative support for the central claim is inflated by label-dependent feature and dataset selection.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on human-rated complexity labels, a specific LLM as a surrogate for human surprise, and hand-chosen aggregation parameters for MSG and MUC. The most consequential free parameter is the per-dataset MUC bit precision, which is selected using the target labels and can inflate the reported gains. No new physical or theoretical entities are introduced.

free parameters (4)
  • MUC bit precision (b) = 7-8 bits, chosen per dataset
    The bits preserved per channel are selected per dataset to maximize Spearman correlation with human complexity ratings, making reported MUC gains partly in-sample fitted. See 'Multi-Scale Unique Color' section.
  • MSG/MUC scale set S = [1, 2, 4, 8]
    Chosen based on ablation studies across 16 datasets; fixed globally but selected after looking at performance on the same data. See Appendix 'Further Details on MSG and MUC'.
  • MSG/MUC scale weights W = [0.4, 0.3, 0.2, 0.1]
    Same ablation-based selection; the paper chose the 'baseline' configuration after comparing with alternatives in Table 4.
  • Square-root transform of numseg/numclass = sqrt (preferred over log)
    The paper reports testing log and choosing sqrt because it gave slightly better regression results, an in-sample model choice inherited from the baseline.
assumptions (4)
  • domain assumption Human complexity ratings on RSIVL, VISC, Savoias, IC9600, and SVG are reliable ground truth and comparable across datasets.
    The regressions and correlations assume these ratings are trustworthy labels; no inter-rater reliability or meta-analysis is reported.
  • domain assumption Gemini-1.5-Flash zero-shot Chain-of-Thought surprise scores are a valid proxy for human surprisal beyond the SVG validation set.
    The paper validates with a single correlation of 0.73 on SVG and then uses LLM scores as a feature; it assumes this generalizes to the final model and to other images.
  • ad hoc to paper Multi-scale averaging of Sobel gradient magnitudes and unique-color counts with fixed weights captures the perceptual dimensions of structure and color relevant to complexity.
    The aggregation scheme (scales [1,2,4,8], weights [0.4,0.3,0.2,0.1]) is a paper-specific modeling choice rather than a consequence of perceptual theory.
  • domain assumption The Bradley-Terry rescaling of the probability matrix to [0.33, 0.66] yields interpretable complexity ratings without distorting the ordinal information.
    The paper applies this rescaling to avoid clustering near zero, but its effect on the final Spearman correlations is not analyzed.

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Cite this review

Pith. "Pith review of Complexity in Complexity: Understanding Visual Complexity Through Structure, Color, and Surprise." pith.science (2026). https://pith.science/paper/YGJI5E7G

@misc{pith2026250115890,
  author       = {Pith},
  title        = {Pith review of: Complexity in Complexity: Understanding Visual Complexity Through Structure, Color, and Surprise},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YGJI5E7G}},
  note         = {Machine review of arXiv:2501.15890}
}
read the original abstract

Understanding how humans perceive visual complexity is a key area of study in visual cognition. Previous approaches to modeling visual complexity assessments have often resulted in intricate, difficult-to-interpret algorithms that employ numerous features or sophisticated deep learning architectures. While these complex models achieve high performance on specific datasets, they often sacrifice interpretability, making it challenging to understand the factors driving human perception of complexity. Recently (Shen, et al. 2024) proposed an interpretable segmentation-based model that accurately predicted complexity across various datasets, supporting the idea that complexity can be explained simply. In this work, we investigate the failure of their model to capture structural, color and surprisal contributions to complexity. To this end, we propose Multi-Scale Sobel Gradient (MSG) which measures spatial intensity variations, Multi-Scale Unique Color (MUC) which quantifies colorfulness across multiple scales, and surprise scores generated using a Large Language Model. We test our features on existing benchmarks and a novel dataset (Surprising Visual Genome) containing surprising images from Visual Genome. Our experiments demonstrate that modeling complexity accurately is not as simple as previously thought, requiring additional perceptual and semantic factors to address dataset biases. Our model improves predictive performance while maintaining interpretability, offering deeper insights into how visual complexity is perceived and assessed. Our code, analysis and data are available at https://github.com/Complexity-Project/Complexity-in-Complexity.

Figures

Figures reproduced from arXiv: 2501.15890 by the authors.

Figure 3
Figure 3. Correlation between residuals (actual complexity - [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Racing sheep with toy riders or a flying skater from [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. A selection of responses from participants describing the strategies they employed to assess visual complexity. Their [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: Comparison of two images having similar values of visual features but with differing [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Representative samples from previous datasets show initial complexity predictions ( [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Initial instructions provided to participants at the beginning of the visual complexity experiment [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Interface of the pairwise comparison experiment for visual complexity assessment. Participants were instructed [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Representative samples from the SVG dataset. G indicates the [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: Examples where MSG and MUC features help improve complexity predictions: (top) an image from VISC dataset [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.