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REVIEW 4 major objections 4 minor 34 references

A Bioplausible Model for the Expanding Hole Illusion: Insights into Retinal Processing and Illusory Motion

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The Expanding Hole Illusion arises from contrast-dependent lateral inhibition in the retina, modeled by a Difference of Gaussians filter, with contrast reversal flipping expansion into contraction.

desk verdict Standard DoG filtering qualitatively reproduces the polarity of the Expanding Hole Illusion, but the paper's motion and pupil claims are unsupported and need quantitative backing. read the letter →

arxiv 2501.08625 v1 pith:QCGJ2FY5 submitted 2025-01-15 q-bio.NC cs.NEeess.IV

Nasim Nematzadeh , David M. W. Powers This is my paper · ORCID
classification q-bio.NCcs.NEeess.IV
keywords ExpandingHoleIllusionDifferenceofGaussiansretinalganglioncellslateralinhibitioncenter-surroundreceptivefieldmotionclassicalpupildilation
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 the Expanding Hole Illusion arises in the retina, not in higher-level interpretation. The proposed mechanism is contrast-dependent lateral inhibition: the center-surround receptive fields of retinal ganglion cells, simulated by a Difference of Gaussians (DoG) filter, amplify the radial luminance gradients of the static pattern in a way that reads as forward motion. Applying the filter at progressively larger spatial scales makes the dark center grow outward in the edge maps, while reversing contrast polarity makes the same sweep show contraction, matching human reports and pupil responses. If this is right, a simple, well-understood neural filter explains a compelling static-motion illusion and connects it to the pupil dilation reported in psychophysical experiments [1].

What carries the argument

The central object is the Difference of Gaussians (DoG) filter, which subtracts a wide, low-amplitude surround Gaussian from a narrow center Gaussian to mimic the antagonistic center-surround receptive field of retinal ganglion cells. The paper fixes the surround ratio at $s=1.6$, sets the window ratio $h=8$, and sweeps the center scale $\sigma_c$ from 4 to 20 in steps of 4, with Laplacian-of-Gaussian pairs from $\sigma_c=4,8$ up to $7,11$, to produce the sequence of edge maps that stands in for perceived motion.

What would settle it

Present observers with a DoG edge map generated at one fixed center scale (say $\sigma_c=12$) rather than the full 4-to-20 sweep; if they still report expansion, then the multi-scale sequence is not the source of the illusion. In parallel, record retinal ganglion cell activity while the static pattern is shown: if the neural response is stationary rather than spreading over time, the retinal lateral-inhibition account is falsified.

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Extended reading notes

Core claim

The paper's central claim is that the static Expanding Hole pattern is misread by the retina's own center-surround circuitry as a moving edge. A DoG filter with surround ratio $s=1.6$ and window ratio $h=8$ is applied to synthetic versions of the illusion; sweeping the center scale $\sigma_c$ from 4 to 20 in steps of 4 produces edge maps in which the central dark region expands, and the same sweep on the polarity-reversed white-hole pattern produces contraction. The contrast-dependent lateral inhibition built into the DoG filter is therefore proposed as the neural source of the illusory motion, and the qualitative match with pupil-dilation findings is taken as evidence that early retinal processing, rather than cognitive inference, generates the effect.

Load-bearing premise

The model assumes that increasing the spatial scale of the DoG filter from 4 to 20 in fixed increments is a valid stand-in for the temporal growth of the illusory hole; no psychophysical measurement ties that particular scale schedule to the perceived speed of expansion, so the simulation's output and the human percept could diverge.

Editorial extensions

If this is right

  • If the illusion is retinal in origin, reversing contrast polarity should always flip perceived motion from expansion to contraction, as the DoG edge maps show for the white-hole version.
  • The strength of the illusion should track the steepness of the luminance gradient: steeper gradients produce stronger lateral inhibition and thus stronger perceived expansion.
  • The model predicts that the illusion survives under conditions that minimize cognitive interpretation, such as brief or peripheral presentation, because the mechanism is in early vision.
  • Any static pattern whose radial luminance profile matches an expanding dark gradient should elicit a similar illusory motion, making the effect a general property of center-surround processing rather than a special pattern.
  • The DoG account ties the pupil-dilation result to a concrete neural response: the same contrast edges that the model amplifies are the ones that trigger the physiological 'dark tunnel' response.

Reading between the lines

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

  • Editorial inference: because the model treats the scale sweep as time, it predicts that the perceived expansion should have a measurable speed; tracking where observers judge the hole boundary over time could yield a quantitative trajectory that the edge-map centroids should match.
  • Editorial inference: the same DoG mechanism should generalize to other radial gradient patterns, including the related tunnel-motion effect, so a ring-free radial gradient alone would be predicted to produce weaker but measurable expansion.
  • Editorial inference: if the retina is the site of the mechanism, then adapting the eye to a static high-contrast radial pattern should transiently reduce the illusion, because lateral inhibition would be fatigued; this psychophysical adaptation prediction is not tested in the paper.
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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

4 major / 4 minor

Summary. The paper proposes a computational model based on Difference of Gaussians (DoG) filtering, interpreted as a classical receptive field (CRF) implementation of retinal ganglion cells, to explain the Expanding Hole Illusion. The authors apply DoG filters at increasing center scales (sigma_c from 4 to 20) and LoG filters at two scale pairs to synthetic versions of the illusion and its contrast-reversed "White Hole" variant, then present the resulting edge maps as evidence of expansion and contraction. They claim that contrast gradients and multi-layered spatial processing account for the perceived motion, that the model output closely mirrors Laeng et al.'s pupil-dilation data, and that the illusion arises from contrast-dependent lateral inhibition in early retinal processing rather than from higher-level interpretation.

Significance. If the central claim were adequately supported, the paper would offer a simple, biologically grounded explanation for a striking illusion and connect low-level retinal processing to a physiological response (pupil dilation). The DoG implementation is standard and the qualitative contrast-polarity asymmetry is visible in the edge maps, which is a useful first observation. However, the paper currently lacks a quantitative link between model outputs and either psychophysical judgments or Laeng et al.'s pupil data, and it does not specify a mechanism that converts a family of static filter responses into a temporal motion signal. The significance is therefore conditional: the idea is plausible and worth pursuing, but the evidence presented does not yet establish the proposed retinal explanation.

major comments (4)
  1. [Section 3.2 / Figure 3] The central inference equates increasing DoG scale sigma_c with perceived temporal expansion, but Equation (1) defines a static spatial filter. Displaying edge maps for sigma_c = 4, 8, 12, 16, 20 is a scale-space decomposition; no readout (e.g., zero-crossing drift, motion-energy stage, or temporal integration rule) converts these maps into a motion signal. As written, the impression of expansion is imposed by the order in which the scales are displayed rather than predicted by the model. Because the edge locations of any high-contrast radial pattern will move outward as sigma_c grows, this step does not establish selectivity for the Expanding Hole illusion over control stimuli.
  2. [Section 4.2] The claim that the model outputs "closely mirrored" Laeng et al.'s pupil data is not supported by any quantitative comparison. No correlation, error metric, statistical test, or explicit mapping from model responses to the measured pupil time course is reported. I recommend defining a quantitative prediction (e.g., integrated edge energy per eccentricity annulus, or a contrast-normalized response measure) and reporting its agreement with the published data, alongside at least one control stimulus matched for spatial frequency but not for the illusion, and a contrast-reversed condition.
  3. [Sections 3.1 and 5] The statement that contrast gradients and multiscale filtering produce the edge maps, and that this explains the illusion through lateral inhibition, comes close to restating the definition of a bandpass contrast filter. To make the explanation noncircular, the paper needs a selective test in which model predictions are compared against human judgments across multiple stimuli that vary in contrast polarity, spatial-frequency content, and illusory strength, with filter parameters not selected post hoc to reproduce the desired polarity.
  4. [Sections 5.3, Abstract, and Conclusion] The Limitations subsection acknowledges that neuroimaging studies and more extensive psychophysical experiments are needed to verify the findings, yet the Abstract and Conclusion state that the results "demonstrate" the mechanism and align "closely" with psychophysical findings. This internal tension should be resolved by either tempering the claims to match the evidence presented or by adding the missing validation so that the stronger claims become justified.
minor comments (4)
  1. [Equation (1)] The symbol "×" in Equation (1) should be explicitly defined as convolution (e.g., using an asterisk), since the surrounding text describes a convolution but the notation is ambiguous.
  2. [Section 3.2] The phrase "series of concentric DoG filters" is misleading: the filters are not concentric in the image; they are multiscale filters with different center-surround sizes. Please rephrase to describe a bank of DoG filters at different scales.
  3. [Figure 5 caption] The caption says the LoG scale increases "from the difference between sigma_c = 4 and sigma_c = 8 to sigma_c = 7 and sigma_c = 11," which is ambiguous. It should state explicitly how many scale pairs were used and what the two intervals were, since the text mentions only two scale intervals.
  4. [Section 5] The Discussion refers to "contrast-based lateral inhibition within the visual cortex," while the model and earlier sections attribute lateral inhibition to retinal ganglion cells. This inconsistency should be corrected to avoid confusion about the claimed locus of the effect.

Circularity Check

2 steps flagged · score 7.0 of 10

The paper's central 'prediction' of expansion is built into its scale schedule: increasing DoG sigma from 4 to 20 already forces any central dark region to grow, and no motion readout or quantitative comparison is provided.

  1. fitted input called prediction [Section 3.2, caption of Fig. 3 (pages 6-7)]
    "The scale of the centre Gaussian (σc) increases from 4 to 20 in increments of 4, intensifying the DoG filter’s sensitivity to contrasts in the central area and simulating the dynamic effect of forward motion."

    The 'expansion' is not a predicted output of a motion model; it is the direct geometric consequence of feeding the same static image through filters of increasing σc. Any high-contrast radial pattern with a dark center would show a growing central filtered region under this schedule, because the filter's centre Gaussian is spatially broader at larger σ. The paper supplies no motion readout (e.g., zero-crossing drift, motion-energy stage, temporal integration rule) that converts these static scale levels into a perceptual expansion signal, and no validation of the scale-to-time mapping is offered. The perceptual claim is therefore built into the chosen input schedule and is not an independent result.

  2. self definitional [Abstract (page 1)]
    "Our results demonstrate that contrast gradients and multi-layered spatial processing contribute to the perception of expansion, aligning closely with psychophysical findings and supporting the role of retinal ganglion cells in generating this illusory motion signal."

    The DoG filter is, by definition, a bandpass/contrast-gradient filter whose output is a map of contrast edges at multiple scales. Saying that the produced Edge-Maps depend on contrast gradients and multiscale filtering restates the mathematical definition of the DoG operator (Eq. 1), not a discovery about the illusion. The only illusion-specific content comes from the hand-selected σ schedule, which already determines the outward drift; the filter itself would respond similarly to any concentric high-contrast pattern, so the conclusion that retinal lateral inhibition specifically generates the Expanding Hole is not tested against a control or alternative explanation.

full rationale

The derivation chain is: static input -> DoG filter bank at increasing σc -> Edge-Maps -> 'simulated motion'. The load-bearing step is the identification of larger σc with later time/forward motion. This identification is an assumption, not a result: the DoG is a linear, static filter, and a family of filters at increasing scale is a scale-space representation, not a motion sequence. For any dark-centered high-contrast image, the central filtered response will coarsen and appear to expand, so the 'Expanding Hole' output is fixed by the chosen schedule before any retinal mechanism is invoked. The claimed agreement with Laeng et al. is asserted qualitatively (Section 4.2: 'The model outputs closely mirrored the regions of the pattern that triggered significant pupil dilation') with no quantitative metric, control stimuli, or model comparison, so it does not independently validate the retinal-lateral-inhibition explanation. The conclusion that contrast gradients and multiscale processing produce the edge maps is also a restatement of what a DoG filter is defined to do. There is legitimate external grounding in the physiology of center-surround receptive fields (Rodieck, Enroth-Cugell), so the paper is not wholly circular; but the central explanatory claim reduces to tuning the scale schedule to the desired polarity. The self-citations to the authors' earlier DoG illusion models (refs 5, 6, 17, 18) support the technique but are not the main circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The observed effect is largely a consequence of the chosen filter and its hand-set parameters, so the model's independent explanatory content is modest. The only assumptions are standard DoG modeling plus the specific scale-to-time mapping, and no new entities are introduced.

free parameters (3)
  • Multiscale scale schedule sigma_c (DoG) and scale pairs (LoG) = sigma_c = 4, 8, 12, 16, 20; LoG pairs (4,8) to (7,11)
    Hand-selected in Section 3.2 to produce the desired expansion and contraction edge maps; no optimization against human data or independent criterion.
  • Surround ratio s = 1.6
    Chosen from the Marr-Hildreth approximation of LoG; it sets the center-surround balance and therefore shapes every edge map.
  • Window ratio h = 8
    Sets the filter window size (windowSize = h * sigma_c + 1); a computational truncation choice that affects effective surround strength.
assumptions (4)
  • domain assumption DoG filtering with a center-surround kernel approximates retinal ganglion cell receptive fields and lateral inhibition.
    The entire model rests on this equivalence, cited from refs 16 and 29-31; it is standard in vision science but is still an assumption applied to this specific illusion.
  • ad hoc to paper Increasing the spatial scale sigma_c of the filter corresponds to the perceived temporal expansion of a static pattern.
    Section 3.2 states that increasing sigma_c simulates the dynamic effect of forward motion; no independent perceptual or neural evidence supports this scale-to-time mapping.
  • domain assumption The synthetic versions of the illusion used in the simulations match the stimuli and perceptual reports of Laeng et al. (2022).
    The qualitative comparison in Section 4.2 assumes stimulus equivalence, but the exact synthetic images and their parameters are not fully specified.
  • domain assumption Contrast-dependent lateral inhibition in early retinal processing is sufficient to produce the illusory motion, without invoking cortical motion areas.
    The paper's conclusion favors early retina, while Section 5.3 lists V1 and MT as future work, indicating that cortical involvement is not ruled out.

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Cite this review

Pith. "Pith review of A Bioplausible Model for the Expanding Hole Illusion: Insights into Retinal Processing and Illusory Motion." pith.science (2026). https://pith.science/paper/QCGJ2FY5

@misc{pith2026250108625,
  author       = {Pith},
  title        = {Pith review of: A Bioplausible Model for the Expanding Hole Illusion: Insights into Retinal Processing and Illusory Motion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QCGJ2FY5}},
  note         = {Machine review of arXiv:2501.08625}
}
read the original abstract

The Expanding Hole Illusion is a compelling visual phenomenon in which a static, concentric pattern evokes a strong perception of continuous forward motion. Despite its simplicity, this illusion challenges our understanding of how the brain processes visual information, particularly motion derived from static cues. While the neural basis of this illusion has remained elusive, recent psychophysical studies [1] reveal that this illusion induces not only a perceptual effect but also physiological responses, such as pupil dilation. This paper presents a computational model based on Difference of Gaussians (DoG) filtering and a classical receptive field (CRF) implementation to simulate early retinal processing and to explain the underlying mechanisms of this illusion. Based on our results we hypothesize that the illusion arises from contrast-dependent lateral inhibition in early visual processing. Our results demonstrate that contrast gradients and multi-layered spatial processing contribute to the perception of expansion, aligning closely with psychophysical findings and supporting the role of retinal ganglion cells in generating this illusory motion signal. Our findings provide insights into the perceptual biases driving dynamic illusions and offer a new framework for studying complex visual phenomena.

Discussion (0). Continue with ORCID to comment.

Reference graph

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