{"id":"40c4ffae-7d7a-42e3-870e-7eca931fd68c","arxiv_id":"2508.17530","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The Maximum Void method detects statistically significant high-dimensional holes in image stacks and tracks lower-dimensional holes across time with zigzag persistence.","lead":"A new statistical pipeline, the Maximum Void method, stacks a time series of grayscale images into a 3D array, finds a statistically significant 2D hole spanning time, and uses zigzag persistence to track how lower-dimensional holes appear, merge, and vanish. The method is demonstrated on simulated wound-like patterns and on time-lapse images of single cells repairing wounds.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The method's Step-2/Step-3 thresholding relies on a unique, persistence-dominant H_{M-1} feature; the C3 application itself shows several persistent H2 features, so the max-persistence birth time in Eq. 19 may select the wrong cavity and the zigzag summary would track the wrong loops.","rationale":"The reader's weakest-assumption diagnosis is correct and identifies the same load-bearing issue I see: the MV method's central thresholding step depends on a unique, persistence-dominant H_{M-1} feature. The manuscript contains direct evidence that this condition is not satisfied in the C3 application, where multiple persistent H2 features appear. That makes the concern internal to the paper's own application rather than a disagreement with an external consensus. The method is otherwise a coherent assembly of existing TDA tools, and the authors do acknowledge a related limitation in Section 6, but acknowledgement does not resolve the fact that the C3 zigzag diagram in Figure 9a is only interpretable if the selected H2 cavity is the wound. The simulation comparison is also weak because it is a single-run, four-example study with no error bars, and no code or data are provided, but those issues would weaken the 'outperforms' claim rather than the core statistical-significance claim. The unproven null model in Eq. (12) is a secondary concern, partly mitigated by the permutation implementation. Since the primary concern is substantial but addressable by restricting the method's scope or by testing for multiple significant H2 features, the reader's CONDITIONAL verdict should stand unchanged.","tokens_in":19713,"tokens_out":5451,"duration_ms":68030,"concrete_test":"Compute the H2 persistence diagram for the C3 image stack used in Section 5 and compare every H2 bar against the permutation null distribution, not just the maximum-persistence bar. If two or more H2 features have permutation p-values below 0.05, rerun Steps 3 and 4 with the birth time of each significant H2 feature and compare the resulting zigzag feature labels against a manually segmented wound at each time point. The method is defensible on the C3 data only if exactly one H2 feature is significant and its birth-time threshold recovers the labeled wound across the full time series.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is not the permutation test itself but the identification step after the null is rejected: the method takes the single most persistent H_{M-1} feature and uses its birth time as the global threshold in Eq. (19). This is justified only under Assumptions 2 and 3, which require the target cavity to dominate all background features in persistence at every time and to have time-slice values closer to each other than to any other partition. The paper's own Section 5 evidence undermines this uniqueness premise: Figure 7c and the accompanying text state that the C3 cell has 'several persistent H2 features' on the persistence diagram, while the Control cell has only one prominent H2. The Maximum Persistence Test considers only the maximum-persistence feature, so it cannot determine which H2 feature is the wound cavity when several are significant. If the chosen maximum is not the true 𝛾1, then the threshold in Eq. (19) includes or excludes the wrong voxels, the lower-dimensional H0/H1 features in Step 3 are not the wound, and the zigzag connections in Section 3.4 summarize the evolution of the wrong loops. The simulation study cannot resolve this because every example was constructed so that a single cylindrical H2 feature exists, as stated in Section 4; that is precisely the regime where Assumption 2 holds by construction, not a test of the C3 regime where the assumption is most doubtful.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes the Maximum Void (MV) method for detecting and tracking topological features (mainly loops, H1) in a time series of grayscale images. The method stacks the image sequence into a spatiotemporal array, computes persistent homology of the upper-level set filtration of that array, and applies a permutation-based Maximum Persistence Test to identify the most persistent higher-dimensional feature (H2 for 2D images). The birth time of this feature is then used as a global threshold to binarize each time slice, and zigzag persistence is computed on the resulting simplicial complexes to connect H0 and H1 features across time. The method is evaluated on simulated image sequences designed to mimic wound healing and applied to two wounded-cell datasets (C3 and Control). The paper claims the MV method outperforms a point-cloud Vietoris-Rips approach in the simulations and provides a useful representation of the temporal evolution of wound loops.","tokens_in":20021,"tokens_out":7675,"duration_ms":85435,"significance":"If the identification step were fully valid, the paper would address a real gap: it offers a data-driven, statistically motivated threshold for TDA on image time series and uses space-time cavities to label feature trajectories across time, overcoming the feature-correspondence problem in persistence summaries. The algorithm is clearly described, the simulation setup is relevant to the application, and the wounded-cell example is a persuasive motivation. The paper also gives a concrete algorithmic pipeline (Algorithm 1) that could be built upon. However, the central claims rest on statistical and identification assumptions that are not adequately supported: the null distribution for birth/death times is stated without justification, the C3 application appears to violate the single-dominant-feature assumption, and the simulation comparison is not replicated. These issues affect the manuscript's main claims rather than its presentation.","major_comments":[{"comment":"The C3 application is presented as a demonstration of the method, but the manuscript itself states in Section 5 that the C3 array has 'several persistent H2 features' on its persistence diagram, while the Control has only one prominent H2. The MV method's Step 3 uses the birth time of the single most persistent H2 feature as the global threshold (Eq. 19), which is justified only under Assumption 2 that the target gamma_1 dominates all background features in persistence at every time. The Maximum Persistence Test considers only the maximum-persistence feature and therefore cannot determine which of several significant H2 features corresponds to the wound. If the selected maximum is a background cavity, the threshold in Eq. (19) binarizes the wrong voxels and the zigzag diagram in Figure 9 tracks loops that are not the wound. Moreover, the simulation study in Section 4 constructs every scenario with exactly one cylindrical H2 feature, so it does not exercise the regime in which the C3 data fall. The authors should either restrict the method's scope to the single-dominant-feature setting or develop and validate a selection procedure that identifies gamma_1 when multiple persistent H2 features are present, including simulations with competing H2 features.","section":"Section 5, Figure 7c; Assumptions 2-3, Eq. (19)"},{"comment":"Equation (12) asserts that under the null hypothesis the birth and death times of all homology features are i.i.d. draws from the pixel intensity distribution F(mu_0, sigma_0^2). This is not established and is generally false for upper-level set filtrations: birth and death values of persistent homology features are functionals of the order relations among pixel values and are not independent draws from the pixel distribution. The permutation test in Algorithm 1 is a reasonable test of spatial exchangeability conditional on the observed pixel values, but the null distribution it generates is not the distribution stated in Eq. (12). Because the abstract and Section 3 describe the threshold as statistically grounded, the authors should either replace Eq. (12) with a correct statement based on exchangeability and the permutation distribution, or prove the distributional claim under explicit assumptions on the noise and filtration.","section":"Section 3.2.1, Eq. (12)"},{"comment":"The paper's claim that the MV method 'outperforms' the PCVR method, detecting true loops 95% of the time versus 50%, appears to rest on a single simulated realization for each of the four scenarios in Figure 6. No number of independent noise replicates is reported, no matching criterion between detected loops and true loops is defined, and the PCVR threshold used to binarize the images is not specified. A single realization cannot support a general claim of superiority. The authors should add replicated simulations, define the detection and tracking criteria precisely, and report standard errors or confidence intervals for the detection rates. They should also report the PCVR threshold value or state how it was chosen, so the comparison is not sensitive to an unfavorable default.","section":"Section 4, Figure 6c"},{"comment":"Step 3 applies the single threshold theta_1^* = min f over G_1(t*) to every time slice. Assumption 3 only says that values of the target partition are closer to each other than to other partitions; it does not ensure that the same level set isolates G_1(t_o) at each time when the feature intensity varies systematically over time. The manuscript should state explicit conditions under which the birth time of the space-time H_{M-1} feature yields the correct partition at every time slice, or it should examine the sensitivity of the zigzag summary to the threshold choice. Without this, the binarized slices in Figure 8 may include different amounts of background at different times, and the resulting zigzag connections could reflect threshold artifacts rather than biological dynamics.","section":"Section 3.3, Eq. (19) and Eq. (20)"}],"minor_comments":[{"comment":"The final sentence contains a grammatical error: 'Since, the wounded cell images exhibit nonlinear, dynamic, spatial, and temporal structures...' should read 'Since the wounded cell images exhibit...' without the comma after 'Since'.","section":"Abstract"},{"comment":"The text near Figure 4 describes the smoothed images as t7 and t12, while the caption refers to t1 and t12; these should be reconciled.","section":"Figure 4 and Section 3.2"},{"comment":"The text uses A_sigma_1, ..., A_sigma_4 for the simulated arrays, while Figure 6b labels them A0_2, A0_3, A0_4; the notation should be unified.","section":"Section 4, notation"},{"comment":"The p-value is reported as 0, but the number of permutations B is not stated anywhere; report the p-value as < 1/B and give B for both the simulation and the application.","section":"Table 1"},{"comment":"The axes of the persistence diagrams are inconsistent: Figure 2d has birth on the y-axis and death on the x-axis, while the caption of Figure 9 states that birth is on the x-axis and death on the y-axis; make the conventions uniform and clearly labeled.","section":"Figures 2 and 9"},{"comment":"Reference [4] and reference [9] are the same Benink and Bement (2005) paper, and references [5] and [6] are the same Abreu-Blanco et al. (2014) paper; these duplicates should be consolidated.","section":"References"},{"comment":"Equation (19) writes the partition as f^{-1}(theta), but f is not an invertible map; express the upper-level set directly in terms of pixel coordinates and intensity values.","section":"Equation (19)"},{"comment":"The PCVR comparison does not state the predetermined threshold used to binarize images; without this detail, readers cannot assess whether the comparison is fair.","section":"Section 4, PCVR comparison"}],"recommendation":"major_revision","confidential_remarks":"This is a borderline case. The core pipeline is coherent and worth publishing if the statistical claims are corrected, but the identification step is not validated in the regime where the paper's own C3 application lives. I would ask for a substantial revision rather than a rejection: the authors need to justify or replace Eq. (12), add replicated simulations with multiple H2 features, and report the details of the PCVR comparison. The paper also relies on the first author's thesis [43] for the Maximum Persistence Test; the manuscript should be more self-contained regarding the validity of that test."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The real contribution here is the full pipeline: stack grayscale images into a 3D array, test the maximum-persistence H2 feature with a permutation null, threshold at that feature's birth time, then connect time-slice H0/H1 features with zigzag persistence. That combination is new as far as the cited literature goes, and the cell-wound application is a sensible use case. The zigzag diagrams in Figure 9 give a genuinely different view of the data than the persistence-only analysis in [12], and the paper is honest about its main limitation: it needs a single persistence-dominant higher-dimensional feature. The discussion section says exactly that.\n\nNow the soft spots, in increasing order of seriousness.\n\nMinor: no code or data. For a method paper in statistical TDA, that makes reproduction harder than it should be.\n\nModerate: the simulation study is a single run of four constructed examples, no error bars, and the comparator variant is described as the 'best performing' one. The 95% vs 50% claim is plausible but not statistically established. Repeated simulations with variance across seeds would fix this.\n\nLoad-bearing: the statistical justification for the threshold is shaky. Equation (12) treats the birth and death times of features under the null as i.i.d. draws from the pixel intensity distribution. That is not derived, and it is not obviously true; persistence pairs are functionals of the whole array, not independent pixel values. The permutation test is a reasonable empirical alternative, but the paper frames it as a model that Equation (12) supports. That support is missing.\n\nThe stress-test note about the C3 cell is correct. Figure 7c shows several persistent H2 features, and the Maximum Persistence Test looks only at the maximum. Step 3 then uses that single birth time as the global threshold. If the max-persistence cavity is not the wound, the zigzag summary tracks the wrong loops. The paper acknowledges this in Assumptions 2 and 3 and in the limitations, but the simulation study is designed so a single cylinder exists, which is exactly the regime where the assumption holds by construction. So the method's key step is untested in the regime where it is most doubtful.\n\nNet: this is a serious paper with a plausible new pipeline and a real application, but it is not ready as is. The statistical foundation for the threshold needs work, and the simulation needs to be repeated and to include multi-cavity scenarios. A serious editor should send it to peer review, because the core idea is worth engaging and the problems look fixable. I would not cite the results as they stand, but I would read the revision carefully.","headline":"A plausible new TDA pipeline for tracking image features over time, but the statistical threshold is built on an unproven null model and the simulations dodge the multi-cavity case that matters most.","tokens_in":20542,"tokens_out":2105,"would_cite":false,"duration_ms":22183,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62R40","62M10","62M40"],"pacs":[],"model":"deepseek-v4-flash","headline":"The Maximum Void method treats time as a spatial dimension in an image stack, uses a permutation test to find one statistically significant cavity, and tracks the evolution of the corresponding loops on a zigzag persistence diagram…","keywords":["Image Processing","Time Series","Topological Data Analysis","Zigzag Persistence","Persistent Homology","Hypothesis Testing","Maximum Persistence Test"],"falsifier":"Run the Maximum Void method on a simulated image sequence containing two separate loops of equal intensity that both persist across the whole time series; if the method's threshold is the birth time of only one of the two cavities, the zigzag diagram should either drop the second loop or jump between loops. If the method still tracks both loops correctly, the single-dominant-cavity assumption is not necessary.","tokens_in":19516,"feed_emoji":"🕳️","tokens_out":6826,"duration_ms":59994,"temperature":0.7,"pith_summary":"The paper proposes a method, the Maximum Void (MV) method, for detecting and tracking holes (loops or connected components) in a time series of grayscale images. The central idea is to stack the images so that time becomes an extra spatial dimension; a loop that persists and evolves over time then appears as a two-dimensional cavity (an H2 feature) in the stack. A permutation-based hypothesis test finds the most persistent such cavity, and its birth time supplies a data-driven threshold that isolates the relevant loops at each time point. These loops are then connected across time with zigzag persistence, producing a summary of how features appear, split, merge, and disappear. In simulations mimicking cell wound healing, the method detects the true loops 95% of the time, compared with 50% for the point-cloud Vietoris-Rips comparison method.","feed_headline":"New test finds true loops in image stacks 95% of the time","feed_subtitle":"Adding time as a dimension turns a loop's evolution into a cavity that can be tracked without preset thresholds.","key_machinery":"The load-bearing mechanism is the Maximum Persistence Test run on the time-stacked array: each pixel intensity is permuted across the whole stack, the maximum persistence of the H_{M-1} features is recomputed, and the observed maximum is compared to this null distribution. The birth time of the single significant H2 cavity is used as the global threshold (Equation 19), and zigzag persistence over unions of consecutive upper-level-set simplicial complexes (Equation 21) links the H1 and H0 features into a time-evolving summary. The method is called the Maximum Void method because it uses this statistically significant higher-dimensional void, or cavity, to define which lower-dimensional loops belong to the feature of interest at every time point.","core_discovery":"The paper claims that topological features in a time series of grayscale images can be identified and tracked statistically without a user-chosen threshold, by treating time as an intrinsic dimension. Under the assumption that one cavity in the image stack is the most persistent and is well separated from background features, the birth time of that cavity is a valid threshold for the whole sequence. Applying the threshold at each time point yields simplicial complexes whose lower-dimensional homology (loops and connected components) is then linked across consecutive times via zigzag persistence; the resulting zigzag persistence diagram records the temporal evolution of each feature. The paper argues that this approach outperforms existing point-cloud-based tracking, and demonstrates it on simulated data and on two wounded-cell image sequences.","pith_inferences":["The method's reliance on one dominant H2 cavity suggests a testable diagnostic: if a time series yields two H2 features of comparable persistence, the zigzag summary will likely flip between them, and an automatic check could flag such ambiguity.","The permutation null assumes exchangeability of pixel intensities, which ignores spatial correlation; smoothing the images likely changes the test's operating characteristics in ways the paper does not quantify.","Because the threshold is the birth time of a single cavity, a natural extension would be a time-varying threshold derived from the same idea, which could handle features whose contrast changes over time."],"forward_implications":["Tracking loops without predefined thresholds becomes possible for any image sequence that has a dominant cavity in the space-time stack.","The zigzag persistence diagram provides a summary that distinguishes splitting, merging, appearance, and disappearance of loops, which persistence-only summaries cannot show.","The method can be used to quantify wound healing dynamics, comparing cells with different treatments by the number and persistence of loops making up the wound over time.","Extending the same stacking logic to higher-dimensional image sequences, such as three-dimensional volumes over time, would track H2 voids through H3 features.","The comparison with the point-cloud Vietoris-Rips method shows that intensity-based upper-level set filtrations are better suited than distance-based Vietoris-Rips filtrations for detecting small-area loops in images."],"supporting_citations":[{"why":"Supplies the smoothing step and single-time persistence estimation for the cell wound images, on which the stacked analysis builds.","marker":"[12]"},{"why":"Defines the Point Cloud Vietoris-Rips (PCVR) method, the comparison baseline in the simulation study.","marker":"[13]"},{"why":"Applies zigzag persistence to dynamical systems, a prior temporal-tracking approach the method extends to grayscale image stacks.","marker":"[19]"},{"why":"Introduces zigzag persistence modules, the mathematical machinery used to connect homology across consecutive time points.","marker":"[25]"},{"why":"Provides zigzag persistence software for image processing, supporting the choice of simplicial complexes rather than cubical complexes.","marker":"[30]"},{"why":"Develops the Maximum Persistence Test, the permutation procedure used to identify the statistically significant cavity.","marker":"[43]"}],"fun_headline_variants":["Time-as-dimension tracks image loops without thresholds","Zigzag persistence follows topological holes over time","Statistical test finds evolving loops in image stacks","No thresholds needed: tracking holes through time in images","Temporal topology: tracking image holes without thresholds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that in the stack of images there is one cavity that stands out from background noise more than any other, and that its pixel values at one time are closer to its own values at other times than to any other structure.","fun_headline_variants_meta":{"raw":{"variants":["Time-as-dimension tracks image loops without thresholds","Zigzag persistence follows topological holes over time","Statistical test finds evolving loops in image stacks","No thresholds needed: tracking holes through time in images","Temporal topology: tracking image holes without thresholds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000478,"raw_usage":{"total_tokens":2340,"prompt_tokens":886,"completion_tokens":1454,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":502,"completion_tokens_details":{"reasoning_tokens":1383}},"tokens_in":502,"tokens_out":1454,"duration_ms":10742,"temperature":1.0,"reasoning_tokens":1383,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:04:34.709251+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the Maximum Void method on a simulated image sequence containing two separate loops of equal intensity that both persist across the whole time series; if the method's threshold is the birth time of only one of the two cavities, the zigzag diagram should either drop the second loop or jump between loops. If the method still tracks both loops correctly, the single-dominant-cavity assumption is not necessary.","supporting_citations":[{"cited_title":"Confidence regions for a persistence diagram of a single image with one or more loops","cited_arxiv_id":"2405.01651","evidence_quote":"Supplies the smoothing step and single-time persistence estimation for the cell wound images, on which the stacked analysis builds."},{"cited_title":"R., and CIOCANEL , M","cited_arxiv_id":null,"evidence_quote":"Defines the Point Cloud Vietoris-Rips (PCVR) method, the comparison baseline in the simulation study."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Applies zigzag persistence to dynamical systems, a prior temporal-tracking approach the method extends to grayscale image stacks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces zigzag persistence modules, the mathematical machinery used to connect homology across consecutive time points."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides zigzag persistence software for image processing, supporting the choice of simplicial complexes rather than cubical complexes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Develops the Maximum Persistence Test, the permutation procedure used to identify the statistically significant cavity."}],"review_version":2}