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Dense line plots hide whether trajectories agree; a path-integrated fidelity score and Structural Inconsistency Field expose where clutter is coherent and where it breaks.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-31 00:40 UTC pith:LV74AWPE

load-bearing objection Solid, usable viz method: density’s missing “agreement” channel via tensor path integrals and SIF, with real limits on ℓ and majority orientation that the paper mostly owns. the 2 major comments →

arxiv 2607.25121 v1 pith:LV74AWPE submitted 2026-07-27 cs.GR

Structuring Line Ensembles with Path-Integrated Fidelity and Structural Inconsistency Fields

Yumeng Xue , Patrick Paetzold , Bin Chen , Yunhai Wang , Christophe Hurter , Oliver Deussen This is my paper
classification cs.GR
keywords line ensemblesdensity plotstructure tensorStructural Inconsistency Fieldpath-integrated fidelityleave-one-outtrajectory visualizationvisual analytics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Large line ensembles force a trade-off: drawing every path preserves identity but collapses into hairballs, while density maps stay readable but only count how many lines pass a place, not whether those lines agree. This paper claims you can keep density as the occupancy overview and add a second field that answers a different question—how consistently each trajectory aligns with the local orientation statistics of the surrounding ensemble. Each trajectory is scored by integrating its tangent agreement against a structure-tensor field, with leave-one-out removal so a line is not scored against a field it partly built. Those passage-centered scores are projected back into image space as a Structural Inconsistency Field that lights up coherent corridors versus crossings, outliers, and connectivity ambiguity. With fixed-grid updates and prefix sums, the same scores support interactive peeling of high- or low-support subsets. Synthetic tests and cases in weather series, aviation tracks, and projected brain fibers argue that density-plus-inconsistency reveals structure density alone conceals.

Core claim

When paired with ordinary density views, path-integrated trajectory fidelity against an ensemble structure-tensor field—corrected by dynamic leave-one-out and reprojected as a passage-centered Structural Inconsistency Field—disambiguates dense line patterns by localizing sustained structural support versus disagreement, outliers, and connectivity-induced ambiguity that scalar accumulation cannot separate.

What carries the argument

Structural Inconsistency Field (SIF): one minus the mean leave-one-out, path-extent-averaged orientation support of every trajectory passage through a pixel, so low values mark coherent support and high values mark conflict or weak evidence.

Load-bearing premise

The method treats agreement with the majority’s undirected local orientation, after removing the line itself and integrating over a chosen path length, as enough to call a dense pattern structurally supported—even in flat crossings and in 2D views of 3D fibers.

What would settle it

On controlled ensembles like the paper’s D1–D3 (hidden cuts, lane changes, connected vs disconnected bridges), check whether SIF-based line scores still separate ground-truth outliers or connectivity better than density (AUROC/AUPRC) when path extent is wrong, leave-one-out is off, or the majority orientation is adversarial or antiparallel counterflow that must be distinguished.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Density maps can be read jointly with SIF so analysts query coherent corridors instead of hotspots that mix incompatible paths.
  • Trajectory-fidelity ranking enables iterative peeling: remove high- or low-support subsets and recompute to expose secondary structure under dominant clutter.
  • Fixed-grid tensor construction plus prefix-sum path extents keep the pipeline interactive for tens of thousands of lines in browser-side settings.
  • Screen-space scoring can recover readable projected scaffolds from fiber or traffic data without deforming geometry the way bundling does.
  • Sparse one- or two-line neighborhoods after leave-one-out should be read with density or passage count as low-confidence evidence, not automatic conflict.

Where Pith is reading between the lines

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

  • Any domain that already ships density or occupancy heatmaps of paths (mobility, climate series, tractography) could add SIF as a second channel without replacing existing overview tools.
  • Direction-aware tensors (not only undirected outer products) would be a direct next test wherever opposing flows must not reinforce each other.
  • Coupling SIF confidence with passage count could turn “high inconsistency” versus “insufficient evidence” into an explicit visual layer the current mask does not separate.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The paper proposes a tensor-guided, path-integrated fidelity measure for large line ensembles: each grid cell accumulates a structure tensor from rasterized trajectory tangents, each trajectory is scored against this field via a trace-normalized quadratic form with dynamic leave-one-out correction, and passage-centered averages of this score are projected back into image space as a Structural Inconsistency Field (SIF, Eq. 6). The SIF is meant to complement scalar density by distinguishing coherent bundles from conflict, outliers, and connectivity ambiguity. The paper evaluates on three synthetic benchmarks (D1–D3) with line-level AUROC/AUPRC against a density baseline (Table 1), a scalability study against a Hausdorff reference (Fig. 10), a controlled LOO ablation on nested spindle ensembles (Table 2, App. E), and several real-world case studies (ACIS temperatures, France aviation, DTI fibers, plus four more in App. F). The central claim is that, paired with density views, the SIF exposes spatially localized coherence and structural breakdown that density-only representations conceal.

Significance. If the results hold, this is a useful, practical addition to the line-ensemble visualization toolbox. Strengths worth naming: (1) the construction is fully explicit and parameter-light at its core — the structure tensor is a strict extension of density (tr(J)=D), the LOO score has a clean counterfactual interpretation, and the SIF is bounded in [0,1]; (2) the LOO ablation (Table 2) is a genuinely controlled experiment with bootstrap confidence intervals showing that without LOO the ranking inverts (AUROC 0.009 vs 0.831), which substantiates the self-bias argument rather than merely asserting it; (3) quantitative line-level separation on D1/D2 is reported with appropriate imbalanced-class metrics (AUPRC alongside AUROC); (4) the method scales to browser-side interactive use via fixed-grid accumulation and prefix sums, avoiding the O(N²) wall of pairwise-distance methods; (5) an interactive online system is referenced, supporting reproducibility. The limitations (majority-rules logic, undirected orientation, isotropic ambiguity, view-dependence) are acknowledged honestly. The significance is narrowed mainly by the fact that 'structural support' is majority-orientation support over a

major comments (2)
  1. [§5.1, Table 1; App. D, Fig. 24] The headline quantitative result reports AUROC/AUPRC for D1 at path extent ℓ=1 and D2 at ℓ=150, i.e., the path-extent parameter appears to be tuned per dataset. Appendix D demonstrates qualitatively (Fig. 24) that D3-C/D3-D separate only at maximal extent, so the metric's discriminative power is demonstrably ℓ-dependent, yet no sensitivity sweep (AUROC/AUPRC vs. ℓ), no selection rule, and no resolution-invariant normalization of ℓ is provided for the quantitative benchmarks. Appendix D also states that the discrete ℓ values 'depend on the discretization resolution' and must be re-chosen when resolution changes. Since Table 1 is the only quantitative evidence that the SIF separates outliers from inliers, the authors should (i) report the AUROC/AUPRC curves over a range of ℓ for D1 and D2, and (ii) give practical guidance on ℓ selection (e.g., relative to bundle length or grid resolution).
  2. [§4.2–4.4; §6 (Limitations); Abstract] The definitions of support (Eqs. 4, 5, 6, 14) score agreement with the majority-orientation structure tensor. The paper is commendably explicit about the consequences (majority-rules logic, undirected vvᵀ accumulation so antiparallel counterflow reinforces rather than conflicts, E≈0.5 ambiguity in isotropic regions, view-dependence of 2D projections of 3D fibers; §6 and App. F.3.1). However, the Abstract and Conclusion phrase the outcome as exposing 'spatially localized coherence and structural breakdown' without the qualifier that this is majority-orientation support under a user-chosen extent. Since App. F.3.1 itself shows a valid minority structure (the 370-line late-starting stock subset) being marked highly inconsistent by the field, the framing in the Abstract/Conclusion should be tightened to match what the metric actually measures, so that readers do not over-read the real-data c
minor comments (6)
  1. [§5.1, Table 1] Table 1, D1 row: the SIF AUPRC of 0.3679 is much better than density (0.0089) but modest in absolute terms given ~1% prevalence. A sentence contextualizing this value (e.g., precision at a fixed recall) would help readers calibrate the claim.
  2. [§4.4, App. B] The symbol ℓ is used both as a continuous arc length (Eq. 13–14) and as a count of rasterized samples in the discrete implementation ('we keep the same symbol ℓ'). Since the two scale differently with grid resolution, consider distinct notation or an explicit conversion; this is also the root of the resolution-dependence noted in App. D.
  3. [§4.2] The matched-filter analogy is evocative but imprecise: a matched filter maximizes SNR against a known template, whereas here the 'template' (tensor field) is itself estimated from the ensemble and modified per query by LOO. A brief qualifier would avoid over-reading.
  4. [§5.2, Fig. 10] Timings are single runs on one browser/machine with acknowledged JIT/GC variability. Even a small number of repetitions with min/median reporting would strengthen the scalability claim, particularly the '~2.4 s at N=10,000' headline.
  5. [§4.2, Eq. (4)] It would help to state the value of ε (and its effect) used in the main-text experiments, as it is only specified in the App. E ablation (ε=0 with the zero-support convention). Similarly, kernel bandwidth σ and grid resolution per experiment should be collected in one place for reproducibility.
  6. [Fig. 1] Fig. 1 axis label shows '120 °F' without units context in the caption; caption should state that values are weekly maxima in °F over the year axis. Minor figure-clarity issue.

Circularity Check

0 steps flagged

No significant circularity: SIF/fidelity are constructive functionals validated against external labels, not self-fulfilling predictions.

full rationale

The paper defines a structure tensor from the ensemble, a leave-one-out path-integrated fidelity Φ(L), and a passage-centered Structural Inconsistency Field M(x;ℓ)=1−mean φ, then evaluates these scores on synthetic tasks with independent ground-truth classes (D1/D2 AUROC/AUPRC vs density) and qualitative real-world cases. That pipeline is definitional engineering of a metric, not a claim that a fitted free parameter predicts a quantity forced by the fit. Self-citations to Xue et al. on density illumination and image-space colorization are used as perceptual/baseline comparisons, not as uniqueness theorems or load-bearing premises that force the present result. LOO is a counterfactual correction against self-support, not circular reuse of the target. Boundary conditions (majority-rules, undirected vvT, ℓ sensitivity) are limitations of the operational definition, not circular reductions of claim to input. No fitted-input-called-prediction or self-definitional X⇔Y step appears in the derivation chain.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 3 invented entities

The method rests on standard multilinear algebra and raster KDE/CDE practice, plus domain choices that orientation consensus after LOO defines structural support and that fixed-grid 2D analysis (including projections) is the operating regime. Free parameters are analysis knobs (grid, kernel, ℓ, ε, peel percentiles), not physical constants fitted to prove a law. Invented entities are named derived fields/scores, not new physical mediators.

free parameters (5)
  • path extent ℓ = task-dependent (examples: 1; 150; 0/400/1000 on D3)
    Controls how much trajectory context enters φ and M; set differently per experiment (e.g., ℓ=1 on D1, ℓ=150 on D2; short/mid/max on D3) and changes qualitative SIF structure.
  • spatial kernel bandwidth h / Gaussian σ and kernel support = implementation/grid dependent
    Sets tensor neighborhood scale and anisotropy; appendix LOO ablation uses σ=1 pixel; main text contrasts 1×1 vs 3×3 aggregation.
  • analysis grid resolution = e.g. 1000×500 (perf); other canvases in appendix
    Fixed-grid binning defines all fields and cost; scalability uses 1000×500 with 1×1 bins.
  • density regularization ε = ε small or 0 with explicit zero-support rule
    Stabilizes Elocal in sparse bins; zero-support convention when LOO mass vanishes.
  • peel / rank percentiles and query windows = case-specific (80/20, 50/50, 3/97, etc.)
    Case studies use chosen cuts (top 80%/bottom 20% flights; top 50% fibers; 3%/97% ships) and manual TimeBox/windows—analysis choices that determine shown subsets.
axioms (6)
  • domain assumption Second-moment structure tensors from tangent outer products are an adequate local summary of orientation mass without sign cancellation.
    Sec. 3.2 builds J(x) from vvT and interprets anisotropy via eigenvalues; standard in image processing/flow viz but still a modeling choice.
  • ad hoc to paper Structural support means agreement of a trajectory tangent with the leave-one-out ensemble tensor along a path, not geometric centrality or pairwise distance.
    Secs. 4.2–4.4 define Elocal, Φ, φ, and M this way; the central empirical claim depends on this operationalization.
  • domain assumption Undirected orientation (vvT) is acceptable, so antiparallel traffic reinforces rather than cancels.
    Stated limitation in Sec. 6; desirable for bidirectional corridors, wrong if counterflow must be separated.
  • domain assumption Fixed-grid 2D screen-space binning (including orthographic projections of 3D fibers) is a valid analysis domain for the claimed interactive structuring.
    Intro and DTI case; authors note view-dependence and need for 3D-aware anatomical validation.
  • standard math Curve density / kernel splatting on a raster is a faithful enough discrete stand-in for continuous occupancy and tensor mass.
    Secs. 3.1–4.1 and appendix A–B inherit CDE/KDE discretizations used in prior density-line work.
  • ad hoc to paper After LOO, absence of remaining tensor mass should score as zero independent support rather than undefined or self-supported agreement.
    Sec. 4.3 and appendix B zero-support convention; drives outlier behavior in sparse tails.
invented entities (3)
  • Structural Inconsistency Field (SIF) M(x;ℓ) independent evidence
    purpose: Image-space field localizing where passage-centered path support is weak versus sustained.
    Defined in Sec. 4.4 as one minus mean passage support; primary named output paired with density.
  • Path-integrated trajectory fidelity Φ(L) with dynamic LOO independent evidence
    purpose: Scalar per-trajectory structural agreement score for ranking and peeling.
    Eq. (5); used throughout case studies as the selection key.
  • Passage-centered support φ(L,sx;ℓ) independent evidence
    purpose: Intermediate quantity averaging LOO local agreement on a trajectory segment centered at a pixel passage.
    Bridge from trajectory integrals back to SIF; Sec. 4.4 and Eq. (14) in appendix.

pith-pipeline@v1.2.0-grok45-kimik3 · 32597 in / 4075 out tokens · 83871 ms · 2026-07-31T00:40:03.375105+00:00 · methodology

0 comments
read the original abstract

When visualizing large-scale line ensembles, trajectory continuity and visual scalability are inherently antagonistic. Trajectory-centric renderings preserve path information but rapidly degenerate into clutter as line density increases and mutual occlusion dominates. In contrast, field-based density representations enhance visibility while sacrificing structural coherence: density reflects accumulation rather than agreement, such that scalar aggregation alone cannot discriminate between consistent and conflicting configurations. Rather than replacing density-based views, we complement them with a path-integrated trajectory-fidelity measure that quantifies the agreement of each trajectory with a surrounding tensor field. By projecting this passage-centered structural support back into image space, we obtain what we call a Structural Inconsistency Field, which localizes regions where dense patterns correspond to coherent structure versus disagreement, outliers, or connectivity-induced ambiguity. Dynamic leave-one-out correction reduces self-bias in the path integral. Efficient fixed-grid updates combined with prefix-sum evaluation enable interactive analysis and iterative extraction of coherent structures. Synthetic benchmarks, scalability analyses, and real-world case studies demonstrate that, when paired with conventional density views, the proposed method disambiguates dense line patterns by exposing spatially localized coherence and structural breakdown that remain concealed in density-only representations.

Figures

Figures reproduced from arXiv: 2607.25121 by Bin Chen, Christophe Hurter, Oliver Deussen, Patrick Paetzold, Yumeng Xue, Yunhai Wang.

Figure 1
Figure 1. Figure 1: Weekly maximum temperature series from 6,187 U.S. weather stations. The density view (a) emphasizes hotspot A, whose query result remains broad and geographically diffuse (b,c). The structural inconsistency field (d) instead makes corridors B1 and B2 salient, yielding more coherent query results and a clearer north–south geographic separation (e,f). Abstract—When visualizing large-scale line ensembles, tra… view at source ↗
Figure 2
Figure 2. Figure 2: Geometric interpretation of the Structure Tensor. (a) For bi￾directional flow, the first-order vector mean cancels out (circle), while the second-order structure tensor preserves orientation (ellipse). (b) High anisotropy (λ1 ≫ λ2) indicates coherent laminar flow. (c) Low anisotropy (λ1 ≈ λ2) is semantically blind, failing to distinguish between structured crossings and unstructured noise. (a) Input Trajec… view at source ↗
Figure 3
Figure 3. Figure 3: Construction of the structure tensor field. (a) Trajectories are rasterized onto the analysis grid. (b) With a minimal kernel (1×1), the tensor records only the instantaneous tangent. (c) A wider spatial kernel (3×3) aggregates neighborhood statistics and reveals crossings or divergences through increased isotropy. outer product using the local normalized tangent. We therefore define the tensor field over … view at source ↗
Figure 5
Figure 5. Figure 5: Dynamic leave-one-out (LOO). (a) A candidate trajectory (in red) is selected for evaluation. (b) Its contribution is removed to form the environment tensor Jenv. (c) The candidate is then evaluated against this unbiased environment. dominated by sample count. Hereafter, Φ(Li) refers to this leave-one￾out corrected form unless stated otherwise. 4.4 Spatial Aggregation While Φ(Li) characterizes an entire tra… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of local and path-aligned support geometries. The red box marks the queried pixel x. The colored cells illustrate the corresponding support geometries as the context grows from a local 3×3 neighborhood to a mid-sized path extent and finally to the maximal path extent. (a) Short path extent WL (sx; ℓ1 ) (b) Long path extent WL (sx; ℓ2 ) [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Passage-centered path extent. (a) For a representative pas￾sage through x, the queried trajectory is evaluated over a symmetric path interval of half-length ℓ1 around x. The blue region denotes the contin￾uous extent, and the gray pixels denote the sampled pixels intersected by the discretized trajectory within it. (b) Increasing the extent to ℓ2 > ℓ1 evaluates the same passage over a longer trajectory seg… view at source ↗
Figure 8
Figure 8. Figure 8: Synthetic datasets. The colors show the generated trajectory categories for cases D1, D2, D3-C, and D3-D in [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Scalability analysis. Binning scales linearly with the number of trajectories, tensor-field construction is nearly constant with respect to N on a fixed grid, and prefix-sum path-extent evaluation keeps path integration lightweight. while the density baseline is negated before evaluation. To determine whether we measure the right outliers, we compare these oriented line scores against the ground-truth out… view at source ↗
Figure 9
Figure 9. Figure 9: Benchmark for synthetic datasets. The columns show scalar density, our structural inconsistency field, and the qualitative image￾space cluster coloring by Xue et al. [60]. Density and inconsistency are continuous scalar fields, whereas the cluster-coloring column uses cate￾gorical colors for image-space groups rather than ground-truth trajectory classes. The first column of [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 11
Figure 11. Figure 11: France aviation case study. The full dataset contains 5,360 trajectories. The density map emphasizes the dominant traffic corridors but leaves minority behaviors visually entangled with them. The structural inconsistency field localizes where structural support weakens. Ranking trajectories by Φ(L) then separates the dataset into a top 80% high-score subset (4,288 trajectories), which captures the main lo… view at source ↗
Figure 12
Figure 12. Figure 12: DTI case study. This orthographic brain projection uses a 12,059-fiber subset sampled from the 120,593-fiber tractography dataset used in FiberClay [27]. Density (a) collapses overlapping anatomical structures into a hairball, while the structural inconsistency field (b) reveals weakly supported passages. Functional-decomposition bundling [26] produces a clean tree-like representation (c), but regions A a… view at source ↗
Figure 13
Figure 13. Figure 13: Supplementary illustration of the zero-order moment (CDE). (a) Continuous kernel integration along curve geometry. (b) Discrete rasterization for fixed-grid approximation. (c) The resulting scalar occupancy field used downstream as the tensor mass term. This appendix complements Sec. 3.1 by using [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Controlled spindle ablation and spatial effect of LOO. (a) Nested noncrossing trajectories colored by the center-outward depth proxy di = −|zi | (blue: central; red: outer). The SIF views are qualitative renderings of the same representative seed on a 700×500 canvas; they use a common scale, are vertically aligned with (a), and use the maximal path extent in both conditions. Red dashed boxes mark sparse o… view at source ↗
Figure 15
Figure 15. Figure 15: Supplementary low-score half of the DTI example. The lowest-scoring 50% of fibers removed from Fig. 12d. Trajectory extraction uses simulation index 4 from the data with Rayleigh number 108 and Prandtl number 1. We initialize 12,059 parti￾cles (matching the DTI subset size) on a deterministic jittered grid and integrate them over t ∈ [20.0,25.0] using fourth-order Runge–Kutta integration, bilinear spatial… view at source ↗
Figure 16
Figure 16. Figure 16: Supplementary Rayleigh–Bénard pathline case study. Pathlines derived from the native 2D unsteady-flow fields in The Well Rayleigh–Bénard convection dataset. Density (a) emphasizes frequently visited recirculation regions. The SIF (b) assigns lower inconsistency to many recirculating bands and higher inconsistency to interfaces and transition regions containing overlapping orientations. From the 12,717 out… view at source ↗
Figure 17
Figure 17. Figure 17: Stock price trajectories. The long bottom band is simultaneously prominent in the density view and low in structural inconsistency in the SIF. A TimeBox query retrieves 658 lines from this band, and peeling them removes it from the residual density view, confirming that it corresponds to a coherent subset of the stock ensemble. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Stock price trajectories, second pattern. The second prominent stock pattern is visually strong in the density view but is marked as high structural inconsistency in the SIF. We therefore use a window query instead of a TimeBox because the lines entering from above or below are part of the phenomenon rather than a distraction. The 1,232-line selection is heavily cluttered, while the filtered 370-line subs… view at source ↗
Figure 19
Figure 19. Figure 19: Hard-drive temperature series. The density-guided and SIF-guided TimeBox choices emphasize different parts of the same data. A denser region yields a 223-line selection that is still strongly affected by fluctuations, whereas the SIF-guided lower-right query returns 229 lines that are visually more regular. This reversal arises because steep oscillations can inflate density through frequent top/bottom cro… view at source ↗
Figure 20
Figure 20. Figure 20: Mediterranean Sea trajectories. The low-inconsistency selection contains 144 lines yet stays concentrated in a compact, coherent corridor. The high-inconsistency selection contains a similar number of lines, 138, but occupies a much larger visual region and exhibits substantially weaker structural agreement. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Ship trajectories. Because this dataset is already dominated by regular shipping lanes, we use the SIF primarily as confirmation that the main routes have low structural inconsistency. We then apply a trajectory-fidelity split at 3%/97%: the retained 97% form visually regular, mostly straight point-to-point routes, while the lowest 3% contain visually irregular, low-fidelity trajectories, including unusua… view at source ↗
Figure 22
Figure 22. Figure 22: Real-data comparison with image-space coloring. Left: the colorization of Xue et al. [60]. Middle and right: the highest- and lowest-scoring subsets from our method. Initial ensemble After first peeling Density (a) Line density plot (d) Updated density High Low Structural Inconsistency Field (b) Structural inconsistency field (e) Updated inconsistency High Low Extraction (c) First subset extraction (f) Ne… view at source ↗
Figure 23
Figure 23. Figure 23: Supplementary peeling workflow. Top row: density, inconsistency, and the first extraction on the full ensemble. Bottom row: the corresponding density, inconsistency, and next extraction after peeling the first subset and recomputing the fields on the remainder. Structural Inconsistency High High Structural inconsistency Low Low Short extent Mid extent Maximal extent D3-C D3-D [PITH_FULL_IMAGE:figures/ful… view at source ↗
Figure 24
Figure 24. Figure 24: Qualitative effect of increasing path extent on D3. Top row: D3-C. Bottom row: D3-D. Left to right: short, intermediate, and maximal path extent. D3-C keeps a lighter central bridge across all three settings. D3-D looks similar at short and intermediate extents because the evaluation has not yet reached the divergent side regions; only the maximal extent exposes the ambiguous support by making the center … view at source ↗

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