{"id":"d941ebad-03eb-47c5-a35b-46887c641e16","arxiv_id":"2607.26578","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Using granular-ball point clusters to initialize anchors and Gaussian scales reduces 3D Gaussian Splatting model size by about 10% with near-identical rendering quality.","lead":"This paper replaces the fixed voxel grid used to place anchors in Scaffold-GS with adaptive 'granular balls' grown from the scene point cloud, cutting initial anchors by 37% and storage by about 10% while keeping visual quality roughly unchanged. The method is useful for anyone who needs smaller 3D Gaussian scene files without retraining the core renderer.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Undefined appearance attribute in the granular-ball stopping rule is the load-bearing weak point; a color-flat/geometry-rich test would settle it.","rationale":"The reader's weakest_assumption identifies the same mechanism: the stopping rule trusts appearance consistency as a proxy for geometric simplicity, and the attribute a_i is never defined. I agree this is the most load-bearing uncertainty in the central claim. The paper's evidence is otherwise internally consistent: Table I reductions roughly match the stated percentages, the ablation cleanly separates GBAI and GBSP, and the D_max sensitivity analysis shows dynamic growth can compensate for very different initializations, which gives some credibility to the claim. However, none of the reported experiments isolate the failure mode where appearance is smooth but geometry is complex. The proposed controlled test would determine whether the appearance-dependent stopping rule is actually necessary or whether a geometry-only partition would perform just as well; it would also force the missing a_i definition into the open. Because the concern is unresolved but addressable, and because the existing data do not currently refute the claim, the appropriate verdict remains the reader's CONDITIONAL; I do not move it.","tokens_in":18764,"tokens_out":11058,"duration_ms":126130,"concrete_test":"Explicitly define a_i as normalized SfM RGB color (or the authors' intended attribute once specified). Construct a test scene with color-flat but geometrically complex structure — e.g., a white Stanford bunny, or synthetically recolor the BungeeNeRF 'Hollywood' facades to a single mean color while keeping geometry unchanged. Train Scaffold-GS and 3DGBGS from the same SfM points with identical seeds, growing/pruning schedules, and loss weights, and compare final anchors, storage, PSNR, SSIM, and LPIPS. If the PSNR gap stays within roughly the paper's reported per-scene spread (±0.5 dB) and the anchor/storage reductions hold, the concern is resolved; if PSNR drops more than 0.5 dB or final anchors are not reduced, the appearance proxy is load-bearing.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim depends on the adaptive partition being a reliable proxy for where anchors are needed. In Eqs. 16, 22, and 23, the stopping rule accepts a granular ball when σ_a(P_j) ≤ τ_a = 0.02 together with r_j ≤ ηv. But a_i — the 'appearance attribute' in Eq. 16 — is never defined: no source (SfM RGB color? learned feature?), no normalization, and no preprocessing. Without knowing whether the three channels are in [0,1] or [0,255], the fixed threshold 0.02 is not even meaningful: if raw RGB is in 0–255, σ_a ≤ 0.02 is almost never satisfied and the appearance term is inert; if normalized to [0,1], it is highly strict. More importantly, the method assumes that low appearance variation implies low geometric complexity. A color-flat but geometry-rich region — white plaster relief, a wire fence, a shiny metal surface with view-dependent highlights — can have small σ_a while still needing several anchors to represent detached or discontinuous surfaces. In such a region the partition would place one or two anchors where fixed voxelization would place more, and the later dynamic growing/pruning may not recover the lost capacity under the same budget. The paper's 19 scenes may simply not contain this failure mode; the per-scene tables do not report color-vs-geometry statistics. Since the headline 'comparable rendering quality' would break precisely in this case, this undefined and unvalidated appearance proxy is the most load-bearing concern.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes 3DGBGS, a variant of Scaffold-GS that replaces fixed voxelization of the SfM point cloud with a recursive granular-ball partition. Granular balls are formed by PCA-based median splits, with a stopping rule based on point count, recursion depth, spatial compactness, and appearance consistency. Anchor positions are set to granular-ball centers (GBAI), and initial Gaussian scales are initialized from a clipped fusion of nearest-neighbor distance and granular-ball radius (GBSP). All subsequent optimization, dynamic anchor growing/pruning, and rendering follow Scaffold-GS unchanged. On 19 scenes from Mip-NeRF360, Tanks&Temples, Deep Blending, and BungeeNeRF, the paper reports average reductions of 37.1% in initial anchors, 10.0% in final anchors, and 9.8% in model storage, with PSNR changes between −0.164 dB and +0.055 dB relative to Scaffold-GS. The key load-bearing assumption is that local appearance variation is a reliable proxy for the fineness of anchor placement needed in a region.","tokens_in":19173,"tokens_out":6449,"duration_ms":69046,"significance":"If the results are correct, 3DGBGS is a useful drop-in compactness improvement for Scaffold-GS-style anchor-based Gaussian splatting. The strengths are the clean ablation design separating GBAI and GBSP, the internally consistent tables, and the fact that the method changes only initialization and scale prior while leaving the rest of the pipeline untouched. The reported anchor and storage reductions are non-trivial, and the quality deltas are small. However, the central adaptive-partition mechanism relies on an appearance attribute that is never defined or analyzed, there are no per-scene quality tables for most datasets, and no seeds or error bars are reported. The single-baseline comparison is appropriate for an initialization-only method, but it limits the generality of the compactness claim. With the appearance proxy made precise and validated, this would be a solid contribution; as written, the central claim is not fully reproducible.","major_comments":[{"comment":"Eq. (16) defines each SfM point as (x_i,a_i) with a_i ∈ R^3 an \"appearance attribute,\" but the paper never states what a_i is: raw SfM RGB color? a learned feature? in [0,1] or [0,255]? The stopping rule in Eq. (23) uses σ_a(P_j) ≤ τ_a with τ_a = 0.02. If a_i is raw SfM color in 0–255, typical σ_a values are orders of magnitude above 0.02, so the appearance term is effectively inert and the partition is purely geometric. If a_i is normalized to [0,1], the threshold 0.02 is extremely strict and the term behaves very differently. Without this definition, the central adaptive-granularity mechanism is not reproducible, and the claimed connection between appearance consistency and anchor placement is untestable. Please define a_i, specify normalization/preprocessing, and report sensitivity to τ_a, including a disabled-appearance ablation.","section":"Section IV-A, Eqs. (16), (22), (23)"},{"comment":"The recursive split trusts σ_a(P_j) ≤ τ_a as evidence that one granular ball can cover a region. This assumes low appearance variation implies geometric simplicity, which is not generally true: a color-flat but geometry-rich surface (e.g., white plaster relief, a wire fence, or a shiny surface with view-dependent highlights) can have small σ_a yet require several anchors for detached or discontinuous surfaces. The paper provides no per-region analysis or counter-example test. If such regions exist, the large granular balls would remove anchors that dynamic growing/pruning may not recover under the same budget, and the \"comparable quality\" claim could break. A concrete test would be to run 3DGBGS on a color-flat/geometry-rich scene, or to disable σ_a by setting τ_a = 0 and compare final anchors and PSNR; if results are identical, the appearance term is inert and should be stated as such.","section":"Section IV-A, Eq. (23)"},{"comment":"The quality comparison is reported only as dataset averages. For the 19 scenes, there is no per-scene quality table for Mip-NeRF360, Tanks&Temples, or Deep Blending; Table III gives per-scene results only for BungeeNeRF. The reported PSNR deltas are small (−0.164 to +0.055 dB), but no standard deviations or seeds are provided. If run-to-run variation in Scaffold-GS-style training is of the same order—which is typical for this pipeline—the conclusion that quality is \"comparable\" is not established. Please report per-scene PSNR/SSIM/LPIPS, or at least the min/max deltas over scenes, and run multiple seeds with variance estimates.","section":"Section V-B, Table I"}],"minor_comments":[{"comment":"The claim that 3DGS \"draws on\" Granular Ball Computing is chronologically unsupported; the 3DGS paper does not cite GBC. Suggest softening to \"shares a similar coarse-to-fine principle\" rather than implying direct lineage.","section":"Sections II-B and II-D"},{"comment":"r_j is defined as the root-mean-square distance from the center, which is not a covering radius. If GBSP is intended as a spatial coverage prior, please justify the RMS choice or use a max-distance radius.","section":"Section IV-A, Eq. (20)"},{"comment":"Storage is defined as \"learned anchor parameters and MLP weights.\" Clarify whether anchor features, scales, offsets, and MLP weights are all included, and whether rendering-time Gaussian attributes are excluded. The exclusion of HAC/ContextGS in Table I is reasonable for the active-anchor focus, but a comparison to SOGS, which reduces feature dimensions, would strengthen the compactness claim.","section":"Section V-A and Table I"},{"comment":"The scene-wise BungeeNeRF ablation is useful, but the table would be more informative if the per-scene PSNR/SSIM/LPIPS were also reported for the full method in Table I; currently only averages are given.","section":"Section V-C, Table III"},{"comment":"No code or model release is mentioned. Providing the implementation would help reproducibility, especially given the underspecified appearance attribute and the hand-set hyperparameters.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper is internally consistent and the incremental contribution is clear. The undefined appearance attribute a_i is a genuine load-bearing concern rather than a presentation issue: it changes what the algorithm actually does, and the reported results are consistent with either a geometric-only partition or a very strict appearance gate. The lack of per-scene quality tables and seeds also undermines the \"comparable quality\" claim. I would send this back for major revision with the requested definitions, ablations, and robustness experiments. The heavy self-citation to the Granular Ball Computing literature is noticeable but does not affect the technical assessment."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is a solid compactness patch for anchor-based 3DGS: swapping fixed voxelization for granular-ball partitioning cuts initial anchors by 37%, final anchors and storage by about 10%, with PSNR drops under 0.2 dB on most benchmarks. Second, the core claim is plausible but the stopping rule that builds the granular balls depends on an appearance attribute that is never defined — that's the load-bearing gap.\n\nWhat's genuinely new: this is the first work I've seen that uses granular-ball adaptive partitioning to decide where anchors go and what scale prior to give them. It changes the spatial scaffold itself, not just the feature predictor. The GBC transfer is non-trivial. The evaluation isolates the effect well: same pipeline as Scaffold-GS, only anchor construction and scale initialization differ. Ablations cleanly separate GBAI (anchor reduction) from GBSP (final-anchor/storage reduction), and the hyperparameter analysis shows reasonable insensitivity to partition depth. The tables are internally consistent with the headline numbers. Honest, well-scoped work.\n\nSoft spots. The main one is in Eqs. 16, 22, and 23. The partition terminates when a region is \"appearance-consistent\" (sigma_a ≤ tau_a = 0.02), but a_i — the appearance attribute — is never defined. No source, no normalization. If it's raw SfM RGB in 0–255, a 0.02 threshold is effectively inert; if normalized to [0,1], it's very strict. You can't evaluate the stopping rule without this. And the assumption that low appearance variation implies low geometric complexity is risky: a white plaster relief or a shiny surface with view-dependent highlights can be appearance-flat but geometry-rich. In such regions the granular balls will be too large, and the later growing/pruning may not recover the lost anchors under the same budget. The 19 scenes may just not contain that failure mode, leaving the comparable-quality claim untested precisely where it matters.\n\nAlso: single baseline, no seeds, no code. For a 10% final-anchor reduction, run-to-run variance could matter. These are standard revision requests, not disqualifiers. The decision to exclude SOGS/HAC/ContextGS is reasoned, though a SOGS comparison would strengthen it.\n\nThe central argument holds up — the reductions are consistent and the quality cost is small. The undefined appearance attribute is fixable: define a_i, normalize, and test on a color-flat/geometry-rich scene. This deserves a serious referee, not a desk reject. I'd recommend conditional acceptance after those points are addressed.","headline":"A well-executed compactness patch for Scaffold-GS — the granular-ball idea is new and the numbers hang together, but the stopping rule's undefined 'appearance attribute' needs to be pinned down before the claim fully lands.","tokens_in":19611,"tokens_out":4109,"would_cite":true,"duration_ms":41366,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Replacing fixed-voxel anchor grids with adaptive 3D granular balls cuts initial anchor counts by 37.1%, final anchors by 10.0%, and stored model size by 9.8% across 19 scenes, at nearly unchanged rendering quality.","keywords":["3D Gaussian Splatting","Granular Ball Computing","Anchor initialization","Novel view synthesis","Compact representation","Scaffold-GS","Scale prior","SfM point cloud"],"falsifier":"Render a scene with a monochrome but geometrically intricate object using both 3DGBGS and Scaffold-GS; if PSNR drops by more than roughly 0.2 dB or the post-training final anchor count exceeds the baseline, the appearance-consistency proxy has failed. A cheaper check: track anchors removed in smooth-colored regions and see whether dynamic anchor growing re-adds them at the same locations during training.","tokens_in":18678,"feed_emoji":"📷","tokens_out":4928,"duration_ms":52357,"temperature":0.7,"pith_summary":"This paper tries to show that the fixed-voxel anchor initialization used by anchor-based 3D Gaussian splatting is wasteful: it spreads support points uniformly over a point cloud that is spatially non-uniform. Its proposed swap, 3DGBGS, partitions the SfM point cloud into adaptive 3D granular balls—large balls over smooth, redundant regions and small balls over complex geometry—then uses ball centers as anchors and ball radii as scale priors. Across 19 scenes from four benchmarks, this cuts initial anchors by 37.1%, final anchors by 10.0%, and model storage by 9.8% while keeping PSNR, SSIM, and LPIPS within a few hundredths of the Scaffold-GS baseline. The change is deliberately drop-in: the MLPs, losses, and growing/pruning logic are left untouched.","feed_headline":"Granular balls cut 3D Gaussian splatting anchors by 37%","feed_subtitle":"Adaptive point-cloud partition keeps rendering quality while trimming storage and computation in novel-view synthesis.","key_machinery":"The machinery is a recursive PCA-based binary partition of the SfM point cloud into disjoint 3D granular balls, each described by a center and an RMS radius. Partitioning stops when a ball is small, too deep, or both spatially compact and appearance-consistent (sigma_a <= tau_a = 0.02); GBAI maps ball centers to anchors, and GBSP clamps each ball radius to [0.25, 4.0] times the nearest-neighbor anchor distance and fuses it with that distance (alpha = 0.5) to initialize learnable log-scales. The stopping criterion is what decides where coarse balls survive, and therefore where anchor savings come from.","core_discovery":"The central claim is that granular-ball organization of the input point cloud, before any Gaussian is generated, is what unlocks a more compact anchor-based 3DGS. Granular Ball Anchor Initialization (GBAI) places anchors at granular-ball centers, and the Granular Ball Scale Prior (GBSP) clips each ball radius against the nearest-neighbor spacing and fuses the two to seed initial Gaussian scales. The result is 30-42.6% fewer initial anchors across the four benchmarks, 8-12% fewer final anchors after the unchanged growing/pruning phase, and 7.9-11.9% less storage, with rendering quality essentially matching Scaffold-GS (PSNR -0.05 to -0.16 dB on three benchmarks and +0.06 dB on BungeeNeRF).","pith_inferences":["The appearance-consistency threshold sigma_a(P_j) <= 0.02 is doing heavy lifting: if SfM point colors are flat across a geometrically intricate surface, the partition will merge points that later anchor growth may not re-seed, so the quality floor likely depends on the color-geometry correlation of the input point cloud.","The insensitivity of final anchor counts to maximum partition depth suggests a testable hypothesis: any initialization that respects local density might give similar final compactness, implying the scale prior GBSP may be the more load-bearing of the two components.","Combining granular-ball anchors with downstream serialization or compression of anchor features should compound storage savings, since the two target different redundancies: spatial support count versus per-anchor bit cost.","A learnable or anisotropic partition (for example, ellipsoidal balls) is a natural extension that would address scenes where local geometry is strongly directional; the paper's own future-work section gestures in this direction."],"forward_implications":["Initial anchor savings largely survive optimization: after identical dynamic growing and pruning, final anchors remain 8-12% lower, so the compact initialization is not erased by regrowth.","Storage drops by roughly a tenth on every benchmark, and the measured MLP-component GFLOPs drop by up to about 30% on one scene, so both training and rendering become cheaper.","Because only anchor initialization and scale prior change, the approach can be dropped into any Scaffold-GS-style anchor pipeline without retuning losses or network architecture.","The maximum partition depth can vary from 10 to 18 with little change in final anchor count, indicating that final compactness is partly absorbed by dynamic growing and pruning, not solely determined by initialization.","On BungeeNeRF the method improves PSNR and SSIM while removing 12% of final anchors, suggesting that scale-aware initialization can sometimes help quality rather than merely trade it away."],"fun_headline_variants":["Granular balls cut 3D Gaussian anchors by 37%","Granular ball 3DGS: fewer anchors, same rendering","Adaptive granular balls compact 3D Gaussian splatting","37% fewer anchors with granular ball partition","Compact novel-view synthesis via granular ball anchors"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The recursive partition assumes that low variation in SfM point appearance (sigma_a <= 0.02) reliably marks a region that one large granular ball can safely cover; if a surface is color-flat but geometrically detailed, those large balls delete anchors that the later growing step may not re-seed.","fun_headline_variants_meta":{"raw":{"variants":["Granular balls cut 3D Gaussian anchors by 37%","Granular ball 3DGS: fewer anchors, same rendering","Adaptive granular balls compact 3D Gaussian splatting","37% fewer anchors with granular ball partition","Compact novel-view synthesis via granular ball anchors"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000641,"raw_usage":{"total_tokens":2845,"prompt_tokens":858,"completion_tokens":1987,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":602,"completion_tokens_details":{"reasoning_tokens":1907}},"tokens_in":602,"tokens_out":1987,"duration_ms":13555,"temperature":1.0,"reasoning_tokens":1907,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T12:57:00.556394+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Render a scene with a monochrome but geometrically intricate object using both 3DGBGS and Scaffold-GS; if PSNR drops by more than roughly 0.2 dB or the post-training final anchor count exceeds the baseline, the appearance-consistency proxy has failed. A cheaper check: track anchors removed in smooth-colored regions and see whether dynamic anchor growing re-adds them at the same locations during training.","supporting_citations":[],"review_version":1}