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REVIEW 5 major objections 5 minor 59 references

Curvature Informed Furthest Point Sampling

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Curvature-informed furthest point sampling (CFPS) swaps low-curvature points out of the FPS core set and claims the swap lifts classification, segmentation, and shape completion without changing the downstream network.

desk verdict A promising sampling idea whose central algorithm is undefined in the write-up: the joint rank is C*S in one place and C+S in another, and the reported gains are not tied to a fixed procedure. read the letter →

arxiv 2411.16995 v1 pith:NRNKFGOV submitted 2024-11-25 cs.CV

Shubham Bhardwaj , Ashwin Vinod , Soumojit Bhattacharya , Aryan Koganti , Aditya Sai Ellendula , Balakrishna Reddy This is my paper · ORCID
classification cs.CV
keywords pointclouddownsamplingfurthestsamplingcurvaturereinforcementlearningREINFORCEshapecompletionclassificationsegmentation
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

Furthest point sampling (FPS) is the standard way to thin a point cloud while keeping coverage, but it ignores local geometry, so sharp or curved regions may be undersampled. The paper proposes curvature-informed FPS (CFPS), which keeps the FPS core set and then swaps out a learned fraction of its low-curvature points for high-curvature points from the discarded set, scoring points by a joint rank that combines the FPS soft rank and the estimated mean curvature. The swap fraction is produced by a small policy network trained with REINFORCE, which makes the sampling layer trainable end-to-end. The paper reports that this single change improves shape completion on MVP (F1-score from 0.50 to 0.52, Chamfer distance from 5.96 to 5.60), classification on ModelNet40 (96.2% versus 94.8%), and segmentation on ShapeNetPart, all without changing the downstream architectures. If the numbers hold, CFPS is a drop-in improvement over FPS in any architecture that already uses furthest point sampling.

What carries the argument

The load-bearing object is the joint rank J = C * S (stated in Section 3.2) or J = C + S (stated in Algorithm 2), which fuses the normalized FPS soft rank S = F/(N-1) with a pointwise mean-curvature estimate C obtained from learned normal and curvature estimators. The other piece is the exchange-ratio policy πφ: a small temporal convolutional network that reads the curvature values and outputs a Beta distribution over the swap fraction G in [0,1], trained by the REINFORCE policy-gradient rule with an exponential-moving-average baseline. Together they convert a fixed, non-differentiable FPS step into a module with a learned swap count, n_exchange = floor(G·N), that is updated end-to-end through the reward signal of the downstream task while the FPS core set itself is recomputed deterministically.

What would settle it

Re-running the ModelNet40 classification with several seeds and fixed, pre-registered hyperparameters would settle whether the reported 96.2% versus 94.8% gap over FPS is stable, since the paper reports single runs without a voting strategy. Separately, computing the joint rank on one cloud with both the product definition (Section 3.2) and the sum definition (Algorithm 2) would show whether the swapped set - and hence the claimed mechanism - is even uniquely defined.

Watch

Extended reading notes

Core claim

The central claim is that FPS's weakness is not its coverage heuristic but its blindness to local geometry, and that this blindness can be fixed without abandoning FPS. The algorithm runs FPS to obtain a soft rank S = F/(N-1) for each point, estimates pointwise mean curvature, forms a joint rank that combines the two, and swaps the lowest-ranked points inside the FPS set with the highest-ranked points outside it, where the number of swapped points is a learned fraction of the input size. The paper argues that points on flat regions are redundant, so trading them for high-curvature points preserves sharp features while FPS still supplies global coverage. On the MVP completion benchmark it reports that VRCNet+CFPS improves the F1-score from 0.50 to 0.52 and reduces the Chamfer distance from 5.96 to 5.60; on ModelNet40 classification it reports 96.2% overall accuracy against 94.8% for FPS; and on ShapeNetPart segmentation it reports higher mIoU than FPS and the APES baseline. The paper claims state-of-the-art results among end-to-end downsampling methods, noting that one-pass learned samplers such as SampleNet and Learning to Sample fall outside its comparison framework.

Load-bearing premise

The method rests on the combined curvature-and-FPS score reliably ranking which points to keep, but the curvature values are used unnormalized, the score is defined as a product in one place and a sum in another, and the learned swap count is not clamped to the core-set size - so the exchanged set can change with the curvature scale or exceed the available points.

Editorial extensions

If this is right

  • Any FPS-based architecture can adopt CFPS without redesign: the reported gains on completion, classification, and segmentation come from swapping the sampling layer only.
  • On the MVP benchmark, the swap improves completion fidelity: F1-score at the 1% threshold rises from 0.50 to 0.52 and Chamfer distance falls from 5.96 to 5.60.
  • On ModelNet10 and ModelNet40, CFPS reports 0.996 and 0.983 accuracy versus 0.990 and 0.97 for FPS (Table 2), and 96.2% versus 94.8% in a separate comparison (Table 6).
  • On ShapeNetPart segmentation, CFPS reports 84.5% category mIoU and 86.7% instance mIoU, above FPS (83.0% for both) and above both APES variants.
  • The benefit concentrates on geometry with high curvature variation: for near-uniform objects such as sofas the ablation shows CFPS matches FPS, while beds, bookshelves, and tables gain most from larger exchange counts.

Reading between the lines

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

  • Because curvature is computed on the fly and the downstream network is left unchanged, CFPS could plausibly be retrofitted to already-trained FPS pipelines as a test-time sampling choice; the paper demonstrates only end-to-end training, so this use is an untested extrapolation.
  • A reader implementing from the text must pick between two different joint ranks (a product in Section 3.2 and a sum in Algorithm 2), and the paper does not say which definition produced the tables; checking both on one cloud would show whether the headline gains depend on that choice.
  • The paper's state-of-the-art claim is scoped: it sets aside one-pass learned samplers such as SampleNet and Learning to Sample on the grounds that they sample once before the network, so the comparison covers only methods that downsample repeatedly inside the network.
  • A reader of the appendix will find the training-strategy ablation hard to reconcile: CFPS-only is listed with F1-score 0.52 while the FPS+CFPS hybrid is listed at 0.507, yet the text describes the hybrid as the best configuration, leaving the configuration behind the headline numbers unclear.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes Curvature Informed Furthest Point Sampling (CFPS), a point-cloud downsampling method that replaces a fraction of the points chosen by furthest point sampling with high-curvature points from the unselected set, where the fraction is learned by a REINFORCE-based policy network. The authors claim state-of-the-art results on single-view partial point cloud completion (MVP), classification (ModelNet10/40), and part segmentation (ShapeNetPart), and they include ablations on the exchange ratio and on training strategies, plus a theoretical regret bound in the appendix.

Significance. If the empirical claims were reproducible, CFPS would be a practically valuable drop-in sampling module: it preserves FPS coverage while adding a learned geometric bias, and it is designed for end-to-end training. The paper also provides a useful comparison of FPS-based and learned sampling methods and reports computational overhead. However, the current manuscript does not establish the central claim because the algorithm is specified inconsistently (joint rank defined as both multiplication and addition, with unnormalized signed curvature), key quantitative results contradict each other, and the theoretical regret bound relies on invalid assumptions. The absence of released code and of error bars further prevents verification.

major comments (5)
  1. [Section 3.2, Algorithm 2] The core swap operation is not well-defined. Section 3.2 defines the joint rank as J = C * S, while Algorithm 2 line 7 computes J = C + S; these define different orderings. Moreover, C is a raw signed mean curvature with no normalization, so the relative weight of curvature and FPS rank depends on the scale and sign of C, and the lowest-C points are strongly concave points rather than flat points. Finally, Algorithm 2 does not clamp nexchange = floor(G * N) to the core-set size K; for the reported N=2048, K=256, and G=0.9, nexchange=1843 > K, which is not a valid exchange. Consequently, the results in Tables 1, 2, 6, and 8 cannot be attributed to a fixed, reproducible algorithm.
  2. [Tables 2 and 6] The classification results are mutually inconsistent. Table 2 reports CFPS achieving 0.983 overall accuracy on ModelNet40, whereas Table 6 reports 96.2% for the same method and dataset, and the FPS baseline likewise differs (0.97 vs. 94.8%). At most one of these sets of numbers can be correct, and without code or a clarification the claimed improvement over FPS cannot be taken at face value.
  3. [Appendix A.1, Table 5] The training-strategy ablation is internally contradictory. The text states that CFPS-only achieves an F1-Score of 0.52, 'slightly lower than FPS-only' (which is 0.50), and it describes the hybrid FPS+CFPS score of 0.507 as 'the best performance.' Numerically 0.52 > 0.50 and 0.507 < 0.52, so either the table values or the narrative are erroneous. This undermines the ablation conclusion about the benefit of the adaptive ratio.
  4. [Appendix C, Eqs. (5)-(9)] The theoretical regret bound is not valid. The quantity Xt = E_{pi*}[R] - E_{pi_phi}[R] is not zero-mean (it is nonnegative under an optimal policy) and is not i.i.d. because the policy parameters phi change over time. Additionally, the Hoeffding interval is misapplied: with |R| <= M, Xt lies in [-2M, 2M], not in [0, 2M] as implied by setting a = 2M and b = 0. Thus Eq. (9) does not follow and the claimed O(sqrt(T log(1/delta))) regret bound is unsupported.
  5. [Tables 1, 2, 3, 6, 8] All reported metrics are single numbers without variance or repeated-run statistics. Given the small reported margins (e.g., F1 from 0.50 to 0.52, accuracy from 94.8% to 96.2%), statistical significance cannot be assessed, and the absence of released code prevents independent verification. This is a load-bearing gap for the paper's central claim of consistent improvement.
minor comments (5)
  1. [Page 2, Introduction] The sentence 'In this paper, We introduce' has a capitalization error; 'we' should be lowercase. There are also typographical errors such as 'paramteres' (Table 4/7 caption) and 'establlishing' (Appendix C.3).
  2. [Tables 4 and 7] Tables 4 and 7 are identical and both present the same computational-complexity data; one should be removed or they should be differentiated.
  3. [Figure 2] Figure 2, the architecture diagram, is referenced but the text does not explain the legend for J, C, S, and G; adding a short description would improve readability.
  4. [References] The paper cites 'Supplymentary' for an architecture diagram; this should be corrected to 'Supplementary.'
  5. [Section 3.1] The curvature definition states H = (k1 + k2)/2 but does not specify how mean curvature is estimated from the MSECNet normals on a point cloud; a citation to the exact estimation method would help reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the paper's claims are empirical comparisons against fixed benchmarks, and its learned exchange ratio is transparently optimized with the downstream loss as reward rather than disguised as an independent prediction.

full rationale

The paper's central claims are empirical: CFPS is compared against FPS, APES, and published methods on fixed benchmarks (MVP completion, ModelNet classification, ShapeNetPart segmentation). No load-bearing step reduces to its own input by construction. The curvature scores come from externally published networks (PCPNet, MSECNet), and the REINFORCE policy is explicitly trained with reward R = -L_theta(X, G), so the exchange ratio is a deliberately optimized component, not a fitted parameter renamed as a prediction. The paper contains no self-citations by the present authors and invokes no uniqueness theorem or ansatz from prior work by the same authors. The internal inconsistency between J = C * S in Section 3.2 and J = C + S in Algorithm 2, together with the unnormalized signed curvature and unclamped exchange count, are algorithmic correctness concerns, not circularity; they do not make the reported benchmark results equivalent to the method's inputs. Accordingly, the appropriate circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests mainly on empirical results; the method uses standard components. Free parameters are the learned exchange ratio and the hand-chosen (and inconsistently defined) ranking combination. Domain assumptions about curvature informativeness and reward stationarity are explicit in Sections 3.1, 3.2, and Appendix C. No invented entities are introduced.

free parameters (2)
  • Exchange ratio G = learned in [0,1] via Beta policy
    G determines how many points are swapped each downsampling step; it is optimized with REINFORCE using the downstream loss as reward.
  • Joint rank combination choice (multiplication vs addition) = undefined; Section 3.2 uses C*S, Algorithm 2 uses C+S
    The choice of how to combine curvature and FPS rank is hand-chosen and inconsistent across the paper; no learned weight or normalization is described.
assumptions (4)
  • domain assumption Mean curvature estimated from MSECNet normals is an informative proxy for geometric importance in downsampling.
    Section 3.1 and Algorithm 2 use curvature as the sole geometric feature for identifying redundant points.
  • domain assumption FPS soft rank S = F/(N-1) captures global structure and is compatible with curvature on a common scale.
    Section 3.2 combines soft rank with curvature without normalization or scale analysis.
  • domain assumption The downstream task loss is a valid reward signal and its non-stationarity does not invalidate the REINFORCE updates.
    Section 4 and Appendix C treat R = -L_theta(X,G) as a stationary bounded reward, but theta changes during training.
  • ad hoc to paper Hoeffding's inequality applies to the regret sequence with E[Xt] = 0 and i.i.d. samples.
    Appendix C.4 asserts Xt has zero mean and is i.i.d.; in RL with a changing policy this is not established.

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Cite this review

Pith. "Pith review of Curvature Informed Furthest Point Sampling." pith.science (2026). https://pith.science/paper/NRNKFGOV

@misc{pith2026241116995,
  author       = {Pith},
  title        = {Pith review of: Curvature Informed Furthest Point Sampling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NRNKFGOV}},
  note         = {Machine review of arXiv:2411.16995}
}
read the original abstract

Point cloud representation has gained traction due to its efficient memory usage and simplicity in acquisition, manipulation, and storage. However, as point cloud sizes increase, effective down-sampling becomes essential to address the computational requirements of downstream tasks. Classical approaches, such as furthest point sampling (FPS), perform well on benchmarks but rely on heuristics and overlook geometric features, like curvature, during down-sampling. In this paper, We introduce a reinforcement learning-based sampling algorithm that enhances FPS by integrating curvature information. Our approach ranks points by combining FPS-derived soft ranks with curvature scores computed by a deep neural network, allowing us to replace a proportion of low-curvature points in the FPS set with high-curvature points from the unselected set. Existing differentiable sampling techniques often suffer from training instability, hindering their integration into end-to-end learning frameworks. By contrast, our method achieves stable end-to-end learning, consistently outperforming baseline models across multiple downstream geometry processing tasks. We provide comprehensive ablation studies, with both qualitative and quantitative insights into the effect of each feature on performance. Our algorithm establishes state-of-the-art results for classification, segmentation and shape completion, showcasing its robustness and adaptability.

Figures

Figures reproduced from arXiv: 2411.16995 by the authors.

Figure 1
Figure 1. 2048 points of a monitor downsampled to 256 points showing CFPS retains more structural [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Architecture diagram of the Curvature-aware Furthest Point Sampling (CFPS) pipeline. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Comparison of downsampling methods across different objects. Each column represents [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Result of changing nep number of exchange points on different classes in MVP dataset [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: VRCNet Architecture for Shape Completion [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.