{"id":"e042fea2-a754-4e00-a5b5-34a7716e3b45","arxiv_id":"2606.20856","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Reformulates SDF volume rendering as first-passage-time distributions via stochastic processes along rays, shows NeuS as special case, and reports improved reconstruction and uncertainty on DTU and MobileBrick.","lead":"The paper introduces Stochastic Signed Distance Processes to model the signed distance field along each ray as a stochastic process, turning volume rendering into a first-passage-time probability problem for multi-view surface reconstruction. A smart generalist might read it to understand a probabilistic reformulation that claims better accuracy and uncertainty estimates than prior SDF methods.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"The practical Bayesian-filtering approximation for first-passage probabilities may deviate from the exact distribution induced by the stochastic process, weakening the claimed advantage over deterministic rendering.","rationale":"The reader's weakest assumption isolates exactly the tractability and fidelity of the Bayesian-filtering approximation; the concrete test above directly probes whether that assumption holds numerically. Because the paper supplies code, the check is executable and would either confirm that the approximation is sufficiently faithful or show that the performance edge is partly an artifact of the discretization. No other internal inconsistency (e.g., in the NeuS special-case reduction) appears more load-bearing given the available description.","tokens_in":1729,"tokens_out":406,"duration_ms":24358,"concrete_test":"On a single ray with a known analytic SDF (e.g., a sphere), compute the exact first-passage probabilities under the paper's stochastic process definition for 32 uniform samples; then apply the paper's practical approximation (as described in the methods section) and measure the L1 difference in the per-interval probabilities. If the mean absolute deviation exceeds 0.05, re-train the model with the exact probabilities (via CPU fallback) and compare DTU Chamfer distance to the published SSDP numbers.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that modeling SDF values along each ray as draws from a stochastic process yields a first-passage distribution whose interval probabilities, when approximated for parallel rendering, produce measurably better surface reconstruction and calibrated uncertainty than NeuS-style deterministic volume rendering. The derivation treats the process as admitting recursive Bayesian updates, but the practical approximation (necessary for GPU efficiency) implicitly truncates or discretizes the state; if this truncation correlates with ray depth or surface curvature, the induced occupancy probabilities can systematically bias the photometric loss and the extracted zero level set. This is the least secure link because the paper positions the approximation as preserving the probabilistic benefits while enabling the reported gains on DTU and MobileBrick.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper introduces Stochastic Signed Distance Processes (SSDP) to reformulate SDF-based volume rendering in multi-view surface reconstruction as probabilistic surface rendering. SDF values along each ray are modeled as a stochastic process inducing a first-passage-time distribution; first-passage probabilities per sampling interval are derived via Bayesian filtering together with a practical approximation enabling parallel rendering. NeuS is recovered as a special case. Experiments on DTU and MobileBrick report improved surface reconstruction and uncertainty quantification over baselines, with code released.","tokens_in":1884,"tokens_out":402,"duration_ms":22062,"significance":"If the approximation is shown to be faithful, the work supplies a principled probabilistic generalization of existing deterministic volume rendering methods, with potential benefits for calibrated uncertainty in implicit representations. Open-sourcing the code is a positive contribution to reproducibility.","major_comments":[{"comment":"The practical approximation to the Bayesian-filtering derivation of interval first-passage probabilities (described in the method section following the stochastic process definition) is load-bearing for the central claim. If the truncation or discretization correlates with ray depth or surface curvature, the induced occupancy probabilities can bias the photometric loss and the extracted zero level set; the manuscript should supply either an error bound or an ablation quantifying this effect on the reported DTU/MobileBrick gains.","section":"Method (Bayesian filtering and practical approximation)"},{"comment":"Table or figure reporting quantitative results on DTU and MobileBrick: the claimed outperformance in surface reconstruction and uncertainty quantification must be accompanied by error bars or multiple-run statistics to establish that the probabilistic formulation, rather than implementation details, drives the improvement.","section":"Experiments"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":"The provided abstract and skeptic note indicate that the approximation fidelity is the least secure link; if the full manuscript does not contain a dedicated analysis of the filtering truncation, this should be requested before acceptance."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments on our manuscript. We address each major comment below and describe the revisions we will undertake.","responses":[{"response":"We agree that the faithfulness of the practical approximation is central to the claims and merits explicit validation. The approximation is derived to preserve the essential properties of the Bayesian filtering result while enabling parallel evaluation. In the revised manuscript we will add an ablation that compares the approximate interval probabilities against a higher-fidelity numerical reference on representative DTU and MobileBrick scenes, reporting the resulting differences in photometric loss and surface metrics. This will directly quantify any systematic effects related to depth or curvature.","revision_made":"yes","referee_comment":"[Method (Bayesian filtering and practical approximation)] The practical approximation to the Bayesian-filtering derivation of interval first-passage probabilities (described in the method section following the stochastic process definition) is load-bearing for the central claim. If the truncation or discretization correlates with ray depth or surface curvature, the induced occupancy probabilities can bias the photometric loss and the extracted zero level set; the manuscript should supply either an error bound or an ablation quantifying this effect on the reported DTU/MobileBrick gains."},{"response":"We concur that statistical characterization of the reported gains is necessary. The current tables reflect single training runs, which were chosen for computational practicality. In the revision we will repeat the full experimental protocol (our method and all baselines) across multiple random seeds on both DTU and MobileBrick, and will augment the tables with mean and standard-deviation values for the key reconstruction and uncertainty metrics.","revision_made":"yes","referee_comment":"[Experiments] Table or figure reporting quantitative results on DTU and MobileBrick: the claimed outperformance in surface reconstruction and uncertainty quantification must be accompanied by error bars or multiple-run statistics to establish that the probabilistic formulation, rather than implementation details, drives the improvement."}],"tokens_in":1351,"tokens_out":414,"duration_ms":23042,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this paper treats the signed distance values along each ray as a stochastic process, derives the first-passage time distribution, and computes interval probabilities via Bayesian filtering. NeuS appears as a special case, and the experiments claim better surface reconstruction plus better-calibrated uncertainty than the baselines on DTU and MobileBrick.\n\nThe new piece is the explicit stochastic-process model and the first-passage derivation. That framing is distinct from the usual deterministic volume rendering used in NeuS-style work. The paper does a straightforward job of showing how the probabilistic view leads to the rendering equation and of spelling out the special-case recovery. Releasing code is also useful for anyone who wants to inspect the implementation.\n\nThe soft spot is the practical approximation required for parallel GPU rendering. The derivation relies on recursive Bayesian updates, but the version that actually runs must truncate or discretize the state. If that truncation introduces depth- or curvature-dependent bias, the photometric loss and the extracted zero level set could shift in ways that are not purely due to the stochastic framing. The abstract gives no error analysis or ablation that isolates the approximation, so it is hard to tell how much of the reported improvement traces back to the new model versus other implementation choices. The central argument itself does not look circular.\n\nThis is for people already working on implicit surfaces and differentiable rendering in computer vision. A reader who wants to see a probabilistic extension of NeuS would get the most out of the derivation and the released code.\n\nI would send it to peer review. The framing is coherent and the claims are concrete enough to evaluate, even if the approximation step will probably need more detail in revision.","headline":"SSDP reframes SDF ray marching as a first-passage stochastic process with Bayesian filtering, recovers NeuS as a special case, and reports gains on DTU and MobileBrick, but the GPU approximation is the part that needs the most scrutiny.","tokens_in":2347,"tokens_out":432,"would_cite":false,"duration_ms":18673,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Modeling SDF values along rays as a stochastic process induces a first-passage-time distribution that supports probabilistic surface rendering.","keywords":["stochastic signed distance processes","first-passage-time distribution","bayesian filtering","signed distance field","surface reconstruction","volume rendering","multi-view reconstruction","uncertainty quantification"],"falsifier":"A direct comparison showing that the first-passage probability approximation produces higher reconstruction error or poorer uncertainty calibration than standard deterministic SDF rendering on the DTU dataset would falsify the advantage.","tokens_in":2626,"feed_emoji":"","tokens_out":615,"duration_ms":22544,"temperature":0.7,"pith_summary":"The paper aims to show that treating the signed distance field along each ray as a stochastic process allows derivation of a first-passage-time distribution for the surface intersection. This leads to a probabilistic formulation of surface rendering where pixel colors arise from a mixture over possible intersection points. Bayesian filtering provides the probability mass for each sampling interval along the ray, with an approximation suitable for efficient computation. NeuS is shown to be a special case within this framework. If valid, the approach would deliver improved surface reconstruction quality along with direct uncertainty estimates from the distribution.","feed_headline":"Stochastic ray SDF models improve surface reconstruction","feed_subtitle":"First-passage probabilities derived via Bayesian filtering outperform deterministic volume rendering on DTU and MobileBrick benchmarks.","key_machinery":"Stochastic Signed Distance Processes (SSDP), which represent the signed distance function along a ray as a stochastic process to generate a first-passage-time distribution for the ray-surface intersection point.","core_discovery":"Stochastic Signed Distance Processes model the SDF along each ray as a stochastic process that induces a first-passage-time distribution. The first-passage probability for each sampling interval is derived using Bayesian filtering and a practical approximation for parallel rendering, leading to better performance than baselines in surface reconstruction and uncertainty quantification on the DTU and MobileBrick datasets.","pith_inferences":["The stochastic process view could extend to other ray-based rendering tasks beyond surface reconstruction.","Approximations in the Bayesian filtering step may trade off exactness for speed in ways that affect uncertainty calibration on unseen data.","Integration with learned priors on the stochastic process parameters might further reduce reliance on photometric loss alone."],"forward_implications":["The first-passage probability per interval follows from Bayesian filtering on the stochastic process.","NeuS volume rendering is recovered as a special case of the stochastic formulation.","Surface reconstruction accuracy exceeds that of deterministic baselines on DTU and MobileBrick.","Uncertainty in the reconstructed surfaces is quantified directly from the first-passage distribution."],"fun_headline_variants":["Stochastic processes represent SDF along rays","First-passage-time distributions from stochastic SDF","Bayesian filtering derives first-passage probabilities","SSDP models ray intersections probabilistically","Stochastic SDF induces first-passage distributions"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The signed distance values along a ray can be modeled as samples from a stochastic process whose first-passage distribution allows a tractable Bayesian filtering approximation.","fun_headline_variants_meta":{"raw":{"variants":["Stochastic processes represent SDF along rays","First-passage-time distributions from stochastic SDF","Bayesian filtering derives first-passage probabilities","SSDP models ray intersections probabilistically","Stochastic SDF induces first-passage distributions"]},"model":"grok-4.3","cost_usd":0.005119,"raw_usage":{"total_tokens":2478,"prompt_tokens":646,"num_sources_used":0,"completion_tokens":62,"cost_in_usd_ticks":51187000,"prompt_tokens_details":{"text_tokens":646,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1770,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":646,"tokens_out":62,"duration_ms":15448,"temperature":1.0,"reasoning_tokens":1770,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T18:02:09.827280+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct comparison showing that the first-passage probability approximation produces higher reconstruction error or poorer uncertainty calibration than standard deterministic SDF rendering on the DTU dataset would falsify the advantage.","supporting_citations":[],"review_version":1}