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GeoRay: Gauge-Aware Feed-Forward Satellite 3D Reconstruction in the Geodetic Frame

Zhe Dong, Wanqing Wu, Yuzhe Sun, Haochen Jiang, Yuchen Ma, Lecheng Ren, Tianzhu Liu, Yanfeng Gu

arXiv:2608.29680v1cs.CV

TL;DR

Satellite photogrammetry needs dense heights in an absolute geodetic frame under RPC cameras, but perspective features, datum ambiguity, and differing monocular and multi-view reliability leave key requirements unmet. GeoRay addresses these through ray-consistent adaptation, a coordinate-equivariant datum mechanism, and calibrated relief fusion; across transfer tiers, it leads compliant feed-forward systems, reaching 2.99 m absolute MAE at 91.9% coverage.

  • Problem

    Satellite photogrammetry requires absolute-frame digital surface models under non-central RPC imaging, where perspective features, height–datum ambiguity, and heterogeneous evidence remain unresolved.

  • Method

    GeoRay uses ray-consistent adaptation, an origin-equivariant datum mechanism, and precision-weighted fusion of monocular and multi-view relief.

  • Results

    2.99 m absolute MAE at 91.9% coverage, with 72.6% completeness-aware accuracy, and the leading compliant feed-forward performance across in-domain and transfer tests.

  • Takeaways & Limitations

    One trained GeoRay model produces dense geodetic surfaces without per-scene optimization while preserving absolute placement across in-domain, cross-dataset, and cross-city tests.

Abstract

from arXiv · show

Feed-forward 3D foundation models reconstruct perspective scenes in one pass. Satellite photogrammetry needs a different product, one that domain adaptation alone does not deliver: dense surface height in an absolute geodetic frame under non-central rational polynomial cameras (RPCs). Perspective-pretrained features are not reliably observable along RPC height rays, absolute elevation carries a low-order height--datum gauge exchangeable with sensor bias to first order, and monocular and multi-view cues fail in different regions. \method{} treats all three. Lightweight ray-consistent adapters make a frozen backbone matchable along native RPC rays. An explicit datum mechanism separates relief from absolute level and is equivariant to the vertical origin by construction, so one trained model serves zero-, one-, and sparse-control inference. Calibrated inverse-variance fusion combines the two relief streams. \bench{}, our absolute-frame benchmark of eighteen systems across in-domain, cross-dataset, and cross-city tiers, scores absolute placement without registration or test-reference leakage. On 26 held-out US3D tiles, \method{} attains $2.99$\,m absolute MAE at $91.9\%$ coverage, improves completeness-aware accuracy by $46.4$ points over the strongest compliant feed-forward baseline, remains the most accurate such system under both transfer shifts, and runs in $24$\,s model-forward time per tile. Code and models will be released at https://github.com/HIT-SIRS/GeoRay

I. INTRODUCTION … B. Satellite 3D Reconstruction under RPC Cameras

GeoRay adapts feed-forward geometry to native RPC satellite imaging, addressing ray-field observability, height–datum gauge freedom, and heterogeneous monocular/multi-view evidence. The paper introduces SatGauge for absolute-frame evaluation and reports strong held-out and transfer performance while positioning the work against classical, learned, and neural-rendering satellite reconstruction.

  • I. INTRODUCTION: Satellite photogrammetry differs from central-perspective reconstruction because pushbroom sensors lack a single projection center and use RPC mappings.These differences motivate transferring feed-forward geometry to native RPC imaging rather than relying on perspective assumptions.
  • I. INTRODUCTION: Three obstacles govern absolute satellite 3D: RPC ray-field observability, height–datum gauge freedom, and heterogeneous monocular and multi-view evidence.The gauge permits vertical placement to exchange with image-space sensor bias to first order, so accurate relief alone does not ensure absolute elevation.
  • I. INTRODUCTION: GeoRay combines ray-consistent low-rank adaptation of a frozen VGGT backbone, complementary frozen MoGe-2 monocular relief, uncertainty prediction, and an analytically origin-equivariant datum mechanism.The multi-view branch estimates relief and uncertainty, while the datum mechanism separates absolute level from relief.
  • I. INTRODUCTION: SatGauge evaluates eighteen systems in the absolute geodetic frame across in-domain, cross-dataset, and cross-city tiers without alignment or reference-derived test inputs.The protocol declares control budgets and jointly reports accuracy, completeness, and relief fidelity.
  • I. INTRODUCTION: 2.99 m absolute MAE at 91.9% coverage is achieved on 26 held-out US3D tiles, with 72.6% completeness-aware accuracy at 2.5 m.GeoRay improves completeness-aware accuracy by 46.4 points over the strongest compliant feed-forward baseline.
  • A. Feed-Forward Geometry Foundation Models: Feed-forward geometry foundation models primarily use central-perspective parameterizations, raising whether their features remain localizable along pushbroom correspondence samples.The related discussion frames this as a representation question for applying perspective-developed models to satellite imagery.
  • B. Satellite 3D Reconstruction under RPC Cameras: Classical satellite reconstruction uses RPC geometry with hand-crafted matching, whereas learned MVS uses differentiable RPC warping and cost volumes with satellite-specific training and dense height supervision.Generic pipelines may instead use local perspective approximations, while neural rendering optimizes individual scenes under satellite cameras.

C. Generalizable Sparse-View Reconstruction … A. Problem Setting: Reconstruction in RPC Object Space

GeoRay frames satellite reconstruction as single-pass prediction of an absolute geodetic height field from sparse RPC views, addressing non-pinhole geometry, uncertainty calibration, and height–sensor-bias ambiguity. Its design combines RPC-ray relief estimation, datum anchoring, and calibrated fusion while distinguishing its output from prior generalizable splatting systems.

  • C. Generalizable Sparse-View Reconstruction: Generalizable Gaussian splatting reconstructs scene primitives in one forward pass, with prior methods improving sparse-view recovery through learned matching, monocular priors, and aggregation.Satellite adaptations include SkySplat and SatSurfGS for multi-temporal orbital imagery, while GeoRay differs in both output and a…
  • D. Uncertainty and Gauge Ambiguity: Established uncertainty methods include heteroscedastic regression, deep ensembles, and post-hoc calibration.
  • III. METHOD: GeoRay’s architecture estimates relief by RPC-ray reasoning, anchors absolute level with a datum head, and returns height with uncertainty through calibrated precision fusion.Backbones are frozen, while the marked trainable modules are optimized around parameter-free analytic operators.
  • D. Uncertainty and Gauge Ambiguity: Absolute geolocation and systematic sensor error are coupled through low-order RPC bias corrections and gauge freedoms in bundle adjustment.The cited prior work motivates making the ambiguity explicit and assigning sparse control a precise role.
  • A. Problem Setting: Reconstruction in RPC Object Space: RPC cameras map normalized geodetic coordinates (ϕ, λ, h) to normalized image coordinates, while pushbroom acquisition prevents a single global pinhole epipolar geometry.Consequently, depth along a pinhole ray is not a meaningful variable for this setting.
  • A. Problem Setting: Reconstruction in RPC Object Space: For a reference-view pixel, sweeping height along the inverse RPC localization ray traces an object-space curve sampled in meters of geodetic height.
  • A. Problem Setting: Reconstruction in RPC Object Space: The disparity rate is nearly constant over the relevant height bracket and is determined by acquisition convergence geometry, serving as a conditioning variable for adaptation and fusion.
  • A. Problem Setting: Reconstruction in RPC Object Space: With N=3 views, the task is single-pass prediction of a geodetically referenced height field bH with per-pixel uncertainty bσ in the absolute vertical datum without reference alignment.Vendor RPC pointing errors are classically corrected by low-order bias compensation, and their coupling with absolute height is formalized later.

B. Architecture Overview … 2) Ray-consistent adaptation:

GeoRay adapts frozen foundation-model features for observability along native RPC height rays, then separates relief from datum level and fuses calibrated multi-view and monocular evidence. Its architecture uses lightweight trainable components while preserving invariances needed for absolute-frame reconstruction.

  • B. Architecture Overview: Frozen VGGT features are adapted with low-rank modules for RPC ray sampling, while a Ray Transformer reasons over geometry-aware tokens formed from metric height hypotheses.The model also queries frozen MoGe-2 once to produce a metric monocular relief estimate.
  • B. Architecture Overview: The datum head anchors absolute elevation to RPC-provided height coordinates and corrects sensor-level residuals, while calibrated fusion combines median-centered relief fields by predicted precision.This mechanism addresses the separation between relief and absolute datum level.
  • B. Architecture Overview: The complete prediction combines the adapted multi-view relief branch, datum estimation, and calibrated fusion with the monocular branch.The supplied architecture overview presents this as the model’s complete prediction.
  • B. Architecture Overview: 12.4 M trainable parameters operate against 1.240 B frozen parameters, with both foundation backbones remaining frozen.The trainable portion consists only of low-rank adapters and lightweight heads.
  • C. RPC Ray-Field Observability: For each reference pixel, the method samples feature maps at height hypotheses projected through RPC geometry and aggregates cross-view correlations into matching tokens.The matching distribution is produced by a scoring head over the aggregated view evidence.
  • 1) The property:: Ray-field observability requires matching distributions to concentrate near true surface heights for textured, unoccluded pixels.It is measured through entropy, mode-to-truth localization, and dependence on disparity rate ρ.
  • 2) Ray-consistent adaptation:: Low-rank adapters are trained with ray-field supervision, and geometry tokens encode normalized height position, step size, disparity-rate–step, viewing angle, and groundsampling distance.These cues are expressed to preserve invariance under changes of vertical origin.
  • 2) Ray-consistent adaptation:: The expected-height readout feeds a lightweight relief decoder that sharpens discontinuities and suppresses per-pixel outliers without altering the datum.The multi-view branch outputs bHmv and bσmv.

D. The Height–Datum Gauge · 1) Observation model and identifiability: · 2) An exact coordinate-origin symmetry:

The paper formalizes a height–datum gauge in which low-order elevation components can be exchanged with RPC sensor bias, while a joint vertical-origin shift leaves ray evidence and reprojections unchanged. It therefore fixes the gauge with control points or an exactly equivariant datum mechanism that combines an origin-carrying multi-view level with an invariant learned residual.

  • 1) Observation model and identifiability:: Low-order affine height components are first-order unobservable when their image-space effects can be reproduced by admissible constant and linear RPC bias updates.In the locally affine, constant-Jacobian limit, the affine family becomes an exact gauge.
  • 1) Observation model and identifiability:: One control point fixes the scalar sub-gauge, whereas ten spatially distributed points probe the full affine family.The control-point correction is unique when its design has full column rank.
  • 1) Observation model and identifiability:: The accuracy of the affine gauge approximation depends on the delivered cameras rather than the reconstruction model and is measured directly in Sec. V-F.The experiments apply the same correction basis to every method.
  • 2) An exact coordinate-origin symmetry:: A joint shift of the training height field and RPC height offsets leaves normalized RPC heights, reprojections, images, and sampled ray evidence unchanged.This is a vertical-origin change, not an image-space bias update.
  • 2) An exact coordinate-origin symmetry:: Any datum estimator using only ray-field internals is structurally blind to the vertical gauge and cannot learn the required unit-slope equivariance.The shift is used as a diagnostic, a design constraint, and a held-out check.
  • 2) An exact coordinate-origin symmetry:: The multi-view hypothesis level carries the origin, while monocular relief is invariant, making their difference a closed-form scalar anchor for datum recovery.The multi-view tile median is exactly equivariant, whereas the monocular median cancels in the final composition.
  • 2) An exact coordinate-origin symmetry:: The datum head preserves exact equivariance by combining the multi-view tile level with a learned residual that depends only on invariant ray statistics.The residual is isolated from the analytic anchor and cannot change its coordinate-origin response.

E. Calibrated Fusion and the Conditional Gain Law … 4) The conditional gain law:

GeoRay fuses monocular and multi-view relief estimates while reserving absolute elevation for its datum mechanism. Its conditional gain law directs multi-view geometry toward regions where monocular uncertainty is higher, with calibration and interval coverage evaluated empirically.

  • 1) From the monocular prior to metric relief:: The monocular branch provides a relief prior: MoGe-2 is queried once, and its standardized scalar depth is learnedly mapped to metric relief.The standardization is deterministic and follows the public implementation.
  • 1) From the monocular prior to metric relief:: Within-tile centering and normalization make monocular relief origin-shift invariant, while the datum mechanism exclusively owns the absolute level.No geodetic offset is taken from the monocular model.
  • 2) Placing two streams on one uncertainty scale:: Monocular calibration predicts metric relief scale and per-pixel uncertainty, but median-centered height loss prevents it from absorbing the absolute datum.The monocular pathway therefore remains a relief estimator rather than an absolute-height estimator.
  • 2) Placing two streams on one uncertainty scale:: The multi-view pathway supplies relief uncertainty alongside its ray-field estimate, and both streams use heteroscedastic likelihood training before fusion.Section V-G evaluates uncertainty ordering and empirical interval scale before fusion.
  • 3) Fusion:: Fusion occurs in relief space using multi-view and monocular inverse-variance estimates, so each source contributes according to predicted precision.The absolute prediction is then formed from the fused relief and datum mechanism.
  • 3) Fusion:: The conditional-independence approximation may make fused uncertainty optimistic, so interval coverage is evaluated in both relief and absolute frames.This limitation motivates explicit empirical coverage checks.
  • 4) The conditional gain law:: Expected multi-view gain increases with predicted monocular uncertainty, making the law prospective because uncertainty is available before reconstruction error is known.Section V-G tests the association against a pairing-permutation null and verifies the required calibration.

F. Training Objective · IV. SATGAUGE: ABSOLUTE-FRAME EVALUATION · A. Three Tiers of Generalization

The training objective jointly optimizes complementary losses while enforcing datum-residual and vertical-origin consistency. SatGauge evaluates absolute geodetic placement without registration or test-reference leakage across three transfer tiers spanning spatial, dataset, sensor, city, and viewing-geometry shifts.

  • F. Training Objective: All trainable components are optimized jointly under fixed loss weights across the reported training runs.
  • F. Training Objective: Each loss has a distinct role: fused height, ray posterior, centered monocular relief, variance calibration, height discontinuities, or tile-level datum residual.Lh, Lray, Lmono, Lnll, Lgrad, and the anchor loss supervise these respective targets or properties.
  • F. Training Objective: The datum residual predicts the multi-view readout’s residual tile-level error from invariant ray statistics, with monocular medians cancelling.
  • F. Training Objective: Two identities vanish identically by construction, contributing no gradient while serving as consistency assertions against vertical-origin leakage.Their held-out value is reported in Sec. V-F.
  • IV. SATGAUGE: ABSOLUTE-FRAME EVALUATION: SatGauge scores predictions first in the absolute geodetic frame and restricts test-time information to imagery, RPC metadata, or training-side statistics.The evaluation avoids registration, test-reference height-range leakage, and pointwise-only scoring that can reward partial surfaces.
  • A. Three Tiers of Generalization: L1 uses spatially disjoint US3D tiles from Jacksonville and Omaha, while L2 applies the unchanged model to IARPA MVS3D with a new region and independent airborne-lidar reference.
  • A. Three Tiers of Generalization: L3 simultaneously changes sensor generation, city, and viewing geometry using SpaceNet-4 Atlanta, so the tiers probe different failure axes.Fig. 4 summarizes the associated relief and acquisition geometry.

B. Evaluation Principles … 2) Geodetic reference handling:

The evaluation prioritizes direct geodetic-frame placement, explicit control conditions, leakage-free test information, and completeness-aware reporting. Metrics separately diagnose alignment, coverage, relief fidelity, discontinuity accuracy, and uncertainty quality, while geodetic handling preserves each benchmark tier’s reference convention without alignment.

  • B. Evaluation Principles: Absolute placement is ranked before registration, while aligned error diagnoses removable translation rather than determining the primary ranking.The evaluation reports absolute error directly and uses bounded translation only diagnostically.
  • B. Evaluation Principles: Every result states whether inference uses zero, one, or ten height controls, with the same correction family available to all methods.Control usage is explicit across evaluated methods.
  • B. Evaluation Principles: Hypothesis ranges and normalizations come from RPC metadata or training statistics, preventing evaluated-reference leakage.Test information is constrained to sources available without using the evaluated reference.
  • A. Experimental Setup: Absolute MAE is measured in the geodetic frame, while aligned MAE follows bounded 3-DoF translation and accepted-registration fraction is reported as Reg.The diagnostic translation is computed for every tile, while the acceptance guard determines which tiles enter the Aln. average.
  • 1) Metrics:: Unpredicted pixels count as failures in PAGcτ, which is defined for every method regardless of Reg.The metric uses τ ∈{2.5, 7.5} m.
  • 1) Metrics:: Coverage uses each benchmark tier’s native denominator, while relief fidelity compares predicted and reference 5–95 percentile height spreads.The evaluation also reports error on strong height discontinuities and uses unweighted means over tiles.
  • 2) Geodetic reference handling:: Heights follow each tier’s released reference convention, and RPCs are used as delivered with hypothesis brackets anchored to their height offset.Absolute scoring means no alignment to the reference and does not claim independently surveyed orthometric accuracy; convention differences appear as tile-constant offsets.

3) Baselines and Comparability: … C. Generalization across Tiers

The evaluation standardizes inputs, geodetic height mapping, RPC handling, and ground-control correction across seventeen baselines, while excluding oracle-calibrated rows from ranking. GeoRay leads absolute-frame reconstruction on held-out US3D tiles and remains strongest among compliant feed-forward methods under both evaluated distribution shifts.

  • 3) Baselines and Comparability:: Seventeen baselines cover classical photogrammetry, supervised satellite MVS, generalizable splatting, zero-shot foundation models, and per-scene optimization.Concurrent methods without public code at submission are discussed but not re-implemented.
  • 3) Baselines and Comparability:: All methods receive fixed view triplets, a common geodetic height grid, matched RPC or perspective handling, and identical seeded ground-control corrections.Rows fitting an affine height map to the test reference are marked as oracle context and excluded from ranking.
  • 4) Implementation:: Training uses 2562 crops, three views, K=96 height hypotheses, 20k AdamW iterations, and rank-16 LoRA adapters on the frozen VGGT encoder.Model selection uses the best dev-validation checkpoint at 16k iterations; MoGe-2 remains frozen.
  • B. Main Results: 2.99 m absolute MAE, 1.78 m aligned MAE, and 91.9% coverage establish GeoRay’s central US3D result on 26 held-out tiles.Its completeness-aware accuracies are 72.6% at 2.5 m and 89.7% at 7.5 m, respectively 46.4 and 27.3 points above the strongest compliant feed-forward baseline.
  • B. Main Results: [2.36, 3.74] m is the 95% bootstrap interval for GeoRay’s mean absolute error, and GeoRay wins all 26 tiles against SkySplat in absolute error and PAGc 2.5.The paired absolute-error margin is [6.81, 10.74] m at 95% confidence.
  • B. Main Results: 24 s model-forward time per tile supports the accuracy–efficiency result in one feed-forward pass without scene-specific optimization.The same pattern persists under sparse ground control.
  • C. Generalization across Tiers: 3.21/2.86 m absolute/aligned error at 86.7% coverage makes GeoRay best among compliant feed-forward methods on L2.Sat-MVSF reaches 3.37 m absolute error but only 39.1% coverage; the L1 advantage survives a new region and independent lidar reference.
  • C. Generalization across Tiers: 23.88/15.74 m absolute/aligned error at 90.7% coverage remains best among compliant feed-forward methods under the joint city, sensor, and acquisition-geometry shift L3.Accuracy degrades under L3, but the reconstructed surface remains substantially more complete and better placed in the geodetic frame.

D. Comparison with Per-Scene Reconstruction · GeoRay (ours)

GeoRay offers a reusable feed-forward alternative to per-scene optimization, delivering competitive absolute accuracy with far lower computation while covering more surface. Scene-specific optimization remains preferable when maximum per-scene accuracy justifies substantially higher compute.

  • D. Comparison with Per-Scene Reconstruction: 2.49 m absolute error in 24.0 s of model-forward time is reported for GeoRay on the common US3D subset.The passage also reports 89.5 s end-to-end time, but the sentence is truncated after that value.
  • D. Comparison with Per-Scene Reconstruction: Qualitative relief comparisons use a shared display range and per-tile median alignment to emphasize local relief and completeness.The comparison is shown on L1 and L2.
  • D. Comparison with Per-Scene Reconstruction: The zero-shot transfer table evaluates US3D-to-IARPA MVS3D (L2) and ATL-SN4 (L3).Its columns follow Table IV; coverage uses each tier’s common scorer.
  • D. Comparison with Per-Scene Reconstruction: 2.89 m in 1964 s is reported for EOGS, while GeoRay covers more of the surface on the common US3D comparison.This establishes the accuracy–compute reference against per-scene optimization.
  • D. Comparison with Per-Scene Reconstruction: 1.68 versus 3.21 m on three IARPA AOIs favors EOGS in accuracy, but GeoRay requires two orders of magnitude less computation.GeoRay therefore complements, rather than uniformly replaces, scene-specific optimization.
  • D. Comparison with Per-Scene Reconstruction: Maximum per-scene accuracy can justify the extra compute, making scene-specific optimization preferable in those cases.This is the stated limitation and complementarity of the feed-forward approach.
  • GeoRay (ours): Unregistered surfaces are rendered at predicted absolute elevations with a shared vertical scale within each row.The figure includes representative in-domain and cross-city reconstructions in the geodetic frame.
  • GeoRay (ours): Table VII compares per-scene reconstruction on the common nine-scene subset using absolute and accepted-registration averages, coverage, and per-scene timing.GeoRay timing distinguishes model-forward from end-to-end time, while aligned aggregation can exclude scenes failing the registration guard.

E. Mechanism I: RPC Ray-Field Observability (C1) · F. Mechanism II: The Height–Datum Gauge (C2) · G. Mechanism III: Calibration and the Conditional Gain Law (C3)

GeoRay addresses three mechanisms underlying absolute satellite reconstruction: ray-consistent adaptation restores RPC-ray observability, the datum mechanism separates height relief from low-order absolute bias, and calibrated uncertainty fusion makes multi-view gains conditional on prediction confidence and geometry.

  • E. Mechanism I: RPC Ray-Field Observability (C1): Adaptation moves the feature-profile peak from a median 6.99 m to 2.72 m from true height, yielding a 2.6× localization gain despite lower raw contrast.Frozen features peak at contrast 0.192, while adapted features peak at 2.72 m with P90 8.62 m and contrast 0.138; the ray readout sharpens the final posterior.
  • E. Mechanism I: RPC Ray-Field Observability (C1): RPC correspondence is necessary: five image–camera corruption families degrade reconstruction by 1.2–30.4×, whereas paired view–RPC permutation costs 1.00×.The paired permutation preserves every image–camera pair and leaves the geometry untouched; four corruption families worsen monotonically over training.
  • F. Mechanism II: The Height–Datum Gauge (C2): The datum estimate tracks injected height-origin shifts with slope 1.00 and maximum residual below 6.53 µm, while the fused field follows with slope 0.9999.Across the tested δ ∈[−7, 7] m sweep, fused-field displacement from the shifted reference remains within 0.008 m at the 95th percentile.
  • F. Mechanism II: The Height–Datum Gauge (C2): At δ = 50 m, the constant gauge mode leaves R = 1.3×10^-4 px against a 75.1 px displacement field, validating the first-order approximation for these cameras.The residual is obtained by fitting the admissible bias update to exact reprojection displacement fields across injected gauge modes.
  • F. Mechanism II: The Height–Datum Gauge (C2): One control point recovers 70.7% of GeoRay’s remaining absolute–aligned gap, reducing error from 2.992 m to 2.137 m, while ten points reach 1.82 m.Under L2 transfer, one point cannot help because the zero-control datum gap is 0.35 m, whereas ten distributed points reduce error to 3.13 m.
  • G. Mechanism III: Calibration and the Conditional Gain Law (C3): Predicted uncertainty supports fusion with NLL = 2.53 and AUSE = 1.02 m, while its calibrated ordering reflects spatially realized error.The reported uncertainty has conservative empirical interval coverage and spatial agreement with realized error.
  • G. Mechanism III: Calibration and the Conditional Gain Law (C3): Absolute-frame interval coverage is 66.7% and 85.1%, below the 86.4% and 97.0% median-centered coverage because the modeled residual excludes the datum component.The calibration head changes fusion weights and ordering, while the heteroscedastic likelihood sets the interval scale at 0.79 without the head.
  • G. Mechanism III: Calibration and the Conditional Gain Law (C3): Fusion gain rises from 0.50 m in the most confident decile to 1.91 m in the least, a 3.8× increase with rank correlation 0.96.After controlling for tile identity, disparity-rate binning is non-monotonic, so the conditional law is stated on predicted uncertainty alone.

H. Ablations and Sensitivity · I. Scope and Outlook · VI. CONCLUSION

GeoRay’s ablations show that ray adaptation and the datum mechanism dominate accuracy, while calibrated fusion and sampling choices have smaller effects. Cross-city analysis, stated limitations, proposed extensions, and conclusion-level evidence position the method as an absolute-frame reconstruction system built around observability, gauge separation, and calibrated evidence fusion.

  • H. Ablations and Sensitivity: 20.47 m is the absolute MAE after removing ray-field adaptation, versus 3.59 m with matched retraining, confirming the importance of native RPC-ray adaptation.This ablation supports adapting perspective-pretrained features to object-space height rays.
  • H. Ablations and Sensitivity: 150.84 m is the absolute error without the datum mechanism, while retaining only the analytic anchor gives 3.63 m versus 2.99 m for the final model.The analytic construction provides most absolute placement, while the learned residual refines it.
  • H. Ablations and Sensitivity: 3.02 m, 3.34 m, and less than 0.1 m are the changes from uncalibrated fusion, two views, and varying K from 48 to 144, respectively.Depth-Anything-V2 and MoGe-2 produce 3.58 m and 3.59 m under the same matched budget, showing prior-independence within this comparison.
  • I. Scope and Outlook: 16.94 m is the strong-L3-shift tier error with sparse affine control, reduced from 23.88 m and recovering 74% of the corresponding affine-oracle gain.Predicted uncertainty highlights difficult regions, whereas geometric control addresses the remaining low-order datum component.
  • I. Scope and Outlook: The formulation intentionally uses a low-order gauge basis, and its uncertainty model describes relief but not the per-tile datum.These are identified as two main limitations.
  • I. Scope and Outlook: Natural extensions include richer sensor-error bases, joint relief–datum uncertainty, variable-cardinality ray aggregation, and coarse-to-fine height sampling for large-area deployment.Overlap-and-blend window decoding could remove faint window boundaries without changing the observability or gauge formulation.
  • VI. CONCLUSION: Native RPC imaging requires height-ray-observable correspondence, separation of absolute elevation from a low-order height–datum gauge, and calibrated fusion of monocular and multi-view evidence.GeoRay addresses these requirements through ray-consistent adaptation and a coordinate-equivariant datum mechanism.
  • VI. CONCLUSION: Across in-domain, cross-dataset, and cross-city tests, one trained model produces dense geodetic surfaces without per-scene optimization and leads compliant feed-forward methods in absolute accuracy.Mechanism experiments link adaptation to RPC-ray localization, camera gauge to sparse-control effects on absolute level, and uncertainty to where multi-view geometry contributes most.
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