Experiment record v2 · 17 August 2026

Noise-aware Gaussian reconstruction, from stable supervision to stable geometry.

Fixed backbone: channel-wise RGB-SVF + 2DGS.
Strong under calibrated synthetic RAW noise.
Wins on part of Dark3R.
Not yet universally better on real scenes.
Main remaining failure: geometry.
Unreliable observations change support, scale, and densification.
Appearance then compensates with large translucent splats.

+2.831 dBRGB-SVF 2DGS vs Vanilla 3DGS · RawNeRF x64

+1.102 dBRGB-SVF 2DGS vs Vanilla 3DGS · Dark3R Chapel 1/500

+2.008 dBE1 RGB-SVF 2DGS vs Vanilla 3DGS · Dark3R Bookshelf

mixedCave D3/D5/D6 and Dark3R Statue prevent a universal-win claim

Implemented: RGB-SVF + 2DGSImplemented: NTF-TGCompleted: real geometry/appearance oracleNext: persistent geometry prior

02 · What is actually validated

One method, three domains, three different answers.

Use one fixed backbone across datasets.
Report texture and geometry modules as separate ablations.
Do not rename every successful run as the method.

Controlled evidence

RawNeRF synthetic

SVF wins every noisy level.
28.942 dB at x64.
NTF-TG reaches 31.561 dB.
Current input is still an 8-bit proxy.

Real low light

Dark3R

Wins Chapel 1/125–1/500.
Wins Bookshelf.
Loses Statue and Chapel 1/800.
Large splats remain.

Real domain shift

Sterkfontein Caves

Only one clear RGB-SVF win: D6.
D3 and D5 are not good enough.
Illumination changes dominate.
No cave claim yet.

Domain	Noise / nuisance	Geometry control	What it tests	Current verdict
RawNeRF Sharpshadow	Calibrated Poisson–Gaussian x0/x4/x16/x64	One clean PINHOLE COLMAP solution	Loss robustness and representation ceiling	Clear strong-noise gain
Dark3R	Real exposure-dependent RAW noise; 1.1–5.3 dB mean SNR in Chapel sweep	Reference poses in current GS study	Real low-light transfer	Scene/exposure dependent
Cave D3/D5/D6	Noise + spotlight + shadows + clipping + low texture	Official reference COLMAP	Generalization beyond stationary sensor noise	No universal improvement

RawNeRFclean held-out target

Open train/test data →

White-balanced and tone-mapped Dark3R Chapel reference target

Dark3R ChapelGT-derived display mapping

Open train/test data →

Sterkfontein D3camera-linear training frame

Open train/test examples →

03 · Current fixed backbone

RGB-SVF makes RAW residuals closer to homoscedastic before 2DGS sees them.

One calibrated shot/read model per RGB channel.
No learned denoiser.
No clean training target.
No 10 dB threshold.
No test-time module.

Linear RAW-derived RGBNoisy observation I and rendered image R remain in camera-linear space.

Per-channel calibrationUse fixed (a_R,a_G,a_B) and (r_R,r_G,r_B).

RGB-SVF transformApply the normalized stable variance function T_c to target and render.

2DGS-MCMCOptimize geometry, opacity and SH under the transformed L1 + SSIM objective.

Optional extensionTexture refinement or persistent geometry control is isolated as an ablation.

Simpler than NTF

No SNR knee.
No confidence exponent.
No two-slope ratio.

Why channel-wise?

R, G, B have different noise.
A scalar transform biases color.
E1 uses three fixed functions.

What it cannot fix

No cross-view reasoning.
Wrong splits may remain.
Large support may remain.

Display only.

GT-derived white balance.
Fixed ×32 exposure.
Same mapping for every method.
Metrics use linear float images.

04 · Formula and implementation

The current objective in full.

Linear heteroscedastic sensor model.
Independent calibration for each RGB channel.

1 · Noise model

\[ \operatorname{Var}\!\left(I_c \mid x_c\right) = a_c x_c + r_c^2, \qquad c\in\{R,G,B\}. \]

\(a_c\): shot noise.
\(r_c\): read-noise standard deviation.
Fixed during training.

2 · Stable variance function

\[ T_c(x) = \frac{ \sqrt{a_c x+r_c^2}-r_c }{ \sqrt{a_c+r_c^2}-r_c }, \qquad x\in[0,1]. \]

Inverse standard-deviation scaling.
\(T_c(0)=0\), \(T_c(1)=1\).
Continuous and threshold-free.

3 · Numerically stable implementation

\[ T_c(x) = x\, \frac{ \sqrt{a_c+r_c^2}+r_c }{ \sqrt{\max\!\left(a_c x+r_c^2,\,\varepsilon_v\right)} +r_c+\varepsilon }, \qquad \varepsilon_v=10^{-8}. \]

Avoids numerical cancellation.
\(a_c=0\Rightarrow T_c(x)=x\).
\(\varepsilon_v\) stabilizes black pixels.

4 · Photometric objective

\[ \begin{aligned} \Delta_{p,c} &=T_c\!\left(R_{p,c}\right)-T_c\!\left(I_{p,c}\right),\\[3pt] \mathcal{L}_{\mathrm{RGB\text{-}SVF}} &= 0.8\, \frac{1}{3|\Omega|} \sum_{p\in\Omega} \sum_{c\in\{R,G,B\}} \left|\Delta_{p,c}\right|\\ &\quad+ 0.2\left[ 1-\operatorname{SSIM}\!\left(T(R),T(I)\right) \right]. \end{aligned} \]

Same transform for render and target.
Renderer is unchanged.
No inference overhead.

Implementation.

One vectorized transform.
Three shot coefficients.
Three read-noise values.
Standard L1 + SSIM.

05 · RawNeRF controlled study

Strongest causal evidence: calibrated synthetic noise.

Same clean PINHOLE poses at every level.
Same held-out clean targets.
x0 / x4 / x16 / x64 scale calibrated Poisson–Gaussian variance.
Not fixed-σ RGB Gaussian noise.

Noise	Vanilla 3DGS	NTF-v1 2DGS	RGB-SVF 2DGS	SVF − Vanilla	Reading
x0	27.990 / .89521 / .23542	29.373 / .93242 / .12282	29.079 / .93289 / .12048	+1.089 dB	near tie with NTF
x4	28.269 / .89327 / .23851	26.787 / .91506 / .14024	30.145 / .93735 / .11172	+1.876 dB	SVF wins all metrics
x16	27.712 / .88404 / .24070	27.828 / .91373 / .13331	30.068 / .92933 / .11427	+2.356 dB	SVF avoids NTF blur
x64	26.110 / .83873 / .25668	28.007 / .88195 / .13892	28.942 / .89007 / .12061	+2.831 dB	best loss-only result

Clean targetheld out

Vanilla 3DGS26.110 dB

NTF-v1 2DGS28.007 dB

RGB-SVF 2DGS28.942 dB

x64 representation study	Pre-training	Texture refinement	PSNR	SSIM	LPIPS
Standard Texture-GS	Linear 2DGS	Linear	30.077	.8882	.0955
NTF-TG	NTF 2DGS	Linear	31.561	.8939	.0927

Limits.

Current sweep uses 8-bit linear proxies.
Repeat with float/14-bit RAW.
Tree geometry remains imperfect.

06 · Dark3R real low-light study

Real evidence exists, but it is conditional.

Chapel 1/125–1/320: NTF is competitive.
Chapel 1/500: RGB-SVF wins.
Chapel 1/800: Vanilla wins.
Bookshelf: E1 wins by +2.008 dB.
Statue: E1 loses by −0.977 dB.

Chapel exposure	Mean SNR	Vanilla 3DGS	NTF-v1 2DGS	RGB-SVF 2DGS	Winner
1/125	5.292 dB	46.003 / .97258 / .02608*	47.161 / .98088 / .02202	46.295 / .97745 / .02422	NTF
1/320	2.556 dB	43.583 / .95555 / .03861	44.743 / .96828 / .03826	44.324 / .96816 / .03593	near tie
1/500	1.682 dB	43.487 / .95135 / .04914	43.218 / .95652 / .05340	44.589 / .96648 / .04301	RGB-SVF
1/800	1.102 dB	41.356 / .92991 / .06385	39.336 / .89475 / .09738	39.855 / .90630 / .11019	Vanilla

Fixed cross-scene protocol	Vanilla 3DGS	E1 RGB-SVF 2DGS	Δ PSNR	Interpretation
bc081 Bookshelf · 1/125 · 2.014 dB	41.695 / .93343 / .06315	43.703 / .96160 / .04001	+2.008	clear real-scene win
bc060 Statue · 1/100 · 2.260 dB	33.826 / .93881 / .04767	32.850 / .93739 / .04976	−0.977	geometry/artifact failure

Dark3R Bookshelf lossless float comparison

Evaluation.

Use lossless float renders.
Exclude earlier 8-bit PNG metrics.
Report aligned and unaligned results separately.

07 · Dark3R artifact diagnosis

The visible blob is not just a color-loss problem.

Large projected footprint.
Low-to-medium opacity.
Weak position and scale constraints.
SH compensates for wrong support.
Result: translucent, view-dependent color fields.

Cause 1

Geometry gradients

Noise perturbs position and scale.
One-view errors may trigger growth.
Wrong support becomes permanent.

Cause 2

Path-dependent growth

Capacity is assigned early.
Later steps rarely repair topology.
Opacity and SH hide the error.

Cause 3

Appearance compensation

Large GS acts as color correction.
PSNR may increase.
Visual quality becomes worse.

Controlled attempt	Bookshelf PSNR	Statue PSNR	Artifact outcome	Conclusion
E1 RGB-SVF backbone	43.703	32.850	large splats remain	reference
Taming-style importance relocation	43.231	33.252	some tail change; artifact remains	symptom-level control
Translucent footprint regularizer	43.181	33.225	some SSIM gain on Statue; artifact remains	global penalty harms useful coverage

Corrected Statue oracle	PSNR	SSIM	LPIPS	Δ PSNR vs E1	What remains fixed
Current noisy E1 reconstruction	32.850	.93739	.04976	—	reference
Noisy geometry + cleaner 1/25 appearance	34.341	.94396	.04434	+1.491	all geometry exactly frozen
Cleaner 1/25 geometry + noisy E1 appearance	33.870	.95747	.03759	+1.021	all geometry exactly frozen
Cleaner geometry + cleaner appearance	35.913	.95561	.03526	+3.064	upper reference

Dark3R target, noisy E1, and cleaner 1/25 final comparison

The oracle is not decisive.

The 1/25 “cleaner” model still contains large GS.
It is not ground-truth geometry.
The metric gains show sensitivity—not clean causal separation.
We need an external geometry prior or validated densification.

08 · Proposed unified extension

Keep RGB-SVF fixed; stabilize geometry with evidence that survives views.

Do not trust current GS depth.
Use cross-view parameter-gradient evidence.
Gate topology growth before appearance.
Optionally add Dark3R confidence as a soft prior.

RGB-SVF residualSame per-channel transform and hyperparameters across scenes.

K distinct camerasAccumulate world-space GS geometry gradients from different views.

Axis coherenceReal structure produces a persistent axis; random sensor noise is closer to isotropic.

Validated growthGate MCMC/splitting first; do not suppress ordinary geometry optimization globally.

Appearance refineTexture capacity only after topology stabilizes; freeze-geometry ablation remains mandatory.

Depth-free persistent axis confidence

\[ \begin{aligned} \mathbf{u}_{g,i} &= \frac{ \nabla_{\boldsymbol{\mu}_g}\mathcal{L}_i }{ \left\|\nabla_{\boldsymbol{\mu}_g}\mathcal{L}_i\right\|_2+\varepsilon },\\[3pt] \mathbf{M}_g &= \operatorname{EMA}_{i} \!\left( \mathbf{u}_{g,i}\mathbf{u}_{g,i}^{\mathsf T} \right). \end{aligned} \]

\[ c_g = \operatorname{clip}_{[0,1]} \!\left[ \frac{1}{2} \left( \frac{ 3\left\|\mathbf{M}_g\right\|_{\mathrm F}^{2} }{ \operatorname{tr}\!\left(\mathbf{M}_g\right)^{2} } -1 \right) \right]. \]

\(c_g=0\): isotropic directions.
\(c_g=1\): one persistent axis.
Outer product removes gradient-sign ambiguity.

Soft external geometry anchor for Dark3R

\[ \begin{aligned} \mathcal{L}_{\mathrm{prior}} = \lambda(t)\sum_g q_g \Big[ &\rho\!\left( \widehat{\mathbf n}_g^{\mathsf T} \bigl( \boldsymbol{\mu}_g-\widehat{\boldsymbol{\mu}}_g \bigr) \right)\\ &+ \eta \left\| \left( \mathbf I- \widehat{\mathbf n}_g\widehat{\mathbf n}_g^{\mathsf T} \right) \left( \boldsymbol{\mu}_g-\widehat{\boldsymbol{\mu}}_g \right) \right\|_1 \Big]. \end{aligned} \]

Prior source: external Dark3R pointmap and confidence.
Do not use current GS depth.
\(\rho(\cdot)\): robust normal constraint.
Second term: weak tangential anchor.
\(\lambda(t)\): decays to a small floor.

Gate topology first

Start with MCMC relocation/splitting.
Do not suppress all geometry gradients.
Avoid the V1 collapse.

Validate candidates

Test each new child on extra views.
Keep it only if residual decreases.
Reject unsupported growth.

Use one stop rule

Current gains peak at 7k–15k.
Use validation-based stopping.
No scene-specific iteration tuning.

09 · Experiment ledger

What has been tried—and what each result means.

Keep validated evidence.
Keep failed branches as ablations.
Do not combine modules without attribution.

Keep

NTF-v1

Boss-proposed origin.
Clear synthetic x64 gain.
Keep as conceptual ablation.

Keep as backbone

RGB-SVF + 2DGS

Simple and threshold-free.
Best loss-only synthetic result.
Fixed E1 for real scenes.

Representation branch

NTF-TG / Texture-GS

31.561 dB at synthetic x64.
Strong Cave LPIPS.
Needs frozen-geometry attribution.

Diagnostic only

Consensus / forward teachers

Remove non-persistent noise.
Blur weak high-frequency detail.
Keep as diagnostic.

Early signal

Persistent axis confidence

D6 7k: +0.177 dB.
Gain disappears by 30k.
Needs validated growth.

Do not use

Signed-direction hard gating

Confidence collapsed near .02.
Suppressed 88% of geometry motion.
Sign assumption was wrong.

Not sufficient

Split geometry/appearance blur

Does not restore topology.
Removes useful high frequency.
Foliage becomes weaker.

Not sufficient

Taming / footprint penalties

Only modest metric changes.
Large splats remain.
Treats the symptom too late.

Limited diagnosis

Real geometry oracle

Freeze checks pass.
Cleaner 1/25 still has large GS.
Not ground-truth geometry.

10 · Paper story and next step

A compact story is possible—if the real geometry module generalizes.

RAW noise corrupts supervision.
It may also corrupt topology growth.
RGB-SVF protects the image objective.
Persistent/external confidence should protect geometry.

RAW sequenceLinear, float/14-bit, calibrated per-channel shot/read noise.

RGB-SVFThreshold-free robust photometric supervision.

2DGS backboneFast explicit scene representation with fixed evaluation protocol.

Persistent geometryCross-view gradient evidence + optional Dark3R soft prior.

Detail allocationValidated densification, then optional texture refinement.

Stage A · topology

Add the Dark3R soft prior.
Add cross-view growth validation.
Test one fixed configuration.

Stage B · appearance

Freeze trusted geometry.
Compare SH and Texture-GS.
Use one supervision schedule.

Stage C · real evidence

Bookshelf.
Statue.
Chapel 1/320–1/500.

Minimum publishable evidence.

Repeat the synthetic sweep in float/14-bit RAW.
Win on a defined real-data class.
Remove large-splat artifacts visually.
Report aligned and unaligned metrics.
Report runtime, GS count, and failures.

11 · Sterkfontein Cave study

Cave transfer is not good enough yet.

D3: RGB-SVF is below Vanilla.
D5: Texture-GS wins; RGB-SVF is below Vanilla.
D6: RGB-SVF gives one positive result.
Lighting changes are stronger than a pure sensor-noise model.
No broad Cave claim yet.

D3 · 30k	PSNR	SSIM	LPIPS	Reading
Vanilla 3DGS	20.339	.6339	.5296	strong pixel baseline
Vanilla 2DGS	20.312	.6339	.5156	matched representation control
NTF + 2DGS	20.402	.6364	.5069	small gain
RGB-SVF + 2DGS	20.254	.6324	.5104	below Vanilla
Standalone Texture-GS	20.208	.6096	.4056	best LPIPS only

Factor-4 · 30k	Vanilla 2DGS	NTF 2DGS	RGB-SVF 2DGS	Texture-GS	Winner
D5 · proxy SNR 2.02 dB	14.409 / .23062 / .70422	14.421 / .23348 / .70832	14.156 / .22100 / .70926	14.639 / .22339 / .61827	Texture-GS
D6 · proxy SNR 5.54 dB	17.369 / .43477 / .48244	17.454 / .43371 / .49546	17.856 / .43373 / .47702	17.344 / .41638 / .43360	RGB-SVF

HDR+ targetD3 held out

Vanilla 3DGS20.339 dB

NTF 2DGS20.402 dB

Texture-GSLPIPS .4056

Current conclusion.

Cave is not the main positive benchmark.
D6 is encouraging, but not sufficient.
Keep Cave as a difficult generalization test.