RAW-Noise Reconstruction · Maintained Experiment Record

NTF works. Textured Gaussians raise the ceiling.

At matched 30k pre-training + 7k texture refinement, NTF-TG reaches 31.561 dB on calibrated ×64 RAW noise—1.484 dB above the standard Textured Gaussians pipeline.

31.561 dBNTF-TG at the matched 37k checkpoint

+1.484 dBover Standard Textured Gaussians

30kfinal textured primitives

Held-out view ×64 noise

Clean targetheld out

Vanilla 3DGS185,472 GS

PSNR26.110

SSIM.839

LPIPS.257

NTF-v1175,689 GS

PSNR27.779

SSIM.868

LPIPS.180

Best NTF-TG render with fixed display ISP

NTF-TGcurrent best

PSNR31.618

SSIM.893

LPIPS.092

Foundation and current ceiling. The visual row records the original NTF-v1 3DGS evidence: +1.669 dB over Vanilla at ×64. The new matched-budget result shows that inserting NTF into the standard Textured Gaussians pre-training stage adds a further +1.484 dB over Standard TG.

02 · How NTF works

Match the loss to RAW sensor uncertainty.

NTF is an analytic training objective, not a learned denoiser. It uses the calibrated shot/read-noise model to reduce unreliable dark residuals while keeping useful gradients and structural supervision.

Camera-linear observationNoisy RAW-derived target I and Gaussian render R

Noise varianceσ²(x) = a·x + r² from shot and read noise

Adaptive transfer TContinuous two-slope asinh; lower sensitivity below 10 dB SNR

SNR confidence wDark, uncertain pixels contribute smoothly less, without a hard binary mask

Gaussian updateConfidence-weighted L1 + transformed-domain SSIM

1 · Sensor noise and notation

I = observed camera-linear target, R = Gaussian render, σ²(Y) = aY + r²

Y is linear luminance; a is the calibrated shot-noise coefficient; r is the calibrated read-noise standard deviation. The same fixed parameters are used for every pixel and view.

2 · Target-SNR transition

τ = 10^10/20, x_τ = ½[τ²a + √(τ⁴a² + 4τ²r²)], x_τ ← clip(x_τ, x_min, 1)

x_τ is exactly the signal level where x/√(ax+r²) reaches the chosen 10 dB SNR. Below it, the loss becomes less sensitive to unreliable intensity changes.

3 · Normalized asinh coordinate and slopes

x_min = 1/(2¹⁴−1) = 1/16383, u(x) = asinh(x/x_min)/ln2

u_τ=u(x_τ), u_max=u(1), ρ=0.125, s_high=1/[ρu_τ+u_max−u_τ], s_low=ρs_high

16383 is the maximum integer value of a 14-bit RAW signal. The slope normalization makes T(1)=1. We originally considered log, but asinh(x/x_min)≈x/x_min near zero: it is locally linear and keeps a finite, non-zero gradient at black, whereas log requires clamping and gives unstable or dead gradients there.

4 · Complete two-slope transfer

T(x) = s_low·u(x)if x ≤ x_τ s_low·u_τ + s_high·[u(x)−u_τ]if x > x_τ

The low-SNR branch has one eighth of the high-SNR slope. The two branches meet continuously at x_τ; there is no hard intensity cutoff.

5 · Per-pixel confidence

Y(I)=0.2126I_R+0.7152I_G+0.0722I_B, SNR(I)=Y(I)/√[aY(I)+r²+ε]

w(I)=clip[SNR(I)/τ, 0, 1]^γ, γ=1

Confidence is computed from the noisy target, detached from backpropagation, and shared by its three color channels. It rises smoothly from zero to one as the observation reaches the target SNR.

6 · Final NTF objective

L_data = Σ_p,c w_p|T(R_p,c)−T(I_p,c)| / [3Σ_pw_p+ε]

L_NTF = 0.8·L_data + 0.2·{1−SSIM[T(R),T(I)]}

The first term suppresses unreliable low-SNR residuals; transformed-domain SSIM keeps spatial structure. Both the render and target pass through exactly the same analytic transform.

WHY 01

Noise no longer dominates dark regions

The transform and confidence jointly reduce the optimization pressure to explain random low-SNR fluctuations as persistent scene content.

WHY 02

Gradients remain alive at black

Unlike a clamped logarithm, asinh has a finite non-zero derivative at zero, which matters when SfM initializes Gaussian color near black.

WHY 03

Reliable structure is retained

Higher-SNR pixels keep the steeper branch, while transformed-domain SSIM preserves spatial structure instead of reducing the objective to pixelwise smoothing.

What changes—and what does not. NTF changes only the training loss. It requires no clean target, no pre-trained denoiser, and no test-time module. In NTF-TG it forms the robust pre-trained backbone; standard linear texture refinement then recovers local high frequency.

03 · Current position

Separate supervision from representation.

The same ×64 Sharpshadow split reveals two consistent effects: noise-aware pre-training improves each compatible backbone, and local texture capacity raises the reconstruction ceiling.

Supervision / training	3DGS	2DGS	Textured Gaussian
Noisy input directly	26.110	28.221	30.077 30k+7k
Conservative multi-view teacher	27.935	28.889	30.763 30k+7k
NTF throughout	27.779	29.142	31.181 30k+7k
NTF pre-training → linear texture	—	—	31.561 30k+7k

ROBUSTNESS

NTF remains the causal core

Within 3DGS, NTF-v1 gains +1.669 dB over Vanilla. Within the planar backbone, NTF-2DGS gains +0.921 dB over Raw 2DGS.

CAPACITY

Texture restores appearance frequency

Relative to NTF-2DGS, matched 7k texture refinement adds +2.419 dB and visibly restores part of the tree’s internal variation.

LIMIT

Leaf geometry is still missing

The tree silhouette remains a large blob. Texture improves appearance on the learned support; it cannot recover absent depth and occlusion boundaries.

04 · NTF + Textured Gaussians

Use the repository’s standard two-stage pipeline.

Textured Gaussians are officially optimized through 2DGS pre-training followed by texture refinement. We change the first-stage photometric objective—not the representation or training scaffold.

COLMAP / SfM seed15.5k points on the controlled Sharpshadow split

30k NTF pre-trainingplanar Gaussian backbone, MCMC growth to a 30k cap

7k linear texture refinementstandard RGB+alpha texture objective; topology growth disabled

NTF-TG31.561 PSNR · .8939 SSIM · .0927 LPIPS

Matched 37k method	Stage 1	Stage 2	PSNR ↑	SSIM ↑	LPIPS ↓
Standard Textured GS	Linear	Linear	30.077	0.8882	0.0955
NTF-TG Full	NTF	NTF	31.181	0.8886	0.1098
NTF-TG	NTF	Linear	31.561	0.8939	0.0927

Tone-mapped clean target, NTF 2DGS, NTF full texture, and NTF initialization with linear texture refinement — **Fixed tree-region comparison · shared display ISP**Texture recovers internal appearance frequency; metrics remain camera-linear.

Method naming. “NTF-TG” is accurate: 2DGS pre-training is the standard optimizer warm-up of Textured Gaussians, not an additional proposed representation. The final model is Textured Gaussians.

05 · Controlled setting

Isolate reconstruction from pose failure.

The synthetic sweep changes only calibrated sensor noise. Every method and noise level shares the same clean PINHOLE COLMAP solution.

Bayer RAWRawNeRF Sharpshadow

→

Poisson–Gaussiancalibrated shot + read noise

→

Linear RGBdemosaic + f4 downsample

Fixed poses31 noisy train / 5 clean test

CONTROL

x0 / x4 / x16 / x64

The multiplier scales calibrated Poisson–Gaussian variance, not a fixed RGB Gaussian standard deviation.

CAUSAL QUESTION

What does noise do to GS?

With pose held fixed, degradation can be attributed to appearance optimization, geometry, and densification.

KNOWN LIMITATION

Current storage is 8-bit

Noise is injected before demosaicing, but the current model input is quantized linear RGB. The definitive sweep should retain float RAW-derived values.

Why not Dark3R SfM here? Re-estimating poses at each noise level would confound pose and reconstruction. Dark3R SfM belongs in the real low-light benchmark, with a separate optional synthetic pose stress test.

06 · Noise sweep

The advantage emerges as noise increases.

Confidence-weighted NTF is the safest current backbone, but low-noise compatibility is not fully solved. The main validated regime is strong noise.

PSNR change versus Vanilla

Confidence-linear candidate, 30k iterations. Single-seed values; final claims require three seeds.

x0

−0.11 dB

x4

−0.95 dB

x16

+0.54 dB

x64

+1.22 dB

Noise	Vanilla	Confidence NTF	Δ PSNR
x0	27.990	27.880	−0.110
x4	28.269	27.321	−0.948
x16	27.712	28.253	+0.541
x64	26.110	27.331	+1.221

Clean targetview 00004

Vanilla

Confidence NTF

Current conclusion. The method should be scoped around strong noise. The final design must be identity-like at x0/x4, begin improving at x16, and retain the clear x64 advantage without per-level hand tuning.

07 · Remaining failure

Better denoising does not guarantee correct geometry.

NTF suppresses noisy supervision, but weak real gradients can be suppressed with it. Fine foliage remains under-reconstructed and can collapse into large, view-stretched splats.

Clean targetfine branches + foliage

Vanilla ×64noise fitting + unstable detail

NTF-v1 ×64cleaner, but still blurred

Strong noise

unreliable photometric gradients

→

Over-suppression

real weak edges resemble noise

+

Wrong densification

missing support or false splats

Interpretation. The x64 result validates the noise-aware objective, but the visible tree artifact prevents a “solved” claim. Geometry and appearance must be diagnosed separately.

08 · Oracle diagnosis

The failure is both appearance and geometry.

Two frozen-geometry oracles separate what was learned from noisy appearance supervision from what was irreversibly lost during geometry optimization.

Clean targetfixed display ISP

Clean geometry and x64 appearance oracle

Clean geometry + ×64 appearanceOracle 1

Global24.418

Tree ROI20.435

Tree grad26.271

x64 geometry and clean appearance oracle

×64 geometry + clean appearanceOracle 2

Global26.527

Tree ROI22.596

Tree grad27.943

Tree failure

observed artifact

=

Appearance suppression

clean supervision recovers +2.11 dB

+

Geometry deficiency

the large blob remains after clean appearance

Scientific conclusion. Appearance-aware supervision is necessary, but not sufficient. The remaining blob is direct evidence that densification and spatial support must also change.

09 · What we learned

Loss-only and hard densification fixes are insufficient.

The search has already eliminated several tempting explanations and narrowed the next method to a noise-aware appearance objective plus soft, budget-aware persistence.

Adaptive NTFstrong x64 objective

PSNR28.072

SSIM.870

GS198k

VST-wavelet teacherbest specialized x64 run

PSNR28.132

Tree ROI24.336

GS229k

Hard persistence gaterejected

PSNR21.278

Tree ROI19.087

GS52.6k

01

Confidence is the safest backbone

It nearly preserves x0 and becomes useful at x16/x64, but x4 compatibility still needs an identity-like gate.

02

A denoised teacher helps appearance

VST-wavelet improves tree-region pixels, yet the large geometric artifact remains.

03

Hard persistence under-densifies

Four-view binary rejection prevents false growth and real growth together. Persistence should be a soft score with a GS-growth budget.

Next design. Use NTF-TG as the single primary representation. First isolate texture with frozen geometry and RGB-only texture; then allocate texture capacity only to cross-view-consistent appearance detail while routing missing geometric detail to a separate densification study.

10 · Research story

Noise-aware pre-training, detail-safe texture refinement.

The controlled result now supports a compact story: NTF prevents strong RAW noise from corrupting the Gaussian backbone; standard texture refinement then restores local high frequency without asking the robust transform to preserve every weak detail.

Track A · Core method

calibrated RAW noise→NTF pre-training→texture refinement

Standard Textured Gaussian optimization with one controlled change: noise-aware formation of the pre-trained backbone.

Track B · Real extreme low light

14-bit RAW→Dark3R pose→depth + confidence

The official Dark3R dataset supplies the real-noise benchmark and a strong Dark3R-NeRF target.

Calibrated RAW residualshot/read-noise-aware NTF supervision

NTF backbone formationrobust planar geometry, opacity, and SH

Stop topology growthstandard Textured GS refinement schedule

Detail-safe texturelinear RGB residual on reliable local structure

NTF-TGstrong-noise reconstruction with local detail capacity

Target: retain NTF robustness while matching high-frequency structure with one Textured Gaussian representation.

Standard TGVanilla 3DGSAbsGSSAD-GSRaw3DGS-styleDark3R-NeRFNTF-TG