cs.GRAug 28, 2026

What Will This Copper Look Like Later? Forecasting Surface Appearance and Rendering It as a PBR Material

Authors: Teejuta Sriwaranon, Borworntat Dendumrongkul, Tanapat Chamted, Pizzanu Kanongchaiyos

Organizations: Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand · Faculty of Information Technology, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

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Abstract

Digital design requires predicting how a metal surface will look later in its oxidation; this paper presents such a pipeline for copper. Given a fixed-camera observation, the system forecasts appearance 10 accelerated units ahead and converts it into the albedo, normal, roughness and metallic maps a renderer consumes. Forecasting is evaluated as an authoring tool would use it, on a copper specimen the system has not observed: an entire recording is held out, so training and checkpoint selection use one specimen and the test set is the whole of a second, recorded on a different day and condition. Under this protocol a learned spatio-temporal model with a monotone oxidation state, the most accurate forecaster within a single recording, is less accurate than copying the last observed frame on an unseen specimen, in both directions, as are three further trained architectures. The only forecaster that transfers is a closed-form global color extrapolation with no trained parameters, improving on copy-last-frame by 13.4% and 50.6%, with a margin that increases with horizon to +16.7% and +55.5% at t+10. Two controls qualify this: correcting every frame for the photometric drift measured on a non-oxidizing reference region leaves both margins intact, ruling out uncontrolled exposure as their source, and a moving-block bootstrap over the 6 independent windows each recording contains separates the larger margin from zero but leaves the smaller one not individually significant. The mechanism is measured: a learned susceptibility map encodes where corrosion begins on the training specimen and misleads on a new one, whereas the global color trajectory is what specimens share. The pipeline therefore deploys the closed-form forecaster for unseen specimens and the learned model only for continuing one already observed. Code, splits, protocol and leakage audit are released.

Figures & tables

Sourcet+1t{+}1t+5t{+}5t+Kt{+}Kmeanvs. persist. (%)
chamber →\rightarrow air
Persistence (copy last)3.42 e-51.71 e-44.58 e-42.14 e-40.00.0
affinergb3.22 e-51.54 e-43.81 e-41.85 e-4+13.4+13.4
patinanet4.21 e-52.31 e-46.93 e-43.06 e-4−43.2-43.2
predformer [ 16 ]1.21 e-49.54 e-44.92 e-44.28 e-4−100.0-100.0
convlstm [ 10 ]5.00 e-56.71 e-42.27 e-39.51 e-4−344.5-344.5
Table 1: Forecasting a copper specimen the model has never seen. Training and checkpoint selection use one recording; the test split is the entire other copper recording – a different specimen under a different condition. MSEfg\mathrm{MSE}_{\mathrm{fg}} ( ↓\downarrow ) at t+1t{+}1 , t+5t{+}5 , t+Kt{+}K and averaged over the horizon; the last column is the mean improvement over copying the last frame.
Figure 1: What the pipeline produces on a specimen it has never seen, followed far enough for the change to be visible. Over the evaluated horizon t+10t{+}10 this copper moves only 1.2%1.2\% of full scale, which the noise-calibrated metric resolves but the eye does not. By t+85t{+}85 it has moved 7.8%7.8\% and the darkening is obvious. Columns marked ∗ are extrapolation well beyond the horizon any model here was trained or evaluated for, and are shown to make the phenomenon legible and to expose the long-range behavior discussed in Section 8 , not as evidence of accuracy there. Where to look at t+10t{+}10 : the change is concentrated on the upper half of the plate, around the base of the mounting rod, where a gold-brown cast appears before the rest of the face darkens. The violet fringe along the upper-right edge and the overall shift toward deep red belong to the starred columns and are not present at the evaluated horizon.
Figure 2: The reverse transfer direction: trained on the open-air specimen, forecasting the chamber one. Same layout as Figure 1 , and the same caveat on the starred columns. Reporting both directions matters because the two recordings differ in difficulty (the open-air one is roughly three times noisier), and a single direction could be read as a property of one specimen rather than of the method. Where to look at t+10t{+}10 : the earliest visible change is on the lit left band of the plate, which warms toward orange, while the shadowed right half darkens slightly. The blue-black cast that dominates the right half in the starred columns is well beyond the evaluated horizon.
Figure 3: Forecast error against horizon on the held-out copper specimen, log scale, with the copy-last-frame reference pinned. Left and right are the two transfer directions.
Figure 4: The forecaster is not tracking the camera. Left: mean RGB of the specimen (solid) and of a non-oxidizing reference region — neutral backdrop, eroded away from the specimen and its mount — over each whole recording. In the chamber the reference is flat to 0.0010.001 while the specimen moves 0.1280.128 ( 105×105\times ); in open air the reference brightens by 0.0260.026 against a specimen change of 0.1190.119 . Right: affinergb ’s improvement over persistence before and after every frame is corrected for the drift measured on that reference region, with 95%95\% moving-block bootstrap intervals over the 66 independent 140140 -frame blocks each recording contains. The advantage survives correction in both directions.
Design decisionchamber →\rightarrow airair →\rightarrow chamber
context frames observed before forecasting
n=3n=32.19 e-47.38 e-5
n=5n=5 †1.72 e-45.43 e-5
n=7n=71.66 e-44.82 e-5
n=10n=101.43 e-44.68 e-5
persistence reference ( n=5n{=}5 windows)2.06 e-41.07 e-4
Table 2: Characterizing the shipped forecaster on the held-out specimen, MSEfg\mathrm{MSE}_{\mathrm{fg}} ( ↓\downarrow ), both transfer directions. One axis varies per block; †\dagger marks the configuration used everywhere else in this paper. Nothing here is trained, so the whole sweep is a few minutes of forward passes. The sweep samples 60 windows per configuration and the usable window set shifts with the context length nn , so the persistence references here differ slightly from Table 1 , which averages every test window at n=5n{=}5 .
Figure 5: Why the learned forecaster does not transfer. Left: the susceptibility map ρ(x)\rho(x) the model uses to decide where corrosion grows. Right: where that specimen actually changed, measured directly from its frames. On the specimen the model was trained on, ρ\rho tracks the real pattern ( r=0.68r=0.68 ). On the held-out specimen it is uncorrelated ( r=0.00r=0.00 ). Note the two specimens also differ in pose and framing, so this is evidence that a fitted spatial prior does not transfer, not that nucleation chemistry is unlearnable.
 +5+5+10+10+20+20+50+50
Texture sourceF LIPLPIPSF LIPLPIPSF LIPLPIPSF LIPLPIPS
affinergb0.2530.2080.2300.1630.2440.1880.3110.220
patinanet0.3280.2890.2770.1950.2610.1890.2440.185
Static control (canvas only)0.4450.3800.4530.3880.4320.3630.3410.289
Table 3: Rendering the forecast on the held-out specimen. F LIP and LPIPS ( ↓\downarrow ) between renders driven by predicted textures and renders driven by the true future frames, identical geometry and lighting. The static control is the conventional time-invariant material; both forecasters beat it at every horizon on both metrics.

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