Fernando Voltolini de Azambuja

Reflective display · color science · software

Prediction experiments and limits

Forecasts that succeeded in bounded cases, and tests of whether those successes carried to other patterns, returns and image regions.

Successful forecasts in defined tests

Predictions were saved before the new measurements. These are separate tests, not a pooled score or a learning curve. Each used a chosen ΔE00 limit of 1; that was an engineering criterion, not a universal visibility threshold.

Prospective prediction results
TestWhat succeededScope
Two full-screen patterns8 of 8 readings within the chosen limitTwo exact entries at the tested starting position.
One new four-color rasterTwo empirical forecasts each passed 4 of 4 readings; the area-only baseline passed 0 of 4.Four observations of one new pattern, not four patterns.
Alternative renderings of two target colorsThe saved output forecasts passed 8 of 8 readings.Forecast accuracy did not mean the output matched the desired color.

The detailed comparisons below distinguish new inputs, returns to familiar pixels, and regions inside images.

Testing forecasts on new measurements

Payload · what we send
The exact native-state pixel map, encoded for the display. A renderer or a test-pattern generator chooses these pixels.
Prediction · what we expect
A model's estimate of the color those pixels will produce under stated conditions. The models below predict XYZ color coordinates.
Measurement · what we observe
The light recorded by the meter: a spectrum, converted to color coordinates. This is what tests the prediction.

Different models can predict different colors for the same unchanged payload. Making a forecast does not change the pixels. The requested image color is a separate goal: we check both how well we predicted the output and how closely that output matches the goal.

In questions 1 and 2, prediction error means the ΔE00 distance between a saved forecast and a fresh measured color. Those two tests chose a limit of 1 before measurement, using nominal-D50 Lab. That is an engineering criterion for those tests, not a universal visibility threshold. Question 3 also checks distance from the requested color, labeled separately.

1 · Can we predict a construction's absolute color?

Why we tested it
Prediction-guided rendering needs an estimate of the absolute color its pixels will produce, not just whether two patterns will differ. Useful predictions must work on new inputs and remain useful when familiar patterns return.
What we saw
For 14 new colors measured twice, a model based on proportional departures from a simple native-color mixture reduced average prediction error from 6.73 to 2.69 ΔE00 compared with directly averaging measured colors. Yet each method met the chosen limit on only 2 of 28 readings. Both forecasts concerned the same unchanged pixels.
What it tells us
Modeling departures from a simple native-color mixture helped on average, but that average gain did not translate into reliable predictions for individual readings.
What the test did not establish
Reliable new-color prediction is not established. In a separate return test of six familiar patterns, the two near-neutral cyan maps were the largest movers. Their later-session means were 1.44 and 1.56 ΔE00 from their earlier-session means; the other four patterns were 0.32–0.99 ΔE00 away. The maximum pairwise separation among the cyan maps' six later-session readings was only 0.19–0.26 ΔE00. The sessions differed in chronology and setup, so this shows occurrence sensitivity without identifying its cause.

Inputs considered by the color models

Native-state contributionsWhich colors, in what proportions?
Spatial constructionArrangement, grouping, phase, and local context.
Display and measurement conditionsPrevious updates, timing, setup, and any environmental terms supported by tests.
Predicted absolute color: XYZ → LabCompare each fresh reading with its prediction. A spectral model can also predict the wavelength-by-wavelength response.

A working hypothesis about possible model inputs, not a validated recipe. Which arrangement and condition terms matter remains open. The empirical forecasts discussed here predict XYZ directly.

The direct model averages measured XYZ from nearby inputs. The ratio model averages how those measurements differ proportionally from a native-color estimate, then applies that ratio to the new input's estimate. The two approaches were compared with forecasts saved before the new readings. Neither changes the displayed pixels by itself.

2 · Does the prediction transfer into an image?

Why we tested it
Full-screen patterns help investigate particular dependencies, but ordinary images contain many constructions next to one another. A forecast that works on an isolated pattern may miss a region inside a picture.
What the methods use
Both methods use the proportions of native states in the same selected 64×64 digital region. The additive baseline weights measured native-state XYZ values by those proportions. The learned local model adjusts that estimate using how previously measured mixtures departed from their additive estimates. This tests prediction inside an image, rather than another uniform patch.
What we saw
In a test with forecasts saved before measurement, six selected regions from three previously unused images were each measured twice. The learned local model was closer than the additive baseline on all 12 readings, but neither method met the chosen limit on any reading.
What the test did not establish
Dependable image-region prediction is not established. The images were unchanged: this did not test improved rendering or whole-image quality, and it did not identify a physical cause.

3 · Can predictions help reproduce the requested image?

The practical goal is to use what we learn about the display to choose native pixels that bring measured colors closer to the image's requested colors, while preserving tone, detail, texture and edges.

A later fixed adjustment helped the warm color but worsened the neutral

In a rendering test of two target colors, a warm tone and a neutral gray, I used previous measurements to adjust the renderer's input. This was a fixed, case-specific adjusted rendering, not a general predictor choosing pixels.

Distance from the original desired color, in ΔE00. Each range covers four fresh readings; lower is closer.
Test colorBaseline renderingAdjusted rendering
Warm tone6.24–6.652.86–2.98Closer on every reading
Neutral gray5.51–5.876.17–6.51Farther on every reading

The adjusted rendering did not improve both colors. Its saved output forecasts also missed the chosen limit on all eight readings. Every adjusted result remained above the test's original-color error limit of 1. The warm improvement was useful, but it did not establish a dependable correction for other colors. This is a different arm from the alternative renderings in the summary above.

Both versions were compared with the same original desired color for each case. These patterned test patches did not test whole-image quality or establish the closest colors the display could reproduce. Inspect the readings and forecasts.

Predicting a color is not the same as reproducing it

A separate construction in that experiment had an accurate output forecast but still missed the desired color. Its forecast was saved before four fresh measurements; the first reading is shown here.

Original desired colorD50 XYZ: 16.485 · 15.565 · 7.728
Saved output forecastD50 XYZ: 14.107 · 12.417 · 5.240
First fresh measurementD50 XYZ: 14.291 · 12.578 · 5.426
Forecast ↔ measured outputΔE00 0.41Within the preset engineering limit of 1.
Requested ↔ measured outputΔE00 5.96Outside the same limit.

All four fresh readings told the same bounded story: forecast error was 0.38–0.47 ΔE00, while requested-color error was 5.81–5.96.

Four-reading warm-color test. Desired colors are image colors scaled to the panel's measured white: sRGB is converted to D50 XYZ, then scaled component by component so sRGB white maps to the measured native white. The requested color and saved forecast were fixed before the fresh measurements. Swatches are approximate sRGB previews computed from the printed D50 XYZ values; the numerical comparisons carry the result. This one construction explains the distinction between prediction and reproduction. Broadly improved reproduction remains open.

All four fresh readings

Fresh measurements in acquisition order
ReadingMeasured D50 XYZForecast errorRequested-color error
114.29114 · 12.57847 · 5.4260620.40895.9641
214.24502 · 12.54802 · 5.4226070.39145.9523
314.39455 · 12.68825 · 5.4772400.47115.8099
414.28953 · 12.60059 · 5.4362320.37925.8571

For prediction-guided rendering, forecast accuracy and requested-color accuracy answer different questions. Dependable prediction-guided reproduction across new images has not yet been demonstrated.

Prediction errors were not only a repeatability problem

In a separate image-history comparison, the readings agreed closely within each tested condition and across the selected preceding images, yet the learned model met its limit on only 2 of 18 readings and the additive baseline on none. A model can miss even when the measurements are relatively consistent.

The successful forecasts and relative improvements therefore do not establish reliable absolute-color prediction across the tested patterns, occurrences and image regions. The records leave several possible contributions unresolved; they do not show that every e-paper display is impossible to characterize.