Oracle headroom without signal: null-calibrated evaluation of candidate selection for thermal heart rate estimation

• Earlier work used oracle gains to motivate richer quality models and larger candidate banks, although inflated gaps can direct effort toward nonexistent headroom.The introduction cites a respiratory study in which oracle MAE fell from 3.03 to 0.44 breaths/min on OMuSense-23 [1].Source: §1 · p. 1
• When K candidates fall within a plausible physiological range, one can land near the reference by chance, even if none contains information about it.Because spectral peak estimators return frequencies inside their passband, a band-limited candidate bank is plausible by construction.Source: §1 · p. 1
• Regional temperature averages had weak cardiac agreement in prior thermal monitoring, motivating an explanation before interpreting a large oracle gain as headroom.Thermal cardiac pulses have been recovered from superficial vessels under controlled acquisition.Source: §1 · p. 1
• The study models uninformed oracle error with an order statistic, measures error across candidate counts, and compares matched null banks with real thermal signals.Its null ladder ranges from white noise to a donor thermal signal, and the evaluation compares errors at equal candidate count K.Source: §1 · p. 1, Figure 1 · p. 1

• Thermal pulse studies analyze superficial-vessel temperature variation, pulsatile temperature modulation, or cardiac-ejection head movement, while regional means average over local effects.Other work estimates heart-rate variability from one-minute facial-temperature features, and iBVP provides synchronized RGB, thermal, and ear PPG recordings.Source: §2 · pp. 1–2
• Quality-aware studies use SQIs and learned mappings from quality to error, but their oracle comparisons do not test candidate banks without reference information [1].Source: §2 · p. 2
• Selection bias, permutation tests, and order statistics motivate rerunning data-dependent processing and respecting repeated-participant structure when calibrating candidate selection.The paper applies this reasoning to per-window rate estimates while keeping candidate count and processing fixed under the null.Source: §2 · p. 2

3.1. Selection comparators

• The oracle is a lower bound for selectors choosing among K candidates, while the reported gap G = Lfix − Lor compares it with a best fixed setting selected retrospectively.Source: §3.1 · p. 2

3.2. Oracle error without information

• At K = 168, the uniform-range model gives 0.40 bpm, and its error falls below the 8.61 bpm constant predictor at K = 7.The 1/K reference curve is not a bound: dependence reduces effective draws, while concentration near typical rates can increase the chance of a close match; the uniform equivalent count Ku summarizes a measured bank.Source: §3.2 · p. 2

3.3. Matched nulls

• The null-calibrated gain ∆K compares oracle error on a real bank with a same-K null bank processed on the same windows; positive gain indicates information beyond selection opportunity.The null ladder preserves progressively more signal properties, from none in white noise to thermal dynamics in donor signals without reference alignment.Source: §3.3 · p. 2

Data

• The analysis uses 96 thermal recordings from 24 participants, divided into 6,816 overlapping 10-second windows with ear PPG as the reference.The first 80 seconds of each recording are divided into windows with a 1-second hop; the reference rate is the Welch peak of detrended PPG filtered between 0.75 and 3.00 Hz.Source: §4 · p. 2

Candidate bank

• The candidate bank combines seven signals, two detrending orders, three bandpass settings, and four estimators, yielding 168 candidates.Signals include six fixed facial-region means and an EfficientPhys output; estimates outside 45–180 bpm or non-finite estimates are invalid, so candidate coverage can differ.Source: §4 · p. 2

Selectors and nulls

• Twelve individual signal-quality indices are tested as selectors alongside a constant predictor that outputs the 74.6-bpm mean reference.The indices include periodicity, spectral measures, signal-to-noise ratio, and statistics of facial-signal variation.Source: §4 · p. 2

Analysis and nulls

• For candidate-count analysis, 300 random subsets are sampled at each K below 168, and windows with under 30% valid candidates are removed.Four null signals pass through the 24 settings of one signal to form K = 24 banks; the donor is usually another condition from the same participant.Source: §4 · p. 3

5.1. Selection levels

• 0.91 bpm oracle MAE compares with 10.74 bpm for the best fixed setting, 18.03 bpm for the best SQI, and 8.61 bpm for the constant predictor; SQI rejection tracks random rejection.Only rejection using true error substantially reduces MAE; the oracle-to-fixed gap is 9.83 bpm.Source: Table 1 · p. 3, §5.1 · p. 3, Figure 2 · p. 3

5.2. Oracle error against candidate count

• 27.38 bpm at K = 1 falls to 7.85, 4.65, 2.82, and 0.91 bpm at K = 5, 10, 20, and 168, respectively.The measured oracle follows the uninformed curve closely; at K = 10, the gap is 9.43 bpm, 96% of the full-bank gap.Source: Figure 3 · p. 3, §5.2 · p. 3

5.3. Matched nulls

• 4.62 bpm for the donor thermal signal nearly matches the real forehead signal’s 4.61 bpm oracle error at K = 24.Real regions range from 4.19 to 5.30 bpm, while white and shuffled signals reach 11.34 and 11.05 bpm; thermal spectral shape and dynamics reproduce the improvement without temporal correspondence.Source: §5.3 · p. 3, Table 2 · p. 4

5.4. Thermal signal diagnostics

• 45.0–52.1 bpm is the dominant thermal peak range, while the reference varies from 69.9 to 85.5 bpm; regional estimates are uncorrelated with the reference.Lags up to 30 seconds and reducing frame rate from 30 to 7.5 Hz do not recover agreement, while the respiratory-band positive control favors matched recordings in 15 of 20 cases (Wilcoxon p = 0.021).Source: §5.4 · pp. 3–4, Table 3 · p. 4

6. DISCUSSION

• 0.91 bpm is the oracle MAE, but the 9.83 bpm gap is explained by candidate multiplicity and thermal drift within the passband, not recoverable cardiac content.A signal adds to the oracle only through ΔK; multiplicity adds the rest.Source: §6 · p. 4
• A bandpass filter on 1/f thermal drift can produce a narrowband oscillation near its lower cutoff, which periodicity-focused SQIs may favor over candidates close to the reference.The proposed explanation is untested, and a learned mapping from quality to error may behave differently.Source: §6 · p. 4
• Oracle reports should state candidate count and formation, comparator coverage, matched-null error at the same K and windows, and selectors and predictors chosen on training participants.The matched null can reuse existing processing on donor signals.Source: §6 · p. 4
• The calibration is inexpensive because ΔK reuses the candidate table without model training, and the order-statistic check applies to passband-confined RGB, radar, or WiFi rate-estimator banks.An oracle MAE not clearly below (b − a)/(2(K + 1)) is not by itself evidence of information in the candidates.Source: §6 · p. 4
• The matched null used 24 settings rather than the full 168-candidate bank, comparator coverage differed, and participant-level confidence intervals were not reported.Findings are limited to fixed rectangles on resized crops, one adapted learned model, and one dataset; they do not exclude local vascular information lost by averaging.Source: §6 · p. 4

7. CONCLUSION

• 0.91 bpm was the oracle MAE for 168 thermal candidates per window, yet every rule without the reference performed worse than a constant predictor.The oracle curve followed an order-statistic model of uninformed guesses, and a donor thermal signal matched the real one at equal candidate count.Source: §7 · p. 4
• Low oracle error does not establish recoverable physiological information or attainable selector accuracy.The matched null was evaluated at equal candidate count.Source: §7 · p. 4
• Oracle bounds become interpretable when reported with candidate count, valid coverage, and a matched null evaluated under the same processing.Future work will apply the protocol to iBVP RGB recordings and extend the matched null to the full bank with donors from other participants.Source: §7 · p. 4

COMPLIANCE WITH ETHICAL STANDARDS

• The analysis was retrospective and used human-subject data from the iBVP dataset.The dataset was obtained from its authors under their data access agreement.Source: COMPLIANCE WITH ETHICAL STANDARDS · p. 5
• The data were obtained under the iBVP data access agreement.Source: COMPLIANCE WITH ETHICAL STANDARDS · p. 5
• Ethical approval was not required for this secondary analysis, as confirmed by the data license.Source: COMPLIANCE WITH ETHICAL STANDARDS · p. 5