Property-Specific Recoverability from Contact PPG to Camera rPPG under Heterogeneous Observation Conditions

Timothy Oladunni; Farouk Ganiyu-Adewumi

Figure 1: Conceptual Framework for Property-Specific PPG-to-rPPG Recoverability. Contact PPG is transformed through a heterogeneous camera observation pathway, and recoverability is evaluated separately for physiological properties. Population-level plausibility does not by itself establish recording-specific correspondence.

Table 1 \| Research Questions, Empirical Tests, and Principal Findings Each row maps a research question to the mathematical or statistical analysis used to evaluate it and the principal empirical conclusion. Detailed effect estimates and uncertainty measures are reported in the corresponding Results tables.
RQ	Research question	Empirical test	Empirical answer
RQ1	How accurately is heart rate recovered from contact PPG after transformation to camera-derived rPPG under the fixed observation pathway?	Endpoint discrepancy $D_{HR}=\|HR^{(p)}-HR^{(r)}\|$ summarized by MAE, RMSE, MAPE, signed error, and Pearson correlation.	Limited HR recovery under the evaluated observation pathway. MAE=15.26 bpm and $r=0.0801$ , indicating substantial endpoint error and weak recording-level association (Table 2 ).
RQ2	Which conventional temporal, spectral, and recurrence properties retain recording-specific correspondence between matched PPG and rPPG?	Property-specific matched-versus-shuffled structural correspondence for ACF similarity, cardiac-band PSD distance, and recurrence-rate difference (Algorithm 1); determinism assessed for discriminative variability.	Selective recording-specific structural correspondence. ACF showed a modest matched advantage, whereas PSD and recurrence-rate differences provided little matched-versus-shuffled separation. Determinism was non-discriminative under the implemented parameterization (Table 3 ).
RQ3	Is maximal Lyapunov exponent ( $\lambda_{\max}$ ) preserved as a recording-specific dynamical property across matched PPG–rPPG recordings?	Study-specific $\hat{\lambda}_{\max}$ estimation and paired discrepancy (Algorithm 2), followed by recording-specific correspondence and a 10,000-permutation condition-preserving subject-permutation null test (Algorithm 1).	No detectable recording-specific dynamical correspondence. Despite population-level dynamical plausibility, matched PPG–rPPG estimates were essentially uncorrelated ( $r_{\lambda}=0.0231$ ), and the observed association was not distinguishable from the condition-preserving subject-permutation null (Table 4 ).
RQ4	Which measured observation factors are associated with endpoint and dynamical discrepancies, and are the heterogeneity patterns property-specific?	Subject-aware mixed-effects models for $D_{HR}$ and $D_{\lambda}$ , with Fitzpatrick group, lighting, motion/activity, interaction block tests, and aggregate RGB-SNR sensitivity analysis (Algorithm 3).	Observation-associated discrepancy was property-specific. $D_{HR}$ varied substantially with motion/activity and Fitzpatrick group, including evidence of a Fitzpatrick $\times$ motion interaction, whereas $D_{\lambda}$ showed a different heterogeneity pattern with little Fitzpatrick- or lighting-associated variation. Aggregate RGB SNR did not materially account for the endpoint heterogeneity (Tables 6 – 11 ).
RQ5	To what extent can measured observation context reduce the PPG–rPPG endpoint discrepancy, as measured by MAE, on unseen subjects?	Subject-disjoint nested-information prediction with linear, ridge, and random-forest learners; out-of-fold MAE and subject-level bootstrap $\Delta MAE$ relative to the rPPG-HR-only calibration model (Algorithm 4).	Partially. Motion and lighting reduced subject-held-out MAE beyond rPPG-HR-only calibration across linear, ridge, and random-forest learners. At $M_{2}$ , MAE was reduced by 13.32%, 13.32%, and 12.77%, respectively, relative to each learner’s $M_{0}$ baseline. Adding Fitzpatrick group or aggregate RGB SNR provided no further improvement, and residual error remained substantial (Figure 8 ).

Table 2

Table 2 \| Fixed camera-rPPG observation benchmark on the 655 available MMPD recordings. Heart rate from the fixed camera-rPPG observation pathway is compared with reference HR derived from synchronized contact PPG. MAE, RMSE, and MAPE quantify absolute endpoint error; Pearson $r$ quantifies recording-level linear correspondence; mean signed error indicates systematic underestimation when negative. The benchmark is used as an implementation and endpoint-recoverability check rather than as an optimization result.
Metric	Fixed camera-rPPG observation benchmark
Available recordings	655
MAE	15.26 bpm
RMSE	20.81 bpm
MAPE	17.97%
Pearson r	0.0801

Table 3

Table 3 \| Matched-versus-shuffled structural recoverability analysis. Matched PPG–rPPG property correspondence is compared with a shuffled-pair null distribution to distinguish recording-specific preservation from cross-recording similarity. Larger matched-versus-shuffled separation indicates stronger evidence of recording-specific structural correspondence.
Metric	Matched	Shuffled	Matched-shuffled interpretation
ACF similarity	0.2863	0.2440	+0.0422; modest recording specificity
PSD distance	0.0515	0.0524	-0.0009; marginal
Recurrence-rate difference	0.0246	0.0263	-0.0017; marginal
Determinism	1.000	1.000	Non-discriminative; excluded

Table 4

Table 4 \| Recording-specific maximal-Lyapunov correspondence test. Pearson correlation quantifies matched recording-level correspondence between valid contact-PPG and camera-rPPG maximal-Lyapunov estimates. The confidence interval and permutation test assess whether the observed correspondence differs detectably from zero and from correspondence expected under disrupted pairing.
N matched	r_lambda	95% CI	Pearson p	Permutation p
645	0.0231	[-0.0542, 0.1001]	0.5579	0.5584

Table 5

Fitzpatrick	Subjects	N	Mean $D_{HR}$	Median $D_{HR}$	Mean $D_{\lambda}$	Median $D_{\lambda}$
III	16	315	11.43	8.79	0.8187	0.6238
IV	4	75	18.01	15.82	0.8082	0.7274
V	6	119	18.29	16.70	0.8016	0.6058
VI	6	116	20.64	18.46	0.8246	0.6801

Table 6

Table 6 \| Subject-aware Model 1 Fitzpatrick contrasts for endpoint discrepancy. Estimates are adjusted differences in absolute PPG–rPPG HR discrepancy ( $D_{HR}$ ), in beats/min, relative to Fitzpatrick III after adjustment for lighting and motion/activity, with a subject-specific random intercept. Positive estimates indicate larger endpoint discrepancy than the Fitzpatrick III reference group.
Contrast	Estimate (bpm)	95% CI	p
IV vs III	+6.37	[-0.12, 12.87]	0.051
V vs III	+6.72	[1.19, 12.25]	0.017
VI vs III	+9.32	[3.78, 14.86]	0.001

Table 7

Figure 2: Heterogeneous recoverability of endpoint and dynamical quantities across Fitzpatrick groups. (A) Distribution of absolute PPG–rPPG heart-rate discrepancy,

D_{HR}

, across Fitzpatrick groups. (B) Distribution of absolute maximal-Lyapunov discrepancy,

D_{\lambda}

. (C) Subject-aware adjusted Fitzpatrick contrasts for

D_{HR}

relative to Fitzpatrick III after adjustment for lighting and motion/activity. (D) Corresponding adjusted contrasts for

D_{\lambda}

. The endpoint discrepancy increases from Fitzpatrick III toward higher-numbered Fitzpatrick groups, whereas the tested dynamical discrepancy does not exhibit the same gradient. Error bars in C–D denote 95% confidence intervals; contrasts are relative to Fitzpatrick III. Panels A–B are unadjusted distributions, whereas C–D are estimates from subject-aware mixed-effects models adjusted for lighting and motion/activity. Fitzpatrick analyses include 625 recordings from 32 subjects after exclusion of the subject with inconsistent Fitzpatrick-group metadata. The contrast between the endpoint and dynamical panels is interpreted as property-specific heterogeneity, not as evidence that nonlinear dynamics are preserved.

Table 7 \| Subject-aware Model 2 Fitzpatrick contrasts for dynamical discrepancy. Estimates are adjusted differences in absolute PPG–rPPG maximal-Lyapunov discrepancy ( $D_{\lambda}$ ) relative to Fitzpatrick III after adjustment for lighting and motion/activity, with a subject-specific random intercept. Confidence intervals and $p$ -values quantify uncertainty in the adjusted contrasts.
Contrast	D_lambda estimate	95% CI	p
IV vs III	-0.006	[-0.224, 0.212]	0.955
V vs III	-0.017	[-0.202, 0.167]	0.856
VI vs III	+0.003	[-0.183, 0.188]	0.980

Table 9

Figure 3: Acquisition-condition dependence of endpoint and dynamical recoverability. Mean

D_{HR}

and mean

D_{\lambda}

are shown across lighting conditions (A–B) and motion/activity conditions (C–D). The two discrepancy measures do not vary in parallel across acquisition conditions, motivating property-specific rather than single-metric characterization of PPG-to-rPPG recoverability. Bars summarize observed condition-specific means from the analysis.

D_{HR}

is expressed in beats/min, whereas

D_{\lambda}

is dimensionless under the estimator used; their numerical magnitudes are therefore not directly comparable across axes. The panels are intended to compare patterns across conditions, are descriptive, and should not be interpreted as causal effects.

Table 8 \| Joint Wald tests of prespecified Fitzpatrick-by-observation-condition interaction blocks. A significant block test indicates heterogeneity of the condition effect across Fitzpatrick groups; nonsignificant blocks are not interpreted from individual cell means alone.
Outcome and interaction block	df	Wald $\chi^{2}$	p
$D_{HR}$ : Fitzpatrick $\times$ Motion	12	28.789	0.004234
$D_{HR}$ : Fitzpatrick $\times$ Lighting	9	9.970	0.352900
$D_{\lambda}$ : Fitzpatrick $\times$ Motion	12	9.468	0.662521
$D_{\lambda}$ : Fitzpatrick $\times$ Lighting	9	8.534	0.481370

Table 11

Figure 4: Adjusted Fitzpatrick-by-motion heterogeneity in endpoint recoverability. Population-level adjusted mean absolute PPG–rPPG HR discrepancy (

D_{HR}

) from the subject-aware Fitzpatrick

\times

motion model is shown across motion/activity conditions. The nonparallel profiles visualize the significant joint interaction block (Wald

\chi^{2}(12)=28.789

,

p=0.004234

). The largest separation is observed in the post-exercise stationary condition, where adjusted discrepancy rises sharply for Fitzpatrick IV–VI relative to III. The figure visualizes population-level model-based adjusted means from the repeated-measures model; inferential interpretation is based on the joint 12-df interaction block test rather than on isolated plotted cell differences. A significant block indicates that the motion/activity pattern differs across Fitzpatrick groups, but does not imply that every motion contrast differs for every group.

Table 9 \| Measured recording-level RGB SNR by Fitzpatrick group (dB). Recording-level red-, green-, and blue-channel SNR values and their aggregate mean are summarized by Fitzpatrick group for the 625-record analysis set. These values are descriptive signal-quality measures and are not interpreted as direct estimates of melanin concentration or tissue optical absorption.
Fitzpatrick	N	SNR_R	SNR_G	SNR_B
III	338	-15.55	-15.51	-15.22
IV	77	-15.96	-15.85	-15.64
V	120	-16.52	-16.02	-15.76
VI	120	-15.97	-16.02	-16.26

Table 13

Figure 5: Measured aggregate RGB SNR versus endpoint discrepancy. Recording-level aggregate RGB SNR is plotted against absolute heart-rate discrepancy

D_{HR}

for the 625-record Fitzpatrick analysis set. The linear association is negligible (Pearson

r=0.014

,

p=0.718

), indicating that the measured aggregate SNR metric does not materially account for recording-level variation in endpoint discrepancy. Points are individual recordings and are identified by Fitzpatrick group for visualization. Aggregate RGB SNR is the mean of the recording-level red-, green-, and blue-channel SNR measures used in the sensitivity analysis. The near-zero correlation indicates that this measured aggregate SNR metric has little linear association with

D_{HR}

in these data; it is not interpreted as a causal test of optical mechanisms or as evidence that optical factors are unimportant.

Table 10 \| Observed versus predicted SNR for the simplified Beer–Lambert-inspired adequacy check. Observed group-level aggregate RGB SNR is compared with the monotonic attenuation pattern generated by the simplified Beer–Lambert-inspired relation. Residuals quantify observed-minus-predicted SNR and are used only to assess adequacy of the specified pattern, not to estimate melanin or establish a causal optical mechanism.
Fitzpatrick	Observed SNR	Predicted SNR	Prediction error
III	-15.43	-10.48	-4.94
IV	-15.82	-14.48	-1.33
V	-16.10	-19.48	+3.39
VI	-16.08	-27.48	+11.40

Table 15

Figure 6: Predicted versus observed SNR and model residuals across Fitzpatrick groups. (A) Observed aggregate RGB SNR is compared with the monotonic pattern predicted by the deliberately simplified Beer–Lambert-inspired relation

\mathrm{SNR}_{dB}=\mathrm{baseline\ SNR}-20\,OD_{melanin}

. The model RMSE is 6.47 dB. (B) Group-level prediction residuals show increasing positive error toward the darker-skin groups, with the largest discrepancy for Fitzpatrick VI. Residuals are observed minus predicted SNR, so increasingly positive residuals indicate that the simple model predicts substantially more attenuation than was measured. This adequacy check shows that the specified one-parameter monotonic attenuation pattern does not reproduce the group-level SNR observations. The model is not a physiological melanin estimator, does not represent the full camera/illumination/tissue imaging chain, and is not used to correct rPPG signals or establish causality.

Table 11 \| SNR-adjusted sensitivity model. Model 1b adds recording-level aggregate RGB SNR to the subject-aware endpoint-discrepancy model while retaining Fitzpatrick group, lighting, motion/activity, and the subject random intercept. The table evaluates whether SNR adjustment materially changes the Fitzpatrick-associated coefficients.
Contrast	Model 1	Model 1b + SNR_RGB	Model 1b 95% CI	Model 1b p
IV vs III	6.37	6.40	[-0.08, 12.89]	0.053
V vs III	6.72	6.77	[1.25, 12.30]	0.016
VI vs III	9.32	9.37	[3.83, 14.90]	0.001
SNR_RGB	,	0.077 bpm/dB	[-0.228, 0.382]	0.621

Table 17

Figure 7: Motion/activity reveals endpoint–dynamical dissociation. Each point represents the condition-specific mean endpoint discrepancy

D_{HR}

and mean dynamical discrepancy

D_{\lambda}

. Conditions with similar or larger endpoint discrepancy do not necessarily exhibit correspondingly larger

D_{\lambda}

; for example, walking has high mean endpoint discrepancy but the lowest mean dynamical discrepancy among the displayed conditions. Because

D_{HR}

and

D_{\lambda}

have different units and scales, the figure evaluates condition ordering and co-variation rather than equality of numerical magnitude. The plot is descriptive and illustrates that acquisition conditions can affect endpoint and dynamical recoverability differently.

Information set	Linear	Ridge	Random forest
$M_{0}$	12.54 (0.00%)	12.54 (0.00%)	12.88 (0.00%)
$M_{1}$	11.15 (11.14%)	11.15 (11.13%)	11.48 (10.87%)
$M_{2}$	10.87 (13.32%)	10.87 (13.32%)	11.23 (12.77%)
$M_{3}$	11.16 (11.02%)	11.15 (11.15%)	11.65 (9.53%)
$M_{4}$	11.23 (10.45%)	11.22 (10.58%)	11.89 (7.69%)

Table 12: Subject-held-out endpoint prediction across learner families. Out-of-fold MAE (bpm) is reported for each nested information set and learner family. Percentages in parentheses denote MAE reduction relative to the corresponding

M_{0}

baseline within the same learner family.

M_{0}

: rPPG HR only;

M_{1}

: +motion;

M_{2}

: +lighting;

M_{3}

: +Fitzpatrick group;

M_{4}

: +aggregate RGB SNR.

Figure 8: Subject-held-out reduction of the PPG–rPPG HR gap using measured observation context. Out-of-fold MAE is shown for linear, ridge, and random-forest learners as predictors are added incrementally: rPPG HR only (

M_{0}

), +motion (

M_{1}

), +lighting (

M_{2}

), +Fitzpatrick group (

M_{3}

), and +aggregate RGB SNR (

M_{4}

). Motion and lighting consistently reduce MAE, with the best result at

M_{2}

; adding Fitzpatrick group or aggregate SNR does not improve the best model. The analysis uses the 625-record, 32-subject condition-aware subset; its raw camera-derived rPPG HR MAE is 15.24 bpm, compared with 15.26 bpm in the full 655-record benchmark. Five-fold GroupKFold validation is subject-held-out, so recordings from a participant do not appear in both training and test folds. For the linear learner, MAE decreases from 12.54 bpm at

M_{0}

to 10.87 bpm at

M_{2}

(13.32% reduction; subject-bootstrap 95% CI for the MAE difference, -2.36 to -0.98 bpm). The remaining error is substantial and does not establish equivalence between rPPG and contact PPG.

Figure S1: Subject-aware Fitzpatrick-associated endpoint gradient. Mixed-effects coefficients for Fitzpatrick IV, V, and VI relative to Fitzpatrick III after adjustment for lighting and motion/activity with a subject random intercept (

N=625

recordings, 32 subjects). Coefficients are expressed in beats/min and use Fitzpatrick III as the reference group; error bars denote 95% confidence intervals. This coefficient-focused display complements the combined descriptive-and-adjusted presentation in Figure 2 .

Figure S2: RGB-channel SNR distributions by Fitzpatrick group. Recording-level red-, green-, and blue-channel SNR distributions are shown for the 625-record Fitzpatrick analysis set. The extensive overlap and comparatively small shifts in central tendency provide the distributional context for Table 9 ; these measurements are descriptive signal-quality summaries and are not direct measures of melanin concentration or tissue optical absorption.

Figure S3: Sensitivity of Fitzpatrick coefficients to aggregate RGB-SNR adjustment. Model 1b adds measured aggregate RGB SNR to Model 1 while retaining Fitzpatrick group, lighting, motion/activity, and the subject random intercept. The displayed Fitzpatrick contrasts change by less than 1% relative to Model 1, indicating negligible descriptive attenuation after SNR adjustment. This is a sensitivity analysis and is not interpreted as causal mediation.

Figure S4: Frozen PPG–rPPG maximal-Lyapunov analysis. The primary matched analysis used 645 recordings with valid PPG and rPPG

\lambda_{\max}

estimates. No detectable matched recording-level correspondence was observed (

r_{\lambda}=0.0231

, 95% CI -0.0542 to 0.1001; permutation

p=0.5584

), despite overlap in marginal values. The rPPG estimates also show marked variance compression relative to contact PPG, supporting the distinction between population-level similarity and preservation of recording-specific dynamical information.

Figure S5: Predicted versus reference HR for the best condition-aware learner. Out-of-fold predictions from the linear

M_{2}

model (rPPG HR + motion + lighting) are plotted against synchronized contact-PPG reference HR. The identity line represents perfect recovery of contact-PPG HR. Although

M_{2}

reduced MAE relative to the rPPG-only learner, predictions remain compressed toward central HR ranges and visibly depart from the identity line at the extremes, illustrating why the result is interpreted as partial gap reduction rather than PPG–rPPG equivalence. Predictions are strictly out-of-fold from subject-held-out validation.

Figure S6: Adjusted Fitzpatrick-by-lighting endpoint profiles. Model-based adjusted mean

D_{HR}

is shown across lighting conditions for Fitzpatrick III–VI. Despite visible differences among cell means, the joint Fitzpatrick

\times

lighting block was not significant (Wald

\chi^{2}(9)=9.970

,

p=0.3529

); therefore, individual plotted differences are not interpreted as evidence of a compounded lighting-by-Fitzpatrick effect. The figure is retained to distinguish visually apparent subgroup variation from interaction heterogeneity supported by the repeated-measures model.

Property-Specific Recoverability from Contact PPG to Camera rPPG under Heterogeneous Observation Conditions

Abstract

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