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Revisiting Ground-Truth Synthesis from High-Speed Video: Exact Validity Conditions and an Audited Consumer Capture Corpus
Abdullah Al Shafi, Sumaiya Rahim Suma
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Abstract
Abstract:Motion-deblurring datasets are commonly synthesised by averaging $N$ consecutive high-frame-rate frames and labelling the result with the central frame. We show that this label is unbiased for every capture timing only when the window is odd and the frames' sample durations are equal. An even window shifts every label by a fixed fraction of the blur length, even under perfect timing. Unequal durations are subtler: their mean misalignment is zero, so dataset statistics cannot reveal them, yet when the offset cannot be read from the blur they convolve the supervision rather than adding noise to it. Auditing 51 smartphone clips recorded at a nominal 240 fps, we find 19 captured near 176 fps, a behaviour recorded only in the container's timing tables. In a controlled test the parity choice costs a fitted linear deblurring filter far more than these timing irregularities do, and interpolation labels, unlike blur labels, can be repaired with the true frame times. We provide a tool that checks both conditions without decoding, and will release the clips and their timing tables.
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- Source: https://arxiv.org/abs/2610.05298v1
- Canonical: https://arxiv.org/abs/2610.05298v1
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Revisiting Ground-Truth Synthesis from High-Speed Video: Exact Validity Conditions and an Audited Consumer Capture Corpus Abdullah Al Shafi Sumaiya Rahim Suma Affiliation: Department of Computer Science and Engineering Affiliation: Khulna University of Engineering & Technology, Khulna, Bangladesh Affiliation: abdullah.shafi99, sumaiya.rahim234@gmail.com Abstract Motion-deblurring datasets are commonly synthesised by averaging N consecutive high-frame-rate frames and labelling the result with the central frame. We show that this label is unbiased for every capture timing only when the window is odd and the frames’ sample durations are equal. An even window shifts every label by a fixed fraction of the blur length, even under perfect timing. Unequal durations are subtler: their mean misalignment is zero, so dataset statistics cannot reveal them, yet when the offset cannot be read from the blur they convolve the supervision rather than adding noise to it. Auditing 51 smartphone clips recorded at a nominal 240 fps, we find 19 captured near 176 fps, a behaviour recorded only in the container’s timing tables. In a controlled test the parity choice costs a fitted linear deblurring filter far more than these timing irregularities do, and interpolation labels, unlike blur labels, can be repaired with the true frame times. We provide a tool that checks both conditions without decoding, and will release the clips and their timing tables. 1 Introduction Most real-world motion-deblurring data is manufactured rather than captured. The recipe of Nah et al. (2017) and Su et al. (2017) records at a high frame rate, averages N consecutive frames to approximate a long exposure, and designates the central frame as the sharp target. The same recipe still underlies new datasets (Lee et al., 2024; Mahmud et al., 2026). Both images are synthetic, and their pairing rests on an assumption that is rarely stated: that the central frame is where the exposure is centred. We give the exact condition under which it is. Writing δ for the displacement between the sharp label and the intensity centroid of the synthesised blur, normalised by the blur length, we show that δ vanishes exactly when a parity term and a timing term cancel (Eq. 1). With equal sample durations the timing term is zero and δ=0⟺N is odd.δ=0 N is odd. An odd window of equal durations is therefore the configuration that guarantees an unbiased label, and both properties can be checked before any synthesis. Each is violated in practice, differently (Figure 1). Figure 1: The sharp label against the centroid of the blur it is paired with. (a) Odd window, equal durations: aligned. (b) Even window: a fixed offset in every pair. (c) Held intervals: an offset that varies and averages to zero. The first is violated by choice. An even window has no central frame, so every pair is offset by 1/(2(N−1))1/(2(N-1)) of the blur length however perfect the capture, 7.1%7.1\% at N=8N=8, in the same direction every time (Figure 1b). Published pipelines use both parities (Section 2). The second is violated by hardware. On the smartphone we audit, 19 of 51 clips recorded at a nominal 240 fps were captured near 176 fps, holding about a third of their intervals for two slots, and only the container’s sample-duration table reveals it (Section 4). The resulting misalignment has zero mean (Figure 1c), harmless for noise on a target’s value (Lehtinen et al., 2018) but not for a perturbation of its position in time: the expected label is the sharp frame convolved with the jitter density, so the supervision is not noisy, it is blurred. This paper makes four contributions. It states the exact validity condition and the misalignment each violation causes (Section 3). It shows that zero-mean timing error convolves the supervision, with a controlled test separating the costs of the two violations (Section 3.1). It audits iPhone-HighFPS, the 51-clip corpus in which the hold behaviour was found and which we will release (Section 4). And it traces the consequences for deblurring and interpolation labels, with a tool that checks both conditions before a dataset is built (Section 5). Scope of the claims. The validity condition is exact for any capture under the locally linear motion model; the audit covers one device across two recording sessions (Section 6). The odd-N identity is the antisymmetry argument behind the midpoint quadrature rule (Davis & Rabinowitz, 1984), and we know of no prior statement of the centroid condition in this setting; what we claim is its statement, quantification and consequences here. We do not claim the capture behaviour is a defect, that we have identified its trigger, or that any published benchmark’s numbers are invalidated. 2 Related work The averaging convention. Nah et al. (2017) and Su et al. (2017) established it; Su et al. (2017) interpolate intermediate frames to avoid ghosting from the gap between exposures, and Nah et al. (2019) upsample the frame rate before averaging. Rim et al. (2022) add saturation, noise and camera processing to the synthesis, and real-captured datasets avoid it altogether (Rim et al., 2020; Zhong et al., 2020). The synthetic pipelines all presuppose uniformly spaced source frames, and none checks that they are. Window parity in practice. Published pipelines fall on both sides of the condition, rarely saying why. Jin et al. (2018) use seven frames rather than eight to avoid ambiguity in the middle frame, the right window for a different reason; GoPro averages 7 to 13 frames around the mid-frame (Nah et al., 2017), and a rendered dataset takes the middle of 121 sub-frames (Lee et al., 2024). A recent smartphone benchmark averages N=30N=30 frames with frame ⌊N/2⌋ N/2 as reference (Mahmud et al., 2026), by Eq. 2 an offset of 1/58=0.0171/58=0.017 of the blur length, about 0.70.7 pixels on a 40-pixel streak, under perfect timing. The same work describes the phone’s high-speed pipeline as offering superior frame-timing stability, which Section 4.2 qualifies for the device we audit. An infrared study takes frame N/2+1N/2+1 for even N up to 13 (Varghese et al., 2021), offsets of 0.1670.167, 0.1000.100 and 0.0710.071 at N=4N=4, 6 and 8. We raise these cases to show the condition binds in practice, not to question any work’s results. Temporal labels and pipeline audits. Interpolation benchmarks assign each ground-truth frame a normalised time (Xue et al., 2019; Choi et al., 2020). Zhong et al. (2024) replace time with a distance-based index to resolve velocity ambiguity and Xu et al. (2019) model acceleration, both assuming the timestamps are right; our concern is whether they are. Dedicated high-speed rigs (Sim et al., 2021; Ciubotariu et al., 2025) lie outside the consumer regime, Ji et al. (2023) note that discontinuous averaging produces unnatural motion artifacts, and Shang et al. (2023) model per-row scanning time, which is intra-frame. Our work joins audits showing that low-level pipeline choices silently bias benchmarks (Parmar et al., 2022; Northcutt et al., 2021). Closest in domain, Kiefhaber et al. (2024) question the content of interpolation ground truth where we question its construction, and the Kye et al. (2026) survey has no timing-integrity axis. The container structures we read are standard in multimedia forensics (Gloe et al., 2014; Iuliani et al., 2019; Yang et al., 2020). The vendor documents one automatic frame-rate reduction, Auto FPS, which lowers 30 and 60 fps video to 24 fps in low light (Apple Inc., 2026a), and none for high-frame-rate capture. 3 When is the central-frame label unbiased? A frame-averaged label is unbiased exactly when the averaged instants are symmetric about it; four propositions make this exact and quantify what each violation costs. Consider a window of N frames with presentation times T0,…,TN−1T_0,…,T_N-1, averaged with equal weight 1/N1/N, with the frame at m=⌊N/2⌋m= N/2 designated the sharp reference, and span S=TN−1−T0S=T_N-1-T_0. Under locally linear motion the blur centroid lies at the mean sample time T¯ T. Define the signed misalignment δ~=(Tm−T¯)/S δ=(T_m- T)/S and its magnitude δ=|δ~|δ=| δ|. With Δ the nominal frame interval, write the durations as dj=Δ(1+bj)d_j= (1+b_j), where bjb_j counts the extra nominal slots interval j occupies. Then Tm−T¯=Δ[m−N−12]⏟parity term+Δ∑j=0N−2bjwj⏟timing term,wj= 1[j<m]−N−1−jN,T_m- T\;=\; [m- N-12 ]_parity term\;+\; _j=0^N-2b_j\,w_j_timing term, w_j\;=\;1[j<m]- N-1-jN, (1) with S=Δ(N−1+∑jbj)S= \,(N-1+ _jb_j). The parity term depends only on window size and survives perfect timing; the timing term depends only on where held intervals fall. Since ∑jwj=m−N−12 _jw_j=m- N-12, δ=0δ=0 exactly when ∑jbjwj=N−12−m _jb_jw_j= N-12-m. Normalising by the exposure span NΔN instead of S would scale δ by (N−1+∑jbj)/N(N-1+ _jb_j)/N, which is (N−1)/N(N-1)/N under perfect timing. P1: the odd-window condition. Set every bj=0b_j=0 to recover uniform spacing, leaving only the parity term. It vanishes exactly when N is odd, so the reference sits at the centroid and δ=0δ=0. For even N, m=N/2m=N/2 and the parity term equals Δ/2 /2; dividing by S=Δ(N−1)S= (N-1) gives δeven=12(N−1) _even\;=\; 12(N-1) (2) under perfect timing. The bias is systematic in time: every pair is misaligned the same way by the same fraction of its blur length, so it survives dataset averaging. In the image, though, a streak from locally linear motion does not reveal which way the motion ran (Jin et al., 2018; Purohit et al., 2019), so under L2L_2 the optimum averages the label shifted both ways: a faint double image rather than a consistent shift. P2: zero mean does not mean harmless. Take N odd, so only the timing term remains. If held intervals fall with probability p then [Tm−T¯]=Δp∑jwj=Δp[m−(N−1)/2]=0E[T_m- T]= p _jw_j= p\,[m-(N-1)/2]=0: the offset averages to zero over a dataset, which needs only a constant marginal hold probability across the window, not independence. The normalised δ~ δ also has zero mean when hold patterns are as likely reversed as forwards, since wN−2−j=−wjw_N-2-j=-w_j for odd N and S is unchanged. Under L2L_2 the optimum is unchanged when a target is replaced by any distribution with the same conditional expectation (Lehtinen et al., 2018), so zero-mean noise on the target’s value would be benign. Here the label is the frame at a perturbed time, not the correct frame with perturbed intensity, so with I(t)I(t) the scene and ε the temporal displacement, ε[I(T¯+ε)]=(I∗pˇε)(T¯),pˇε(e)=pε(−e),E_ \! [I( T+ ) ]\;=\; (I* p_ )\!( T), p_ (e)=p_ (-e), (3) the clean frame convolved with the reflected jitter density: the L2L_2 optimum is a blurred target. P3: the scale in closed form. If holds fall independently, Var[∑jbjwj]=p(1−p)∑jwj2Var[ _jb_jw_j]=p(1-p) _jw_j^2, and for odd N ∑jwj2=m(m+1)(2m+1)3N2,m=N−12, _jw_j^2\;=\; m(m+1)(2m+1)3N^2, m= N-12, (4) so a builder who measures p can estimate the misalignment their synthesis will incur, to order of magnitude, without any per-sample computation. P4: a bound on the supervision. By Eq. 3, jitter of standard deviation σδ _δ convolves the label with a kernel of width σδL _δL for blur length L in pixels. For any estimator that cannot read the offset from the blurred input, this limits the sharpness available in the supervision regardless of sample size. A hold leaves a gap in the streak that could make its offset readable; a linear filter fitted under random direction is symmetric and cannot express such a shift, so the test of Section 3.1 shows only that the hold offset is not linearly recoverable. The mechanism belongs to the errors-in-variables family (Fuller, 1987), except that the conditional mean is blurred rather than shrunk toward zero. The validity condition. Unbiasedness requires the timing term to cancel the parity term, which under equal durations means N odd. Unequal durations break it for either parity except in balanced cases, such as N=5N=5 with the first and last intervals held (times 0,2,3,4,60,2,3,4,6 in units of Δ , mean T2=3T_2=3), which a builder cannot control at capture time, so the guarantee requires both properties. The even-window offset keeps its sign and survives averaging; the timing offset has zero mean and does not, so the quantity to report is the spread rather than the mean. 3.1 What the misalignment costs a fitted estimator The two violations should cost a learned estimator very different amounts. On identical inputs, an eight-frame window costs a fitted linear deblurring filter 0.420.42 dB at 16 to 32 pixels of blur, about eight times the 0.050.05 dB that real hold patterns cost a seven-frame window at the same blur lengths (Table 1). Table 1: What each violation costs a fitted linear deblurring filter: PSNR loss of the conventional label against the frame at the true centroid, mean and standard deviation over five seeds, with the net shift the filter learns. Violation Blur length Cost (dB) Learned shift Even window, random direction 16–32 px 0.42±0.050.42± 0.05 none: offset becomes blur Even window, random direction 32–48 px 0.73±0.070.73± 0.07 none Even window, direction fixed 16–32 px 0.85±0.030.85± 0.03 1.08 of the 1.72-px offset Real hold patterns 8–48 px 0.040.04 to 0.050.05 none Synthetic scenes, crops of standard test images split into disjoint training and test halves, translate horizontally at constant speed, the direction drawn at random so the model cannot know it. We fit the L2L_2-optimal linear filter to the conventional label and to the frame at the true centroid: a 3×813× 81 ridge fit on 150,000 pixels from 500 windows, its support wider than the longest blur it must invert. Both are scored on the same 200 held-out windows against the centroid frame, rendered directly even when it falls between sampled frames. Under random direction the filter learns no net shift, so the parity offset becomes blur, exactly as P1 predicts. Fixing the direction makes the offset learnable, and the filter reproduces most of it, moving its output off the centroid, short of the whole because the ridge penalty and the L2L_2 objective trade shift against sharpness. The hold patterns of the four affected clips of Figure 2c, transplanted onto the scenes, cost little, with a seed standard deviation of about 0.020.02 dB and a positive cost in every seed, and the filter recovers none of the hold-induced offset. These costs are measured against a correctly centred label. A dataset built with an even window trains and evaluates on labels carrying the same offset, so, as with the aggregation in P2, its own metrics report none of it. Whether real capture produces held intervals, instants the sensor never captured, is a question the container’s timing table can answer without decoding a frame. 4 iPhone-HighFPS: an audited consumer capture corpus Read directly from the container, the timing tables split a corpus of consumer clips into two populations, and only one satisfies the validity condition. Figure 2: The corpus at a glance. (a) Effective capture rate per clip; the dashed line is the nominal 240 fps, which uniform clips meet and affected clips miss at 174–179 fps. (b) Share of intervals at each sample duration (log axis): one ten-tick slot for uniform clips; a second mode at twenty ticks, exactly twice nominal, for affected ones. The ±1± 1 tick spread is quantisation dither. (c) Held intervals, one mark each, in 320 consecutive mid-recording intervals of four affected and two uniform clips: clusters separated by clean runs, and none in uniform clips. 4.1 Corpus and timing extraction The corpus, which we will release as iPhone-HighFPS, is 51 camera-original QuickTime files from one smartphone (iPhone 17 Pro, iOS 26.0), HEVC at 1920×10801920× 1080 and nominal 240 fps: 60.4 minutes and 741,919 frames (23.7 GB) of handheld outdoor urban footage from two sessions. No file carries an encoder fingerprint indicating re-encoding, vendor camera metadata is intact on all 51, and both populations carry identical writing metadata, so the transfer route cannot explain their difference. The same footage also underlies the iPhoneBlur deblurring benchmark (Shafi & Alam, 2026), distinct from Mahmud et al. (2026), which reports capture rates below the nominal 240 fps. We read timing from the stts atom, which stores exact integer sample durations, so nothing is decoded. The timescale is 2400 ticks per second (one tick is 416.7μ416.7\, , 10%10\% of a frame interval), and presentation times add signed ctts offsets from −41-41 to +31+31 ticks; decode order gives identical results. The negative offsets are permitted by QuickTime (Apple Inc., 2026b) but excluded from a version-0 ctts by the ISO format (ISO/IEC, 2026), so an ISO-strict parser reads each negative offset as unsigned and shifts that sample by about 2322^32 ticks. Edit lists, present in all 51 clips, do not alter the analysed range, and frames must be extracted without resampling to a constant rate, which silently duplicates and drops them. Rounding to whole ticks makes even a constant rate dither, so we separate rounding from genuine variation by the residual of cumulative timestamps from a linear fit. A clip is uniform when its residual is at most 0.750.75 ticks and non-uniform above 1.51.5, and no clip falls between. An interval is held when it exceeds 1.51.5 times the clip’s median, which separates one ten-tick slot from two. Two frames are near-duplicates when their mean absolute difference falls below 1.01.0 at 8-bit depth, a bimodal statistic with no pair within an order of magnitude of the threshold. 4.2 Two capture populations Figure 3: Why the timing is real. (a) Frames present in each clip against the number a uniform 240 fps stream of the same duration would hold: affected clips fall well below the identity line, so frames are missing. (b) Residual of cumulative timestamps from a linear fit, three clips per population on separate scales: affected residuals wander far outside the ±0.75± 0.75 tick band (shaded); uniform ones are the bounded sawtooth of dither. Table 2: The corpus separates under identical device, operating system and nominal settings. Residuals are the maximum absolute deviation of cumulative timestamps from a linear fit, in ticks; rounding alone stays near half a tick. Frame counts sum to the corpus total of 741,919. Uniform Affected Clips / duration / frames 32 / 26.8 min / 385,263 19 / 33.7 min / 356,656 Sample durations (ticks) 9,10,11\9,10,11\ 9,10,11,19,20,21,30\9,10,11,19,20,21,30\ Share at one / two nominal slots 100.00% / — 64.16% / 35.82% Effective rate 239.90 fps 174–179 fps Linear-fit residual (ticks) 0.52–0.53 47.97–417.26 Table 2 summarises the separation, clean on every timing measure and absent from every visual one, and Figure 2 shows it per clip. Uniform durations take the values 9, 10 and 11 ticks, 10 accounting for 99.46%99.46\%, and the residual never exceeds 0.530.53 ticks: a constant 239.90 fps dithered onto integer durations. In the affected population 20 ticks, exactly twice nominal, accounts for 35.51%35.51\% of intervals; grouped by whole slots, 64.16%64.16\% occupy one, 35.82%35.82\% two and 0.02%0.02\% three, which is why the model uses bj∈0,1b_j∈\0,1\. Residuals reach 417 ticks (Figure 3b). Durations fall exactly on their slot value at nearly the same rate in both populations (99.46%99.46\% against 99.31%99.31\%), so the ±1± 1 tick dither is a property of the clock and the holds are not. The missing frames. An uneven table could also come from a container that padded a slower stream with repeated frames, or that mislabelled the durations of a uniform one. An independent clock rules out both. A second media track in the same file, timed on its own clock, matches the video track’s duration to within 2 ms in every clip, about half a frame interval. Over that duration the affected clips hold 356,656 frames where 240 fps would give 484,752 (Figure 3a). A representative affected clip holds 4,318 frames in 24.6 seconds where 240 fps would give 5,904, a deficit of 1,586 frames. Repeated frames and mislabelled durations each make further predictions, and the data contradict every one (Table 3). The sensor therefore delivered about 176 distinct frames per second, recorded by doubling durations on a clock quantised to the nominal rate. 4.3 What the populations are not explained by Every affected clip holds between 34.2%34.2\% and 37.9%37.9\% of its intervals, mean 35.8%35.8\%, and every uniform clip exactly 0.0%0.0\%: the populations correspond to the two recording sessions, with no intermediate case. Ordinary explanations for an uneven timing table each make a prediction, and Table 3 sets every prediction against the measurement. None is supported by these comparisons. The state is decided 1.3 to 6.1 seconds into a recording (median 1.8) and then held, matching the time auto-exposure and autofocus take to settle, which we note as a hypothesis. The documented Auto FPS lowers 30 to 24 fps, a factor of 0.800.80 against the 0.730.73 here, but only in low light, and the affected clips are, if anything, the brighter ones. Table 3: Evidence and ruled-out explanations. Each row is a hypothesis that would produce an uneven timing table, what it predicts, and what the corpus shows. Session-level comparisons are descriptive: with two sessions, clip-level tests carry no session-level weight. Hypothesis It predicts The corpus shows Verdict Padded stream repeated, near-empty frames 0.00%0.00\% near-duplicates; no frame under 2%2\% of median size; post-hold frames no smaller (ratio 1.101.10) excluded Mislabelled durations clock disagreement; motion ratio 1 clock agrees to 2 ms; motion across holds 1.72×1.72× normal (IQR 1.591.59–1.941.94, nine clips with flow above 0.050.05 px at 480-px width, threshold set post hoc) excluded Drift within a clip held fraction changes 36.30%36.30\% to 35.91%35.91\% by decile (Wilcoxon p=0.070p=0.070) no detectable drift Thermal build-up rises with duration, recovers none over 15.4–301.9 s; 35.8%35.8\% after a 46-hour gap not supported Low light (Auto FPS) affected clips darker mean luminance 139.6139.6 (affected) vs 132.3132.3 (uniform) on a 0–255 scale (Mann–Whitney p=0.108p=0.108) not supported Visible to a builder headers or frames differ identical headers, metadata, codec; sharpness median ≈2500≈ 2500 in both not detectable Tied to scene motion hold density tracks flow Spearman +0.00+0.00 (IQR −0.07-0.07 to +0.13+0.13, 11 clips) no 4.4 Placement of held intervals Figure 4: How held intervals are placed. (a) Gaps between consecutive held intervals, pooled over the affected population. Mass at one and two frames, a second mode beyond ten, and nothing between: the signature of clustered placement. (b) Autocorrelation of the held-interval indicator: median across all 19 affected clips, against the simultaneous 95%95\% band of a permutation null pooled over clips (grey), the band the significance tests use. (c) Lengths of runs of consecutive held intervals. The holds are not scattered: they cluster, so whole averaging windows rather than single frames are affected. Against a null that permutes each clip’s held-interval indicator 2,000 times, with a simultaneous band controlling the family-wise error rate, all 19 clips show significant autocorrelation (p=0.0005p=0.0005, the resolution limit), positive at lags 1 to 3 (mean +0.237+0.237, +0.196+0.196 and +0.424+0.424, each surviving Benjamini–Hochberg correction). Gaps between holds are bimodal (Figure 4a): 50.9%50.9\% are one frame, 36.7%36.7\% two, none four to eight and 12.3%12.3\% ten or more, over-dispersed against a memoryless process (standard deviation 3.703.70 against 2.232.23). Holds thus arrive in short clusters separated by clean runs of ten to fourteen frames, which drives the autocorrelation to −0.47-0.47 at lags 11 and 12 (Figure 4b). The clusters recur with a period of 22.6 frames (22.3 to 22.9 in every clip), about 128 ms or 7.8 Hz, matching no documented device periodicity. The rate does not drift (detrending reduces the timestamp residual by 0.0%0.0\%), and a constant target rate predicts the hold sequence no better than chance (53.92%53.92\% against 54.07%54.07\%). A 22.6-frame cadence carrying about eight holds reproduces both the 35.8%35.8\% held fraction and the 176 fps rate, so the behaviour is rate-driven per cluster and irregular within one. 4.5 Predictions against measurement Figure 5: The model against the audit. (a) Misalignment under perfect timing (Eq. 2): zero for odd N, 1/(2(N−1))1/(2(N-1)) for even N. (b) Measured median and p95 misalignment in the affected population (solid) against P3 at p=0.359p=0.359 (dashed), treating the timing term as Gaussian (median 0.674σ0.674σ, p95 1.96σ1.96σ): the scale agrees, but the median rises with N where P3 predicts a fall, because holds are not independent. (c) Cumulative distribution of δ at N=7N=7: a point mass at zero for uniform clips; up to δ≈0.1δ≈ 0.1 for affected ones. Figure 5 sets the audit against Section 3. P1 holds to the precision the clock allows: in the uniform population the misalignment is 0.00000.0000 at the median for N=7N=7, 11 and 13, with a standard deviation of 0.00060.0006 to 0.00090.0009 from ±1± 1 tick dither, 25 to 37 times below the affected spread. P3 (Eq. 4) recovers the order of magnitude from p alone, at worst 22%22\% short at the 95th percentile for N=13N=13. Direct simulation reproduces the closed form to within 3.63.6 to 6.4%6.4\%, so the gap reflects its assumptions, and the median’s trend in N is reversed because the independence it assumes fails. Measured over 118,848, 71,298 and 59,409 averaging windows of the affected clips, σδ _δ is 0.02550.0255, 0.02280.0228 and 0.02200.0220 at N=7N=7, 11 and 13. By P4, at an illustrative blur length of 30 to 50 pixels this would be a label blur of 0.660.66 to 1.281.28 pixels, longer than our own affected clips produce (Section 5.1); an extrapolation, since the offset scales with blur length. What this does to the labels built from these clips is the question of Section 5. 5 Consequences for supervision The same violation has opposite consequences for the two kinds of label built from high-speed video: blur labels averaged over held intervals cannot be repaired, while interpolation labels can. 5.1 Deblurring labels on this corpus The affected clips are the low-motion ones. Median dense flow per 240 fps interval, pooled over all sampled intervals rather than motion-selected windows, is 1.181.18 pixels in the uniform population against 0.140.14 in the affected one (p95 4.954.95 against 1.911.91). The consequence across this footage is small; since the offset scales with blur length, benchmarks that select high-motion windows would see larger offsets, which this corpus cannot measure. Transplanted onto the six longest uniform clips, the measured hold patterns put the blur label a median 0.190.19 pixels (p95 1.531.53) from the true centroid at blur lengths of 10 to 12 pixels, against 0.750.75 pixels for an even window on the same footage. The even-N violation, by contrast, applies at any motion. 5.2 Interpolation labels are repairable For interpolation triplets at stride k the middle frame is designated t=0.5t=0.5, while its true normalised time is ttrue=(Ti+k−Ti)/(Ti+2k−Ti)t_true=(T_i+k-T_i)/(T_i+2k-T_i). In the uniform population the two agree to tick dither (standard deviation 0.00120.0012 or less). In the affected population (Table 4), at stride 8, whose input frames are 16 nominal intervals apart (a 15 fps pair), the designated midpoint sits near normalised time 0.610.61 at the 75th percentile. The signed error still averages to zero, so aggregate reporting conceals it exactly as in P2. Table 4: Interpolation label error ttrue−0.5t_true-0.5 in the affected population (uniform: median zero, p95 at most 0.00310.0031). The signed mean vanishes; the p95 coincides at strides 4 and 8, which reach the same attainable ratio, t=7/11t=7/11. Population Stride signed mean sd |⋅||·| p50 p75 p95 affected 4 −2.0×10−6-2.0× 10^-6 0.0680 0.0385 0.0833 0.1364 affected 8 −1.2×10−5-1.2× 10^-5 0.0856 0.0833 0.1087 0.1364 affected 16 −1.0×10−5-1.0× 10^-5 0.0346 0.0322 0.0455 0.0581 Unlike the blur label, the interpolation label is repairable: the true time survives in the container, and a time-conditioned model can be given ttruet_true instead of 0.50.5 (Zhong et al., 2024). On real footage carrying the measured hold patterns, doing so gains 1.411.41 dB at stride 8 for a flow-based interpolator with the time-conditioned warping of Jiang et al. (2018), better in 85%85\% of 277 triplets. The blur label cannot be repaired this way: it is produced by averaging unevenly spaced samples with equal weights, and no relabelling recovers an exposure that never physically occurred. The remedy we can state is to synthesise only from windows whose durations pass the timing check. Because held intervals cluster, filtering keeps 29%29\% of 7-frame windows in affected footage, 11%11\% at N=11N=11 and 3%3\% at N=13N=13, and the surviving windows lie inside clean runs by construction, so they are not a random sample of the footage. 5.3 Screening a corpus before synthesis Both conditions can be checked before a single frame is averaged. Our screening tool reads a QuickTime or MP4 sample-duration table in milliseconds without decoding. Durations pass when the linear-fit residual is at most 0.750.75 ticks (7.5%7.5\% of the nominal interval, so the test transfers to other timescales) and no duration exceeds 1.51.5 times the median, and parity is checked against the intended N. iPhone-HighFPS is a diagnostic instrument, not a training corpus: its verified-uniform part is 26.8 minutes, far too small to compete with established benchmarks (Choi et al., 2020; Sim et al., 2021). Subsampling a uniform clip by stride k gives the same scene at 240/k240/k fps with every container sample time known, and displacement is linear in stride to within 4%4\% over a factor of 32. Scenes are diverse (median nearest-neighbour cosine similarity between 32×3232× 32 thumbnails 0.5540.554, p90 0.6730.673) and consistently sharp within each clip (coefficient of variation 0.020.02 to 0.070.07). The affected clips, with a container timestamp per frame, test interpolation at arbitrary times. The screening tool and analysis code are available at https://github.com/C-loud-Nine/Highfps_GT_Synthesis. We will release iPhone-HighFPS upon publication: the 51 clips, partitioned by population, with per-clip timing metadata. Redaction re-encodes the files but preserves and verifies each sample-duration table and frame count; frame sizes and independent-clock values, which the copies cannot reproduce, are given per clip. 6 Limitations The model assumes locally linear motion within the window, as the convention itself does. We characterise the population-optimal predictor analytically and test it only with a linear filter on synthetic scenes. A deep network may read direction cues from the blur, which would lower the hold-pattern cost and raise the parity cost as the double image sharpens toward a shift. The interpolation gain likewise comes from one flow-based interpolator. Measurements come from one device, one operating system version and two sessions, with between-session spread in held fraction 53 times the mean within-session spread, so the effective sample for session-level claims is two, not 51; the released tool exists to test whether the findings transfer. We have not identified the mechanism: we find no support for thermal accumulation or low light and exclude drift and fixed-rate decimation, but the trigger is not observable from the files. We do not quantify the effect on benchmarks built from this footage, including iPhoneBlur (Shafi & Alam, 2026), nor trace it through other datasets, whose camera originals are rarely distributed. Three remedies go untested: duration weighting cannot supply samples the sensor never produced, a reference at T¯ T (Su et al., 2017) reduces the offset without evening the sampling, and misaligned-pair losses (Zhang et al., 2019) target spatial misregistration. Extracted image pairs lose the sample-duration table, so the condition becomes uncheckable after release, and rolling-shutter readout time is absent from this metadata, so intra-frame timing is out of scope. 7 Conclusion Frame averaging is sound for every capture timing only when the window is odd and the sample durations within it are equal, and both can be checked before synthesis. None of the synthesis procedures we cite checks durations, and where parity is chosen deliberately it is for other reasons. Three practices follow. Builders should choose an odd window and verify durations from the container before averaging. Datasets should report the spread of label offsets rather than their mean, since a zero mean certifies nothing. Extracted pairs should carry their true timestamps, which repair interpolation labels and are otherwise lost. Ground truth is only as valid as the timing it assumes. 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