The Paired Thermal Channel Is Two Orthogonal Axes: A Controlled Attribution Study of Calibration Cost and Detection Gain in Infrared Person Detection
Authors: Tian Zhang, Yang Chen, Bing Bai, Weikai He, Xiang Gao, Zhirong Su
Organizations: School of Information Engineering, Shandong Management University, Jinan, China. · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. · School of Aeronautics, Shandong Jiaotong University, Jinan, China. · School of Business, Shandong Management University, Jinan, China.
The calibrated thermal channel in infrared person detection comprises two structurally orthogonal axes. True calibrated ΔT outperforms scale-matched grayscale pseudo-ΔT by +0.0221 mAP (paired Wilcoxon p=0.0098, Cohen's d=+1.08), confirming that the calibrated channel carries information the grayscale channel lacks. The calibration axis is driven by the joint pairing-scale condition. Preserving both paired correspondence and absolute calibrated scale raises expected calibration error (ECE) from ≈0.05 to 0.142. The 2×2 interaction (p=0.0059) localizes the rise to this condition. Breaking either factor alone returns ECE to the broken-factor level (true-vs-const p=0.002; true-vs-shuffled p=0.002). Under post-hoc temperature scaling, the pairing cost survives recalibration (p=0.002), while the scale cost is largely absorbed (p=0.16). As regards the detection axis, the gain stems from structural de-structuring. Phase randomization, which destroys spatial structure while preserving per-sample variance, yields +0.0185 mAP over true ΔT on FLIR ADAS (p=0.014, d=+0.96). The FLAME3 gain is +0.0064 mAP (p=0.078, n=8). On the calibration axis, the same intervention is insignificant on FLIR ADAS (p=0.47) but significant on FLAME3 (p=0.0078). These findings rest on a five-arm controlled attribution with temperature-evidential learning (TEL) as the testbed. TEL obtains a single evidence-derived routing scalar together with a complementary diagnostic entropy, and establishes a finite-evidence degeneracy theorem proving that the acquisition product degenerates to this scalar with a closed-form bound. A physical 0.5∘C threshold admits cross-dataset physical readings, whereas a gray threshold of 20 inverts without physical interpretation.
Figures & tables
Figure 1: Temperature-evidential learning (TEL) as one evidence chain. (a) Dual-channel decoding. Channel A renders G , while Channel B retains the calibrated temperature matrix T . The annular contrast geometry is sampled at dilation factors r∈{0.1,0.2,0.4} , using T values from Channel B and box positions from the detector backbone. (b) Temperature-evidential modulation. The multi-scale contrast ΔT(s) (Eq. ( 3 )) passes through the sigmoid gate m(ΔT) (Eq. ( 4 )). The temperature-aware prior gk,πk produces eaug,k (Eq. ( 9 )), and the modulation factor 1+γm produces emod,k (Eq. ( 10 )), from which a single evidence-derived routing scalar u is read; a diagnostic entropy Ψ=E[H(p)] is computed alongside on a dashed branch and does not participate in routing. (c) Two-ended routing. The same u drives annotation, pseudo-labeling, and discard (Eq. ( 22 )); the partition relies on separation of the two ends of the distribution, not on monotone ranking in between. (d) Replay and distillation weighting (Eqs. ( 35 ) and ( 37 )) appear as dashed design extensions. Solid arrows denote forward data flow and core computation. Dashed arrows denote auxiliary inputs, control signals, and the closed-loop feedback that returns the updated detector to the next round. All downstream decisions in (b)-(d) use the temperature matrix retained in Channel B.
Figure 2: Physical evidence of the temperature matrix. (a) Two nighttime patches in which the grayscale contrast is low ( ∣ΔG∣≈2.2 ) while the calibrated ΔT remains measurable ( ≈0.28∘ C). The inset text reports the exact number of interior and annular background pixels. (b) Conditional distribution P(ΔT∣y=person) as a function of the illumination drift coordinate s , stratified into quintiles. P(y∣s) is stationary, while P(ΔT∣y,s) drifts with s . Data points mark median ± IQR. (c) Empirical validation of the KL separability sandwich in Eq. ( 19 ). The red line is the measured median Λ(b) with interquartile range (IQR) error bars, obtained by using the thermal camera’s native 8-bit grayscale rendering (strictly pixel-aligned with the 14-bit TIFF) to compute the true local grayscale ratio x . The black dashed line is the theoretical upper bound Λ(b) . The empirical median grayscale-to-temperature noise ratio is x≈1.10 . The empirical median strictly falls within the theoretical bounds, confirming that the calibrated temperature channel ΔT provides a reliable source of local separability evidence. The empirical median temperature noise is σmed=0.39∘ C (IQR: [0.22,0.72]∘ C).
Signal
ε
ρ
err∣acc
ub
Coverage
Mean ± std across the 45 seed pairs
u / margin / conf
0.086±0.021
0.712±0.072
0.0364±0.014
0.0660±0.016
45/45
H
0.116±0.021
0.520±0.084
0.0281±0.010
0.0736±0.014
45/45
95% bootstrap CI (2000 resamples, pair as unit)
u / margin / conf
[0.080,0.092]
[0.690,0.734]
[0.032,0.041]
[0.061,0.071]
—
H
[0.110,0.122]
[0.495,0.545]
[0.025,0.031]
[0.070,0.078]
—
Table 1: Empirical validation of Eq. ( 27 ) over all 45 seed pairs. Margin and conf are identical to each other; u is numerically indistinguishable from them because K=2 . Coverage is the fraction of seed pairs for which the bound exceeds the accepted error.
Pair
Pearson ρ
95% CI
Spearman ρ
95% CI
Signal-to-signal correlations
u , H
−0.0765
[−0.0782,−0.0748]
−0.2662
[−0.2687,−0.2639]
u , margin
−0.9255
[−0.9263,−0.9247]
−0.3079
[−0.3109,−0.3047]
u , conf
−0.9255
[−0.9263,−0.9247]
−0.3079
[−0.3110,−0.3050]
H , margin
−0.2590
[−0.2608,−0.2573]
−0.6202
[−0.6224,−0.6180]
H , conf
−0.2590
[−0.2608,−0.2573]
−0.6202
[−0.6225,−0.6180]
Table 2: Signal correlations on the FLIR ADAS prediction protocol, pooled over ten seeds. Values are Pearson ρ and Spearman ρ with 95% bootstrap confidence intervals on the pooled RoIs.
τlow
measured (mean ± std)
[min,max]
bound
0.40
0.0802±0.0704
[0.0126,0.2231]
0.1667
0.45
0.0308±0.0158
[0.0129,0.0592]
0.1837
0.50
0.0237±0.0058
[0.0162,0.0378]
0.2000
0.55
0.0332±0.0051
[0.0254,0.0454]
0.2157
0.60
0.0470±0.0027
[0.0423,0.0524]
0.2308
Table 3: Empirical validation of Corollary 3 on an oracle-based image-level protocol, averaged over ten seeds. Thresholds below 0.40 are omitted because the discard branch contains too few samples for a reliable estimate.
a
b
consistency κroute
(qlo,qhi)
1.0
0.0
1.0000
(0.4520,0.9883)
0.5
0.0
1.0000
(0.4520,0.9883)
1.0
10.0
1.0000
(0.4520,0.9883)
2.0
−5.0
1.0000
(0.4520,0.9883)
Table 4: Empirical validation of Corollary 4 . Four strictly increasing affine reparametrizations of the temperature channel, T′=aT+b , are applied; the routing partition is unchanged in all four cases.
mean
std
var
u
0.3673
0.2175
0.047301
Ψ
0.4982
0.0204
0.000416
Δ
0.1827
0.1086
0.011792
Table 5: Empirical statistics of the routing scalar, the diagnostic entropy, and the acquisition product, pooled over n=5.4×105 RoIs and ten seeds on FLIR ADAS.
regime
u range
frac(IoU>0.5)
mean IoU
router branch
background
bins 0–6
≈0
≈0
discard
transition
bin 7
0.0948
0.0861
pseudo
detection
bin 8
0.9274
0.7652
pseudo
saturated
bin 9
0.3184
0.2895
annotate
Table 6: Three-state structure of the routing scalar u on FLIR ADAS, pooled over ten seeds. The umed values of the four regimes are 0.263 – 0.271 (bins 0–6), 0.2718 (bin 7), 0.5620 (bin 8), and 0.9943 (bin 9). Regime labels describe the u -stratified structure. Router branches follow Eq. ( 23 ) with pooled ten-seed thresholds Q0.3=0.267 and Q0.9=0.714 . Bins 0–6 are grouped as a single background regime. Their median u spans Q0.3 , so some samples within this regime route to pseudo. The saturated regime is the only regime where mean IoU decreases relative to the preceding bin; this drop is what makes u a two-ended separator and not a monotone ranking.
Dataset
Modality
Calibrated T ?
Role
FLIR ADAS
RGB + 14-bit TIFF
✓
Primary
FLAME 3
Radiometric Long-Wave Infrared (LWIR)
✓
Auxiliary
Table 7: Datasets used in this work.
Contrast
Metric
Δ
t -test p
Wilcoxon p
Cohen’s d
Reading
true − pseudo
mAP
+0.0221
0.0077
0.0098 ( W=3 )
+1.08
primary, Wilcoxon
true − shuffled
ECE
+0.0882
0.039
0.002 ( W=0 )
+0.76
primary, true higher
true − pseudo
ECE
−0.0097
0.77
0.064
−0.095
secondary, n.s.
true − pseudo
Recall
+0.0008
0.66
n.s.
+0.14
secondary, n.s.
true − pseudo
LCR
+0.0044
0.60
n.s.
+0.17
secondary, n.s.
true − const- ΔT
ECE
+0.0916
0.019
0.002 ( W=0 )
+0.90
secondary, Holm-pass
Table 8: Paired contrasts on FLIR ADAS over ten seeds under the two-stage protocol. All Cohen’s d values are paired-effect sizes, computed from the per-seed paired differences. The primary family is true-vs-pseudo on mAP and true-vs-shuffled on ECE ( m=2 , Holm threshold 0.025 ); the secondary family is true-vs-pseudo ECE/Recall/LCR and true-vs-const- ΔT ECE ( m=4 , Holm thresholds 0.0125 , 0.0167 , 0.025 ). The detection-axis attribution (var-phase-vs-true mAP and ECE) is pre-specified and reported as a dedicated contrast pair. Rows below the third rule are exploratory. Positive Δ means the first arm is larger.
Probe
emod mean
Δemod
Top score
zero modulation
0.002453
reference
0.8647
true ΔT
0.003395
+38.42% ( p=4.2×10−25 )
0.8862 ( +2.48% , p=8.7×10−43 )
random modulation
0.002668
+8.78% ( p=2.97×10−2 )
0.8651 ( +0.05% , p=9.5×10−3 )
Table 9: Attribution-consumption probe on FLIR ADAS ( 200 images). The modulated evidence magnitude emod and the top detection score are compared across zero modulation, true calibrated ΔT , and random modulation.
Table 10: Overall comparison on FLIR ADAS (10-seed prediction, all bins pooled). The primary acceptance test is TEL(true ΔT ) versus Grayscale pseudo- ΔT .
Table 11: Auxiliary validation on FLAME 3 (radiometric wildfire detection, ∣ΔT∣≈30 – 60∘ C). Mean ± std over eight seeds. All p values are paired Wilcoxon signed-rank tests over the eight paired seeds, where the smallest attainable two-sided p is 0.0078 .
Variant
ECE (raw)
T (median)
ECE TS
Δ ECE
Baseline (no modulation)
0.4585
2.645
0.4588
+0.0003
Random modulation
0.0373
0.807
0.0166
−0.0206
Grayscale pseudo- ΔT
0.1512
0.661
0.0860
−0.0652
Shuffled true ΔT
0.0534
0.706
0.0172
−0.0361
const- ΔT
0.0500
0.872
0.0342
−0.0156
TEL (true ΔT )
0.1415
0.763
0.0837
−0.0578
Table 12: Post-hoc temperature scaling on FLIR ADAS (10 seeds). T is fitted per arm on the validation set with NLL as the objective; ECETS uses M=15 . T is the median across seeds; the true arm’s mean is affected by seed s2 ( T=3.89 ; Section 4.5 ). Raw ECE is reproduced from Table 10 ; Δ ECE is computed from per-seed means before rounding.
Variant
paired
absolute
mean
p50
p90
none
–
–
0.493
0.500
0.500
random
×
×
0.083
0.032
0.062
true
✓
✓
0.222
0.110
0.637
shuffled
×
✓
0.115
0.062
0.164
const- ΔT
✓
×
0.158
0.059
0.652
Table 13: Confidence distribution over 10 seeds (paired protocol).
Quantity
Value
95% CI
p
Interaction contrast cˉ
+0.0756
[+0.011,+0.140]
t -test 0.0475 ; Wilcoxon 0.0059
Cohen’s d
+0.73
—
—
Leave-one-out cˉ (sans s2)
+0.0437
—
<0.005
Component ECEtrue−ECEconst
+0.0916
—
—
Component ECEshuffled−ECErandom
+0.0161
—
—
Table 14: Joint-condition interaction test on ECE over ten paired seeds. The 2 × 2 contrast c=(ECE1,1−ECE1,0)−(ECE0,1−ECE0,0) is positive and significant under the Wilcoxon signed-rank test.
Figure 3: Δ ECE (true − random) versus per-box separability ratio ρ bins, with GT-derived quintile boundaries q20/q40/q60/q80=0.703/1.271/1.843/2.588 .
Figure 4: Cross-dataset reversal of the two axes. The same phase-randomized intervention (var-phase − true) produces a detection-axis effect of the same sign and comparable magnitude on FLIR ADAS and FLAME 3, and a calibration-axis effect that is absent on FLIR ADAS ( p=0.47 ) and significant on FLAME 3 ( p=0.0078 , the smallest attainable at eight seeds). Each axis is significant on the dataset where its structural counterpart is most pronounced, and insignificant on the other.
true vs. pseudo redundancy; random superiority check
Table 15: Data conditions and their discriminating power. Each dataset supplies a distinct validation axis.
Figure 5: Cross-dataset physical contrast.
Threshold τ
FLIR person pass
FLAME3 fire pass
Physical reading
0.5∘ C
10.5%
99.95%
FLIR: cold-background persons; FLAME 3: all fires
5∘ C
0%
99.9%
FLIR: no person reaches 5∘ C; FLAME 3: most fires
40∘ C
0%
53.5%
FLIR: no person reaches 40∘ C; FLAME 3: strong fires only
τG=20 (8-bit gray)
73.6%
36.0%
no physical reading
Table 16: Cross-dataset pass rates of physical and gray thresholds.
Figure 6: [email protected] versus ΔT bucket midpoint on FLIR ADAS for five variants: none, pseudo, random, TEL (true), and var-phase. All five curves rise with ΔT up to B4, the high-transition bucket, and then decline at the redundant end (B5). The var-phase curve lies above true at B1, B2, and B4, below it at B3 and B5, with the largest positive gap at B4, the bucket where the injected-variance and true-variance scales are best matched. This is the qualitative counterpart of the paired +0.0185 mAP effect reported in Table 8 . Buckets are test-set GT ΔT median quintiles with boundaries q20/q40/q60/q80=0.2424/0.2721/0.3392/0.5015∘ C.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Signal
Pair
err∣acc
ub
Gap
u
(7,8)
0.0556
0.0575
+0.0019
u
(2,9)
0.0273
0.0352
+0.0078
u
(1,8)
0.0616
0.0698
+0.0082
u
(3,9)
0.0360
0.0480
+0.0120
u
(2,3)
0.0267
0.0396
+0.0129
H
(7,8)
0.0348
0.0551
+0.0203
Appendix
Table 17: Tightest seed pairs for the pseudo-label error bound in Eq. ( 27 ). Only u and H are shown; margin and conf are omitted because they track u under K=2 .
Seed
τ=0.40
τ=0.45
τ=0.50
τ=0.55
τ=0.60
0
0.0140
0.0144
0.0227
0.0355
0.0486
1
0.0619
0.0234
0.0162
0.0340
0.0484
2
0.1667
0.0541
0.0285
0.0311
0.0463
3
0.0436
0.0306
0.0245
0.0311
0.0423
4
0.0179
0.0179
0.0192
0.0295
0.0464
5
0.2231
0.0592
0.0378
0.0454
0.0524
Appendix
Table 18: Per-seed discard error Pr(y^=y∣u<τlow) under the oracle-based image-level protocol.
Pair
s0
s1
s2
s3
s4
s5
s6
s7
s8
s9
Pearson ρ
u , H
−0.092
−0.145
−0.008
−0.075
−0.009
−0.060
−0.013
−0.147
−0.062
−0.189
u , margin
−0.922
−0.930
−0.943
−0.922
−0.921
−0.929
−0.932
−0.926
−0.915
−0.921
H , margin
−0.259
−0.191
−0.275
−0.267
−0.330
−0.268
−0.298
−0.193
−0.296
−0.169
margin, conf
+1.000
+1.000
+1.000
+1.000
+1.000
+1.000
+1.000
+1.000
+1.000
+1.000
Δ , H
−0.027
−0.091
+0.047
−0.008
+0.057
−0.005
+0.049
−0.089
+0.007
−0.130
Appendix
Table 19: Per-seed signal correlations on the FLIR ADAS prediction protocol. Redundant pairs ( u –conf, H –conf, Δ –conf) are omitted; they are identical to the corresponding margin pairs because K=2 .
Set
n
Signed Pearson
Signed Spearman
Unsigned Pearson
Unsigned Spearman
FLIR train
48,649
+0.7126
+0.7183
+0.5068
+0.5709
FLIR test
12,267
+0.8136
+0.8847
+0.8073
+0.8812
FLAME 3
2,126
+0.7570
+0.8450
+0.7569
+0.8450
FLIR subset correlations
FLIR subset
Spearman
n
LCR ( ∣ΔT∣< p25)
+0.9338
3,067
Appendix
Table 20: ΔG – ΔT correlation.
Dataset
Quantity
p25
p50
p75
Other
FLIR ADAS
∣ΔT∣ ( ∘ C)
0.208
0.271
0.357
LOW_DT 0.207
FLIR ADAS
eff. SNR
5.75
8.96
13.98
SNR >1 97.4%, SNR >3 91.0%
FLAME 3
∣ΔT∣ ( ∘ C)
29.89
42.04
59.58
—
FLAME 3
∣ΔG∣
11.81
16.56
23.56
—
Appendix
Table 21: physical-quantity measurements.
α
true
random
0.00
0.5005±0.0433
0.5223±0.0029
0.25
0.4879±0.0290
0.5199±0.0007
0.50
0.4827±0.0260
0.5157±0.0039
0.75
0.4776±0.0231
0.5148±0.0046
1.00
0.4720±0.0207
0.5133±0.0062
1.25
0.4665±0.0187
0.5116±0.0076
Appendix
Table 22: [email protected] as a function of modulation amplitude α over seeds s0, s1, and s2. All points except α=1.0 are out-of-distribution extrapolations.
Router
Set
νTK / 152
per-image fraction (mean ± std)
max
fixed ( τhigh=0.7 , τlow=0.3 )
train
132
0.031±0.072
0.382
quantile ( Q0.9 , Q0.3 )
train
147
0.092±0.118
0.428
fixed
test
138
0.069±0.110
0.421
quantile
test
148
0.152±0.131
0.467
Appendix
Table 23: Per-image switch fraction under the fixed-threshold and quantile routers, on the training and test evaluation sets. νTK is the aggregate count out of 152 checkpoint pairs. The per-image fraction appears alongside.
Visible-infrared object detection relies on complementary RGB and thermal cues, but its performance is often degraded by cross-modal spatial misalignment. Most existing methods rely on implicit feature adaptation to handle weakly misaligned scenarios, while large-offset geometric discrepancies remain insufficiently addressed. In this paper, we propose a Joint Feature-domain Registration and Detection network (JFRDet), an end-to-end visible-infrared oriented object detector tailored for severely cross-modal geometric discrepancies. JFRDet introduces a Cross-Modal Affine Alignment (CMAA) module to estimate an image-level affine transformation for explicit multi-level feature alignment. Note that illumination changes directly affect the reliability of RGB cues, an Illumination-Guided Complementary Fusion (IGCF) module adaptively exploits modality reliability under varying illumination conditions for cross-modal fusion. Then, an Alignment Quality-Consistency Gating (AQCG) strategy stabilizes joint optimization by modulating detection supervision according to alignment reliability and gradient consistency. We further construct DroneVehicle Misaligned (DVMA), a benchmark for evaluating visible-infrared oriented object detection under severe cross-modal geometric misalignment. The proposed JFRDet achieves 69.7% mAP50 on DVMA, which represents state-of-the-art (SOTA) performance. The code and dataset will be available on GitHub.
Qi Ming, Yuyang Wang, Mingjing Zhao +7
Beijing University of Technology, China · Central South University, China · Beijing Electronics Science & Technology Institute +4
Infrared pedestrian detectors are increasingly deployed in all-weather perception systems, but their robustness against physical adversarial attacks remains insufficiently understood. Existing infrared physical attacks are mostly instance-specific, requiring perturbations to be optimized for particular samples, poses, or scenes, which limits scalability under changing deployment conditions. This paper proposes Universal Physical Patch Attack (UPPA), a universal cold-patch framework for infrared pedestrian detection. UPPA is built on the observation that infrared physical perturbations should exploit smooth, low-frequency thermal structures rather than visible-light texture patterns. It represents the attack carrier as topology-constrained Bézier Curved-Blocks, providing a compact and manufacturable geometric parameterization, and optimizes one shared perturbation with Particle Swarm Optimization (PSO) under Thin Plate Spline (TPS) deformation and Expectation over Transformation (EOT) imaging transformations. The optimized pattern is then deployed as wearable cold patches without sample-specific re-optimization during deployment. Experiments on five infrared datasets and nine pedestrian detectors show consistent digital attack performance, strong cross-dataset and cross-model transferability, and a 92.59% attack success rate in real-world physical experiments. Ablation, visualization, and defense analyses show that Curved-Blocks disrupt pedestrian thermal feature aggregation and remain difficult for image-restoration-style defenses to remove. These results reveal a practical universal physical vulnerability in current infrared pedestrian detection systems and provide a benchmark for robustness evaluation.
Chengyin Hu, Yikun Guo, Yuxian Dong +7
China University of Petroleum-Beijing at Karamay, No. 355, Anding Road, Karamay, 834000, Xinjiang, China. · Guangdong University of Technology, Guangzhou, Guangdong, China. · Tianjin University, Tianjin, China. +1
Infrared small target detection still faces two persistent challenges: training instability from non-monotonic scale loss functions, and inadequate spatial attention due to generic convolution kernels that ignore the physical imaging characteristics of small targets. In this paper, we revisit both aspects. For the loss side, we propose a diff-based scale loss that weights predictions according to the signed area difference between the predicted mask and the ground truth, yielding strictly monotonic gradients and stable convergence. We further analyze a family of four scale loss variants to understand how their geometric properties affect detection behavior. For the spatial side, we introduce Gaussian-shaped convolution with a learnable scale parameter to match the center-concentrated intensity profile of infrared small targets, and augment it with a rotated pinwheel mask that adaptively aligns the kernel with target orientation via a straight-through estimator. Extensive experiments on IRSTD-1k, NUDT-SIRST, and SIRST-UAVB demonstrate consistent improvements in mIoU, Pd, and Fa over state-of-the-art methods. We release our anonymous code and pretrained models.
Hao Li, Man Fung Zhuo
Department of Electrical and Computer Engineering, University of Arizona, Tucson, USA