Human Pose Estimation by Probabilistic Mixtures of Gaussian and Uniform Distributions

Santiago Reina Alguacil; Ezequiel López Rubio

cs.CVOct 8, 2026

Human Pose Estimation by Probabilistic Mixtures of Gaussian and Uniform Distributions

Authors: Santiago Reina Alguacil, Ezequiel López Rubio

Organizations: Department of Computer Languages and Computer Science, University of Málaga, 29071 Málaga, Spain · Instituto de Investigación Biomédica de Málaga y Plataforma en Nanomedicina – IBIMA Plataforma BIONAND, 29590 Málaga, Spain · ITIS Software, University of Málaga, 29071 Málaga, Spain

Abstract

Despite advancements in sub-pixel decoding, modern Human Pose Estimation (HPE) architectures remain constrained by deterministic coordinate extraction from discrete heatmaps, which systematically fails under dense occlusions and Out-of-Distribution (OoD) ambiguities. To address these limitations, we propose a post-hoc continuous probabilistic framework that intercepts raw heatmaps and models them as a Gaussian Mixture Model (GMM) augmented with a spatially agnostic uniform distribution, requiring no architectural modifications or retraining. This continuous representation allows us to comprehensively explore the distinct contributions of density modeling to HPE. We show that the spatial expectation of our fitted GMM achieves precision parity with leading sub-pixel decoders without heuristic post-processing. Leveraging this continuous space, our test-time augmentation aggregates probability distributions rather than discrete activations, mitigating multi-scale heatmap poisoning. Furthermore, because our multimodal GMM parameterization isolates competing spatial hypotheses, it naturally interfaces with geometric regularizers such as Markov Random Fields. However, our analysis exposes the inherent vulnerabilities of 2D kinematic priors under perspective foreshortening and visual degradation. Crucially, this density formulation yields significant improvements in uncertainty quantification: our calibrated geometric covariance volume outperforms standard peak-intensity heuristics in OoD anomaly detection under severe occlusion. For in-distribution calibration, dynamically fusing our geometric metric via Adaptive Softmax reduces or matches baseline Area Under the Sparsification Error (AUSE) across benchmarks and degradation levels. Finally, we establish that this continuous parameterization is extensible to multi-view 3D architectures, bypassing the $\mathcal{O}(N^3)$ voxel memory bottleneck.

Figures & tables

Feature/Capability	Standard	DARK/UDP	RLE	Proposed (GMM + Uniform)
Output Paradigm	Discrete Pixel	Sub-pixel Coordinate	Sub-pixel Coordinate	Continuous Distribution
Quantization Mitigation	None	Hessian / Taylor Exp.	Normalizing Flows	MC Sampling & Uniform Jitter
Uncertainty Output	Peak Value ( $P_{max}$ )	Peak Value ( $P_{DARK}$ )	Unimodal Variance	Multimodal Covariance Volume
Multimodal Awareness	No	No	No	Yes (Explicit)
OoD Rejection	Poor (Heuristic)	Poor (Heuristic)	Moderate	High (Covariance Volume)

Table 1: Comparison of Uncertainty and Output Paradigms in HPE Frameworks. Our proposed continuous formulation bridges a critical gap in the literature, explicitly transitioning the output paradigm from deterministic point-estimates to multimodal probability distributions with robust OoD rejection mechanisms.

Figure 1: Overview of the proposed continuous probabilistic framework for Human Pose Estimation. (1) Stochastic Test-Time Augmentation: Multi-scale and flipped image crops are passed through a frozen pose backbone. (2) Continuous Spatial Aggregation & Sampling: Raw heatmaps are aggregated via continuous inverse transforms and confidence weighting, followed by temperature-sharpened Von Neumann rejection sampling ( $N=1000$ ). (3) Probabilistic Mixture Modeling: The EM algorithm concurrently fits candidate models ( $K=1$ vs. $K=2$ Gaussians plus Uniform noise), resolved objectively via Bayesian Information Criterion (BIC). (4) Kinematic MRF Graph Decoding: Ambiguous bimodal states are resolved by Maximum a Posteriori (MAP) Belief Propagation over invariant skeletal anchors, producing the final pose with calibrated spatial covariance ellipses ( $\boldsymbol{\Sigma}$ ).

Figure 2: Empirical motivation and mechanics of the orthogonal Uniform component ( $\pi_{\text{uniform}}$ ). Top Row: Input image instances under escalating resolution loss ( $\text{Clean }1.00\times\rightarrow\text{Extreme }0.062\times$ ). Bottom Row: Corresponding activation heatmaps, Monte Carlo candidate samples, and fitted continuous components for the left ankle. In structured visual regimes ( $\leq\text{High}$ ), spatial evidence concentrates cleanly around genuine anatomical modes, assigning $\geq 91.9\%$ of the probability mass to the Gaussian components ( $\pi_{g}$ ) and leaving uniform absorption minimal ( $\pi_{u}\leq 8.1\%$ ). Under extreme resolution destruction ( $\text{Extreme }0.062\times$ ), unstructured background noise contaminates the feature map. Rather than forcing a Gaussian to expand and corrupt the true coordinate expectation, the EM algorithm naturally diverts diffuse, non-Gaussian outliers into the uniform component ( $\pi_{u}=14.51\%$ , magenta dots), preserving the compact geometric integrity of the genuine anatomical modes (cyan/orange ellipses).

Figure 3: Example of the resolution degradation applied to simulate real-world low-quality inputs. Rather than injecting artificial Gaussian noise or uniform blur, we apply deterministic downsampling to organically reduce spatial information.

Dataset	DARK (Argmax)	Ours (GMM)	$\Delta$ OKS
COCO	0.7079	0.7077	-0.0002
CrowdPose	0.8278	0.8270	-0.0008
OCHuman	0.6281	0.6280	-0.0001

Table 2: Baseline Precision (Clean Images): Comparing the Taylor-expanded DARK decoder against our continuous GMM expectation.

Figure 4: Ablation on Continuous Point Estimation: Baseline Precision across visual degradations. The continuous GMM expectation (blue) maintains geometric parity with the DARK sub-pixel decoder (orange) across all levels of corruption.

Figure 5: Motivation for bimodal modeling ( $K=2$ ). (a) Global pose estimation on an occluded instance from OCHuman. The deterministic baseline ( DARK , dashed red line) suffers from an ankle swap due to coordinate collapse, whereas our continuous formulation ( Ours , solid cyan line) preserves the correct anatomical alignment against the Ground Truth (solid green line). (b) High-resolution zoom on the lower limb region. The Monte Carlo samples (amber dots) delineate a dual activation mass, where while DARK prematurely snaps to the contralateral false peak ( $\text{Mode }2:w_{2}=0.43$ , red cross), our GMM fits two Gaussian components ( $K=2$ ), retaining both spatial hypotheses and placing primary confidence on the correct mode ( $\text{Mode }1:w_{1}=0.56$ , solid gold $2\sigma$ ellipse). (c) Heatmap demonstrating the dual-peak topography intercepted prior to deterministic thresholding.

Figure 6: Anatomy and mitigation of heatmap poisoning during multi-scale Test-Time Augmentation (TTA). (a) Representative zoomed-in crop (

0.85\times

) where the target left knee falls outside the physical field of view, causing the network to emit a diffuse, poisoned heatmap (

\mathcal{C}_{k}=0.655

w_{k}=29.3\%

). (b–c) In-bounds scales (

0.925\times

and

1.00\times

) capturing genuine visual evidence with sharp activation modes (

\mathcal{C}_{k}\geq 0.750

). (d) Traditional unweighted arithmetic averaging across all TTA scales: the flat, out-of-bounds map dilutes the genuine peak, spreading background noise and degrading localization (

\mathrm{OKS}_{\mathrm{GMM}}=0.69

). (e) Our quality-gated continuous aggregation: sharpness and peak confidence dynamically penalize the corrupted scale, preserving a sharp, well-defined mode (

\mathrm{OKS}_{\mathrm{GMM}}=0.82

). (f) Global pose recovery profile across all 17 keypoints: unweighted averaging degrades overall pose accuracy below the baseline (

0.80\rightarrow 0.69

), whereas our weighted aggregation achieves

+0.13

OKS recovery, successfully restoring the poisoned target joint from near-zero accuracy to

\mathrm{OKS}_{k}=0.99

Figure 7: Impact of the MRF decoder on bimodal keypoints as a function of the dominant Gaussian weight. The MRF provides the highest precision gains when the GMM is highly uncertain ( $\sim 0.5-0.6$ ), effectively leveraging structural priors to resolve local ambiguity. As the GMM confidence approaches 1.0, the MRF correctly converges to the GMM’s local prediction ( $\Delta$ OKS approaches zero).

Figure 8: 3D Thermodynamic Surface of the Adaptive Softmax Fusion ( $\beta=0.1$ ). This continuous aggregation avoids the non-differentiable ridges of Max-Pooling. When the geometric volume is near zero, the surface delegates the output to the baseline confidence. However, when structural ambiguity expands the GMM volume, the exponential weighting dynamically overrides the baseline, pushing the fused uncertainty toward 1.0. This smooth transition establishes an universal sweet spot.

Figure 9: Heuristic confidence vs. volumetric spatial alert in Out-of-Distribution (OoD) absence detection. (a) Scene from CrowdPose where the target keypoint (left eye) is completely absent. The deterministic baseline ( DARK ) commits a false lock onto the background (red cross). (b) Spatial activation overlay and continuous GMM fit. Despite the absence of visual evidence, DARK reports a misleadingly confident peak (

P_{\text{DARK}}=0.70

). In stark contrast, our continuous formulation captures the underlying spatial diffusion, yielding an expanded uncertainty ellipse ((

\det(\boldsymbol{\Sigma}_{\text{final}})=34.58

, dashed gold ring). (c) Diagnostic uncertainty profile. While the baseline heuristic alert (

1-P_{DARK}=0.30

) projects false confidence, our calibrated geometric volume alert ((

\det(\boldsymbol{\Sigma}_{\text{final}})=34.58

)) saturates to maximum uncertainty, reliably flagging the missing keypoint.

Figure 10: The limitation of 2D kinematic regularizers: Constructive alignment vs. Projective foreshortening error propagation. Top Row (Constructive Kinematic Guidance in Canonical Poses): In un-foreshortened poses (a1) , local GMM sampling jitter leaves the initial prediction retracted ( $d=18\,\text{px}$ , red cross in b1 ) relative to the empirical prior band ( $\mu=34\,\text{px}$ , green dashed ring). In (c1) , the pairwise kinematic potential guides the ankle toward the anatomically expected configuration ( $d=26\,\text{px}$ , cyan arrow), improving localization accuracy. Bottom Row (Destructive Rigidity under Projective Foreshortening): In scenes with acute camera perspective (a2) , the lower limb extends along the optical axis, naturally projecting as a compressed segment in 2D ( $d=8\,\text{px}$ to Ground Truth, b2 ). While the independent GMM localizes this foreshortened joint accurately, the rigid 2D Euclidean prior ( $\mu=24\,\text{px}$ ) penalizes the perspective shortening as an anatomical violation. Consequently, the MRF pairwise potential displaces the coordinate by $19\,\text{px}$ across the image plane ( c2 , red dashed arrow) to satisfy the distorted 2D graph, inducing a catastrophic strict swap.

Appendix figures & tables31 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Degradation	OKS			Loose Swaps			Strict Swaps
Dataset	Degradation	DARK	GMM	$\Delta$	DARK	GMM	$\Delta$	DARK	GMM	$\Delta$
COCO	Baseline (Clean)	0.7137	0.7129	-0.0008	98	97	-1	18	18	0
	Resize Low	0.6912	0.6907	-0.0005	116	113	-3	26	26	0
	Resize Medium	0.6082	0.6076	-0.0007	215	214	-1	66	67	+1
	Resize High	0.4485	0.4465	-0.0020	404	388	-16	135	138	+3
	Resize Extreme	0.2505	0.2494	-0.0011	438	437	-1	139	139	0

Appendix

Table S1: Ablation on Stochastic Aggregation: Comparison of DARK (Discrete TTA) vs. continuous GMM aggregation across three datasets and five degradation levels. The analysis highlights an architectural trade-off: while the discrete DARK baseline achieves slightly higher raw OKS, continuous aggregation acts as an effective spatial filter, reducing minor bilateral ambiguities (Loose Swaps). For catastrophic inversions (Strict Swaps), the GMM yields minor regressions in canonical datasets (COCO, CrowdPose) but outperforms the discrete baseline in severely occluded environments (OCHuman) ( DARK : Discrete TTA, GMM : Ours (GMM)).

Dataset	Degradation	OKS				Loose Swaps				Strict Swaps
Dataset	Degradation	DARK	GMM	+MRF	$\Delta_{M,G}$	DARK	GMM	+MRF	$\Delta_{M,G}$	DARK	GMM	+MRF	$\Delta_{M,G}$
COCO	Baseline (Clean)	0.7137	0.7129	0.7138	+0.0008	98	97	101	+4	18	18	20	+2
	Resize Low	0.6912	0.6907	0.6911	+0.0004	116	113	113	0	26	26	28	+2
	Resize Medium	0.6082	0.6076	0.6071	-0.0004	215	214	215	+1	66	67	70	+3
	Resize High	0.4485	0.4465	0.4481	+0.0016	404	388	394	+6	135	138	142	+4
	Resize Extreme	0.2505	0.2494	0.2524	+0.0030	438	437	435	-2	139	139	135	-4

Appendix

Table S2: Ablation on Global Structural Priors: Isolating the effect of the MRF structural constraint applied over continuous GMM probability distributions, compared against DARK (Discrete TTA). While the MRF generally improves global coordinate precision (OKS) relative to the independent GMM, enforcing this global skeletal prior increases bilateral swap errors (both Loose and Strict Swaps), occasionally exceeding the swap error rates of discrete TTA in crowded, degraded scenarios ( DARK : Discrete TTA, GMM : Ours (GMM), +MRF : Ours (+MRF)).

Dataset	Degradation	Unimodal Anchors ( $K=1$ )			Ambiguous Nodes ( $K=2$ )
Dataset	Degradation	Ratio (%)	Ours (TTA)	$\Delta_{\text{MRF}}$	Ratio (%)	Ours (TTA)	$\Delta_{\text{MRF}}$ (Gain)
COCO	Baseline (Clean)	95.1%	$0.8851\pm 0.18$	$0.0000$	4.9%	$0.4945\pm 0.38$	+0.0254 (+2.54%)
	Resize Low	93.6%	$0.8649\pm 0.20$	$0.0000$	6.4%	$0.4517\pm 0.38$	+0.0021 (+0.21%)
	Resize Medium	86.1%	$0.8002\pm 0.27$	$0.0000$	13.9%	$0.3106\pm 0.37$	$-0.0001$ ( $-0.01\%$ )
	Resize High	67.1%	$0.6843\pm 0.34$	$0.0000$	32.9%	$0.2106\pm 0.33$	+0.0060 (+0.60%)
	Resize Extreme	40.6%	$0.4948\pm 0.38$	$0.0000$	59.4%	$0.1285\pm 0.26$	+0.0056 (+0.56%)

Appendix

Table S3 : Decoupled Performance Breakdown of the MRF Structural Prior on HRNet-W32. Evaluating the net impact of the pairwise kinematic constraints over 85,255 keypoints. Unimodal nodes (

K=1

) act as invariant anchors (

\Delta\text{OKS}=0

), while the MRF selectively optimizes bimodal ambiguities (

K=2

), delivering consistent precision gains.

	All (Global)			Visible			Occluded
Dataset	DARK ( $1-P_{DARK}$ )	DARK (Entropy)	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )	DARK ( $1-P_{DARK}$ )	DARK (Entropy)	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )	DARK ( $1-P_{DARK}$ )	DARK (Entropy)	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )
COCO	0.0581	0.1437	0.0945	0.0570	0.1404	0.0902	0.1026	0.2037	0.1322
CrowdPose	0.0515	0.1591	0.0911	0.0379	0.1262	0.0657	0.0599	0.1845	0.1067
OCHuman	0.1573	0.2373	0.2143	0.1491	0.2320	0.2002	0.2636	0.3130	0.2203

Appendix

Table S4 : Global Sparsification Error (AUSE). Lower values indicate better calibration. While the baseline performs better in clean, isolated scenarios, the geometric GMM volume (

\det(\boldsymbol{\Sigma}_{\text{final}})

) achieves lower sparsification error under severe multi-person occlusions (e.g., 0.2203 vs. 0.2636 on OCHuman Occluded).

	COCO		CrowdPose		OCHuman
Degradation Level	DARK ( $1-P_{DARK}$ )	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )	DARK ( $1-P_{DARK}$ )	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )	DARK ( $1-P_{DARK}$ )	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )
00_Baseline_Clean	0.0527	0.0654	0.0422	0.0766	0.1381	0.2037
01_Resize_Low	0.0544	0.0701	0.0432	0.0766	0.1429	0.2069
02_Resize_Medium	0.0689	0.0899	0.0528	0.0861	0.1548	0.2105
03_Resize_High	0.0943	0.1266	0.0676	0.1054	0.1819	0.2229
04_Resize_Extreme	0.1155	0.1235	0.0987	0.1253	0.2165	0.2024

Appendix

Table S5 : Global AUSE evolution under progressive visual degradation. As spatial resolution degrades and feature maps lose sharpness, baseline calibration deteriorates. Conversely, the GMM covariance volume reflects the increased spatial dispersion, remaining competitive under high degradation.

	Unimodal ( $K=1$ )			Bimodal ( $K=2$ )
Dataset	DARK ( $1-P_{DARK}$ )	Entropy	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )	DARK ( $1-P_{DARK}$ )	Entropy	Ours ( $\det(\boldsymbol{\Sigma}_{\text{final}})$ )
COCO	0.0637	0.1493	0.0914	0.1364	0.1822	0.1479
CrowdPose	0.0507	0.1424	0.0912	0.1759	0.2429	0.1924
OCHuman	0.1588	0.2309	0.2174	0.2519	0.2995	0.2710

Appendix

Table S6 : Global AUSE segregated by unimodal vs. bimodal predictions. Across all datasets and metrics, bimodal detections (

K=2

) yield a higher AUSE than unimodal ones (

K=1

), confirming that mixture bimodality serves as an indicator of heightened spatial ambiguity.

Figure S1 : Continuous Expected Calibration Error (ECE) across distinct prediction regimes (

K=1

vs.

K=2

). The x-axis represents log-volume

\log(1+\det(\boldsymbol{\Sigma}_{\text{final}}))

and the y-axis is the empirical mean error (

1-\text{OKS}

). While the global evaluation (Top Row) mixes predictive states, decoupling the analysis clarifies the uncertainty response: the unimodal regime (Middle Row) clusters at low error values, whereas isolating bimodal predictions (Bottom Row) displays a monotonic relationship between covariance volume and error magnitude.

	COCO			CrowdPose			OCHuman
Degradation	DARK (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )	DARK (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )	DARK (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )
00_Baseline_Clean	0.0528	0.0421 (0.19)	0.0388 (0.12)	0.0422	0.0418 (1.54)	0.0413 (0.52)	0.1382	0.1383 (0.01)	0.1352 (0.04)
01_Resize_Low	0.0545	0.0465 (0.22)	0.0423 (0.10)	0.0432	0.0432 (1.22)	0.0425 (0.57)	0.1430	0.1437 (0.00)	0.1409 (0.03)
02_Resize_Medium	0.0690	0.0613 (0.21)	0.0554 (0.12)	0.0528	0.0527 (0.90)	0.0522 (0.66)	0.1549	0.1551 (0.04)	0.1517 (0.02)
03_Resize_High	0.0945	0.0816 (0.31)	0.0743 (0.19)	0.0677	0.0678 (1.05)	0.0671 (0.61)	0.1820	0.1813 (0.16)	0.1749 (0.08)
04_Resize_Extreme	0.1162	0.1014 (0.45)	0.0960 (0.31)	0.0988	0.0983 (4.19)	0.0948 (1.80)	0.2216	0.1940 (0.77)	0.1864 (7.18)

Appendix

Table S7 : Global AUSE comparison of fusion strategies under different degradation levels, accompanied by their respective oracle optimal

\beta

values. Both Max-Pooling and Softmax consistently improve upon the baseline when

\beta

is perfectly tuned.

	Global (All Points)			Occluded Joints Only
Degradation	COCO	CrowdPose	OCHuman	COCO	CrowdPose	OCHuman
Clean	0.1924	1.5392	0.0082	0.1924	1.5392	39.0817
Low	0.2245	1.2217	0.0000	0.2424	0.0707	45.5893
Medium	0.2078	0.8978	0.0382	0.4157	0.0825	49.2388
High	0.3055	1.0473	0.1650	0.1309	0.9697	45.5893
Extreme	0.4489	4.1886	0.7696	0.2619	1.6624	36.1850

Appendix

Table S8 : Optimal empirical sensitivity hyperparameter (

\beta

) values determined via logarithmic Grid Search for the Max-Pooling fusion strategy. Clean scenarios require a small penalty (e.g.,

0.0082

), while heavily occluded subsets require high sensitivity (e.g.,

39.08

), demonstrating the difficulty of finding a single static operating point.

Dataset	Degradation	DARK (Base) AUSE	Max-Pool AUSE ( $\beta=0.1$ )	Softmax AUSE ( $\beta=0.1$ )
COCO	Clean	0.0527	0.0435	0.0388
	Low	0.0544	0.0477	0.0420
	Medium	0.0689	0.0628	0.0555
	High	0.0943	0.0862	0.0755
	Extreme	0.1155	0.1098	0.0996
	General	0.0581	0.0524	0.0460

Appendix

Table S9 : Sparsification Error (AUSE) using a fixed

\beta=0.1

. Unlike Max-Pooling, the continuous Softmax strategy smoothly balances the contributions without per-image parameter tuning, matching or improving upon the DARK baseline across datasets and degradation levels.

Figure S2 : Grid Search optimization curves for the sensitivity hyperparameter

\beta

evaluated on HRNet-W32 (COCO). Softmax fusion (orange curve) consistently achieves lower AUSE, with an empirical optimum near

\beta=0.1

Dataset	Ours (Volume)	Ours (Uniform)	DARK (Entropy)	DARK ( $1-P_{DARK}$ )
COCO	0.7364	0.7387	0.7042	0.8122
CrowdPose	0.8787	0.5408	0.3256	0.5160
OCHuman	0.7209	0.5712	0.4643	0.6441

Appendix

Table S10 : Global AUROC for OoD Anomaly Detection (vis == 0).

Dataset	Metric	Clean	Low	Medium	High	Extreme
COCO	Ours (Volume)	0.7663	0.7798	0.7832	0.7414	0.6753
COCO	DARK ( $1-P_{DARK}$ )	0.8974	0.9062	0.8861	0.8130	0.7053
CrowdPose	Ours (Volume)	0.9231	0.9216	0.9139	0.8729	0.8053
CrowdPose	DARK ( $1-P_{DARK}$ )	0.4858	0.4859	0.4928	0.5181	0.5439
OCHuman	Ours (Volume)	0.7312	0.7295	0.7291	0.7268	0.6926
OCHuman	DARK ( $1-P_{DARK}$ )	0.6511	0.6496	0.6524	0.6529	0.6265

Appendix

Table S11 : Evolution of AUROC for OoD detection across image degradation levels. As spatial resolution drops, deterministic baseline confidence degrades substantially. In dense datasets like CrowdPose, GMM covariance volume retains high discriminative performance (

0.8053

) under extreme degradation, whereas the baseline drops close to random classification (

0.5439

Figure S3 : Distribution of the uniform weight (

\pi_{\text{uniform}}

) as visual degradation escalates. Boxplots demonstrate the metric’s responsiveness to extreme noise.

Figure S4 : Out-of-Distribution (OoD) Anomaly Detection ROC curves decoupled by mixture cardinality (

K=1

vs.

K=2

). In dense environments (CrowdPose, OCHuman) with unimodal predictions (Middle Row,

K=1

), baseline peak confidence degrades to

0.38

AUROC due to confident detections on adjacent individuals. Conversely, continuous GMM covariance volume maintains strong discriminative ability (

0.94

AUROC on CrowdPose) by evaluating spatial dispersion rather than peak intensity.

Panel of Figure 28 — Figure S5 : KDE density estimations comparing the distribution of In-Distribution versus OoD points. The bimodal separation achieved by covariance volume (blue curve on the right) accounts for its higher AUROC performance.

Figure S6 : Impact of image degradation (Clean to Extreme) on OoD anomaly detection capabilities (AUROC).

Dataset	Degradation	OKS			Loose Swaps			Strict Swaps
Dataset	Degradation	DARK	GMM	$\Delta$	DARK	GMM	$\Delta$	DARK	GMM	$\Delta$
COCO	Baseline (Clean)	0.6868	0.6870	+0.0002	119	126	+7	22	22	0
	Resize Low	0.6603	0.6607	+0.0005	140	145	+5	32	32	0
	Resize Medium	0.5767	0.5764	-0.0003	225	232	+7	77	77	0
	Resize High	0.4140	0.4132	-0.0008	365	353	-12	108	115	+7
	Resize Extreme	0.2270	0.2267	-0.0003	381	359	-22	108	115	+7

Appendix

Table S12: ResNet50 Ablation on Stochastic Aggregation: Comprehensive comparison of DARK (Discrete TTA) vs our continuous GMM aggregation across three datasets and five degradation levels ( DARK : DARK (Discrete TTA), GMM : Ours (GMM).

Dataset	Degradation	OKS				Loose Swaps				Strict Swaps
Dataset	Degradation	DARK	GMM	+MRF	$\Delta_{M,G}$	DARK	GMM	+MRF	$\Delta_{M,G}$	DARK	GMM	+MRF	$\Delta_{M,G}$
COCO	Baseline (Clean)	0.6868	0.6870	0.6875	+0.0005	119	126	122	-4	22	22	23	+1
	Resize Low	0.6603	0.6607	0.6615	+0.0008	140	145	146	+1	32	32	34	+2
	Resize Medium	0.5767	0.5764	0.5765	+0.0001	225	232	231	-1	77	77	81	+4
	Resize High	0.4140	0.4132	0.4139	+0.0007	365	353	359	+6	108	115	115	0
	Resize Extreme	0.2270	0.2267	0.2277	+0.0010	381	359	381	+22	108	115	123	+8

Appendix

Table S13: ResNet50 Ablation on Global Structural Priors: Isolating the effect of the MRF structural constraint applied over the continuous GMM + TTA probability distributions. ( DARK : DARK (Discrete TTA), GMM : Ours (GMM), +MRF : Ours (+MRF)).

	COCO			CrowdPose			OCHuman
Degradation	DARK (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )	DARK (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )	DARK (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )
00_Baseline_Clean	0.0641	0.0458 (0.28)	0.0416 (0.15)	0.0429	0.0422 (1.94)	0.0408 (1.22)	0.1598	0.1596 (0.06)	0.1547 (0.05)
01_Resize_Low	0.0677	0.0507 (0.28)	0.0456 (0.15)	0.0459	0.0448 (2.09)	0.0430 (1.43)	0.1646	0.1618 (0.08)	0.1571 (0.05)
02_Resize_Medium	0.0782	0.0668 (0.26)	0.0606 (0.14)	0.0498	0.0494 (2.09)	0.0474 (1.32)	0.1677	0.1663 (0.12)	0.1608 (0.06)
03_Resize_High	0.1053	0.0887 (0.33)	0.0821 (0.19)	0.0672	0.0676 (1.94)	0.0660 (0.71)	0.1873	0.1823 (0.22)	0.1764 (0.10)
04_Resize_Extreme	0.1168	0.0962 (0.71)	0.0913 (0.38)	0.0971	0.0965 (0.83)	0.0933 (2.09)	0.2172	0.1955 (9.77)	0.1865 (13.30)

Appendix

Table S14 : ResNet50 Global AUSE comparison of fusion strategies accompanied by their oracle optimal

\beta

values.

Dataset	Degradation	DARK (Base) AUSE	Max-Pool AUSE ( $\beta=0.1$ )	Softmax AUSE ( $\beta=0.1$ )
COCO	Clean	0.0639	0.0489	0.0420
	Low	0.0673	0.0542	0.0460
	Medium	0.0782	0.0659	0.0563
	High	0.1002	0.0923	0.0793
	Extreme	0.1167	0.1107	0.0969
	General	0.0662	0.0567	0.0484

Appendix

Table S15 : ResNet50 Sparsification Error (AUSE) using a static

\beta=0.1

. The continuous Softmax strategy consistently outperforms or matches the DARK baseline.

Figure S7 : ResNet50 Out-of-Distribution (OoD) Anomaly Detection ROC curves decoupled by mixture cardinality (

K=1

vs.

K=2

Figure S8 : ResNet50: Impact of image degradation (Clean to Extreme) on OoD anomaly detection capabilities (AUROC).

Dataset	Degradation	OKS			Loose Swaps			Strict Swaps
Dataset	Degradation	UDP	GMM	$\Delta$	UDP	GMM	$\Delta$	UDP	GMM	$\Delta$
COCO	Baseline (Clean)	0.6926	0.6936	+0.0011	123	116	-7	25	25	0
	Resize Low	0.6700	0.6697	-0.0003	140	133	-7	30	30	0
	Resize Medium	0.5922	0.5886	-0.0036	225	229	+4	73	77	+4
	Resize High	0.4377	0.4313	-0.0064	385	372	-13	140	140	0
	Resize Extreme	0.2607	0.2567	-0.0040	423	415	-8	142	133	-9

Appendix

Table S16: ViTPose-Small Ablation on Stochastic Aggregation: Comparison of UDP (Discrete TTA) vs our continuous GMM aggregation across three datasets and five degradation levels ( UDP : UDP (Discrete TTA), GMM : Ours (GMM).

Dataset	Degradation	OKS				Loose Swaps				Strict Swaps
Dataset	Degradation	UDP	GMM	+MRF	$\Delta_{M,G}$	UDP	GMM	+MRF	$\Delta_{M,G}$	UDP	GMM	+MRF	$\Delta_{M,G}$
COCO	Baseline (Clean)	0.6926	0.6936	0.6944	+0.0008	123	116	120	+4	25	25	27	+2
	Resize Low	0.6700	0.6697	0.6712	+0.0015	140	133	137	+4	30	30	31	+1
	Resize Medium	0.5922	0.5886	0.5900	+0.0015	225	229	226	-3	73	77	77	0
	Resize High	0.4377	0.4313	0.4327	+0.0014	385	372	377	+5	140	140	145	+5
	Resize Extreme	0.2607	0.2567	0.2569	+0.0002	423	415	430	+15	142	133	139	+6

Appendix

Table S17: ViTPose-Small Ablation on Global Structural Priors: Isolating the effect of the MRF structural constraint applied over the continuous GMM + TTA probability distributions ( UDP : UDP (Discrete TTA), GMM : Ours (GMM), +MRF : Ours (+MRF)).

	COCO			CrowdPose			OCHuman
Degradation	UDP (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )	UDP (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )	UDP (Base)	Max-Pool ( $\beta$ )	Softmax ( $\beta$ )
00_Baseline_Clean	0.0604	0.0448 (0.21)	0.0413 (0.18)	0.0438	0.0435 (1.43)	0.0416 (1.94)	0.1389	0.1441 (0.06)	0.1368 (0.06)
01_Resize_Low	0.0640	0.0489 (0.24)	0.0445 (0.15)	0.0458	0.0460 (1.66)	0.0442 (1.54)	0.1434	0.1471 (0.08)	0.1395 (0.07)
02_Resize_Medium	0.0766	0.0599 (0.31)	0.0546 (0.18)	0.0570	0.0586 (1.54)	0.0570 (1.43)	0.1548	0.1544 (0.12)	0.1499 (0.08)
03_Resize_High	0.1100	0.0906 (0.38)	0.0843 (0.22)	0.0728	0.0751 (1.94)	0.0730 (0.97)	0.1886	0.1815 (0.22)	0.1761 (0.15)
04_Resize_Extreme	0.1280	0.1023 (0.97)	0.0980 (0.45)	0.1079	0.1063 (5.28)	0.1024 (3.88)	0.2261	0.1959 (0.83)	0.1909 (4.89)

Appendix

Table S18 : ViTPose-Small Global AUSE comparison of fusion strategies accompanied by their oracle optimal

\beta

values.

Dataset	Degradation	UDP (Base) AUSE	Max-Pool AUSE ( $\beta=0.1$ )	Softmax AUSE ( $\beta=0.1$ )
COCO	Clean	0.0597	0.0460	0.0415
	Low	0.0640	0.0512	0.0451
	Medium	0.0766	0.0655	0.0561
	High	0.1097	0.1017	0.0877
	Extreme	0.1277	0.1233	0.1055
	General	0.0670	0.0582	0.0506

Appendix

Table S19 : ViTPose-Small Sparsification Error (AUSE) using a static

\beta=0.1

Figure S9 : ViTPose-Small Out-of-Distribution (OoD) Anomaly Detection ROC curves decoupled by mixture cardinality (

K=1

vs.

K=2

). Note that the baseline heuristic curve is labeled as DARK in the plot legend, representing the native UDP confidence (

1-P_{\text{UDP}}

) in this architecture.

Figure S10 : ViTPose-Small: Impact of image degradation (Clean to Extreme) on OoD anomaly detection capabilities (AUROC).

Figure S11 : Modular latency and throughput breakdown across backbones and execution configurations. Stacked bar charts illustrate the relative time consumed by Backbone Forward passes (blue), TTA Aggregation (green), GMM EM fitting and model selection (red), and MRF spatial graph decoding (purple). While the single-threaded CPU implementation of the EM loop currently limits throughput to $0.5-0.7\text{ FPS}$ , batch-tensor GPU parallelization across all 17 joints provides a direct path to higher throughput toward interactive frame rates.

Backbone	Configuration	Forward (ms)	TTA Fuse (ms)	GMM EM (ms)	MRF (ms)	Total Latency (ms)	Throughput (FPS)	Peak VRAM (MB)
HRNet-W32	Vanilla DARK (Baseline)	75.7	–	–	–	76.9 $\pm$ 4.3	13.0	247
	Ours (Basic: Single + GMM)	75.7	–	1311.7	–	1387.4 $\pm$ 8.6	0.7	247
	Vanilla TTA (Multi-scale + DARK)	720.9	3.3	–	–	725.5 $\pm$ 10.0	1.4	247
	Ours (TTA + Continuous GMM)	720.9	3.3	1311.7	–	2035.9 $\pm$ 12.5	0.5	247
	Ours (Full: TTA + GMM + MRF)	720.9	3.3	1311.7	1.58	2037.4 $\pm$ 12.5	0.5	247
ResNet-50	Vanilla DARK (Baseline)	26.8	–	–	–	27.3 $\pm$ 17.5	36.6	265

Appendix

Table S20: Computational Efficiency and Modular Latency Breakdown across Pipeline Configurations. Comparison of inference latency (ms), modular stage breakdown, throughput (FPS), and peak GPU memory (VRAM) across standard backbones on COCO resolution (

256\times 192

). Evaluated under the production execution pipeline matching the experimental benchmark protocol.

Human Pose Estimation

Human pose estimation recovers people’s body keypoints, 3D skeletons, or meshes from images, video, and other sensor data.

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MEOM: Multi-View Expected-OKS Maximization for Human Pose Triangulation
Aug 31, 2026Ziliang Xiong, Henglin Shi, Per-Erik Forssen3D Human Pose Estimation
Computer Vision Laboratory, Department of Electrical Engineering, Linköping University, Sweden
HYPERPOSE: Hyperbolic Kinematic Phase-Space Attention for 3D Human Pose Estimation
May 11, 2026Vinduja Thekkath, Ashish Musale, Ajay Waghumbare +13D Human Pose Estimation Attention Mechanisms
L2A: Learning to Accumulate Pose History for Accurate 3D Human Pose Estimation
May 9, 2026Zehua Wang, Changwang Mei, Huaijiang Sun +23D Human Pose Estimation
Nanjing University of Science and Technology · Lenovo

Aug 31, 2026J/K move · Enter open · S save

MEOM: Multi-View Expected-OKS Maximization for Human Pose Triangulation

Ziliang Xiong, Henglin Shi, Per-Erik Forssen

Computer Vision Laboratory, Department of Electrical Engineering, Linköping University, Sweden

3D Human Pose Estimation

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Conventional algebraic triangulation solves 3D human pose estimation (HPE) from multi-view 2D keypoints. The typical approach, decoding 2D keypoints from predicted heatmaps, is unreliable as heatmaps can be multimodal under occlusion, and collapsing them into single peaks discards their spatial distribution. We seek to use the entire heatmap to estimate 3D poses more accurately, which requires solving two problems: how to robustly fuse heatmaps across views, and how to assess the reliability of heatmaps. For the former, we introduce a novel objective, Multi-viewExpected-OKS Maximization (MEOM), that locates a 3D joint where the views agree in probability mass. For the latter, we adopt highest-density-region (HDR) calibration as a diagnostic of that mass, independently of distance-based metrics. The proposed framework covers two settings, with and without 3D supervision. Without 3D supervision, we optimize 3D poses from pretrained heatmap predictors by maximizing MEOM, achieving comparable performance with state-of-the-art methods that rely on larger backbones, temporal fusion, and simulated 3D data. On ambiguous Human3.6M (H36MA) and occluded CMU Panoptic frames, the advantage is substantial. When 3D labels are available, we train the model end-to-end with a combined MEOM and MSE loss, achieving 19.11 mm absolute MPJPE on Human3.6M outperforming the state-of-the-art volumetric approach on absolute MPJPE at half the inference cost.

Abstract

Human Pose Estimation

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MEOM: Multi-View Expected-OKS Maximization for Human Pose Triangulation

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