Human Pose Estimation by Probabilistic Mixtures of Gaussian and Uniform Distributions

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 O(N 3) voxel memory bottleneck.