Conformal prediction provides distribution-free reliability guarantees for vision systems, but these guarantees depend on how prediction errors are measured in the output space. Many vision tasks produce outputs on curved spaces (e.g. gaze directions on the sphere or 3D head rotations), yet intermediate prediction heads, residuals, uncertainty estimates, or conformal scores are often defined in flat coordinate charts such as yaw-pitch or Euler angles. We show that this scoring choice introduces systematic geometric distortion near coordinate singularities (large pitch angles on the sphere and poses approaching gimbal lock in 3D rotations). Across four datasets (ETH-XGaze, Gaze360, BIWI, AFLW2000-3D), slice-conditional coverage at a nominal 90% target drops by 30-50 percentage points in these regions, falling to 38.9% on ETH-XGaze and 42.0% on Gaze360 at gaze pitch above 70 degrees, and to 57.5% on BIWI and 55.2% on AFLW2000-3D at head pose pitch above 60 degrees near gimbal lock, despite marginal coverage remaining near 90%. We prove that this is structural. Scalar thresholding changes the size of chart-coordinate prediction sets but leaves their distorted axis ratios unchanged. To diagnose this hidden failure mode, we show that a simple geometric quantity, the Riemannian volume density, strongly correlates with where coverage collapse occurs. Finally, we show that coordinate-free geodesic scoring removes this distortion. It requires no retraining and adds negligible computational cost.
Md. Ahanaf Arif Khan, Md. Tawhidur Rahman, Sangeeta Biswas +4cs.CV
Existing head pose datasets predominantly feature subjects of Western or East Asian origin, leaving South Asian populations, particularly Bengali individuals, largely underrepresented. We introduce Bengal-HP_RU, the first publicly available head pose dataset centred on Bengali subjects, comprising 12,894 labelled head images annotated with continuous yaw, pitch, and roll values. Images were collected from Wikimedia Commons under free licences and processed through an automated pipeline followed by manual label correction. The dataset is partitioned by Wikimedia uploader identity to prevent data contamination, yielding 10,494 training and 2,400 test images across 296 unique uploaders. Bengal-HP_RU exhibits substantial diversity in subject age, gender, occlusion, illumination, and background, reflecting realistic in-the-wild conditions. The dataset is publicly available at https://doi.org/10.17632/xbw9kr37jb.2.