Cosine-Consistent Deep Metric Learning with Sub-Gaussian Risk Analysis for Contactless Palmprint Verification

Contactless palmprint verification must generalize to unseen identities while remaining robust to variations in hand pose, scale, illumination, camera distance, and background. This study presents a cosine-consistent deep metric-learning framework combining landmark-first Hybrid region-of-interest (ROI) extraction, contrast-limited adaptive histogram equalization (CLAHE) enhancement, an ImageNet-initialized ResNet18 encoder, trainable generalized-mean (GeM) pooling, a compact projection head, batch-normalization neck (BNNeck), batch-hard triplet learning, and auxiliary identity supervision. The principal contribution lies not in introducing a new backbone or individual architectural component, but in the mathematically consistent integration of metric learning and verification with a rigorously controlled open-set evaluation protocol. The triplet objective operates on L2-normalized pre-batch-normalization (pre-BN) descriptors, whereas enrollment and cosine-based verification use L2-normalized post-batch-normalization (post-BN) descriptors. For unit-normalized vectors, squared Euclidean distance is shown to be a strictly decreasing affine function of cosine similarity, establishing exact ranking equivalence within each embedding space. A training-distribution lower bound relates the triplet margin and violation probability to the expected pre-BN score difference, without extending this result to post-BN test scores. Conditional sub-Gaussian false acceptance rate (FAR) and false rejection rate (FRR) bounds and Hoeffding-based plug-in threshold evaluations are also developed, with empirical score statistics explicitly distinguished from finite-sample risk certificates. Experiments on Tongji Session 1 and BMPD use one fixed participant-disjoint split, validation-only threshold selection, five model-training seeds, controlled one-factor ablations, and participant-level bootstrap confidence intervals for principal verification measures. The results provide the clearest empirical support for auxiliary identity supervision under the more variable BMPD acquisition conditions. The effect of ROI normalization is acquisition-dependent, while the effects of CLAHE, pooling, BNNeck, mining strategy, embedding normalization, and triplet margin are generally smaller or more variable across seeds and datasets. Normalized Euclidean and cosine matching produce identical verification results when applied to the same normalized post-BN descriptors.