<![CDATA[Cross-spectral cross-distance face recognition (CSCD-FR) is a challenging biometric task involving visible (VIS) and near-infrared (NIR) facial images acquired at varying stand-off distances. Beyond the spectral discrepancy between VIS and NIR images, increasing acquisition distance degrades resolution, blurs images, and reduces facial detail, making recognition considerably more difficult. Although deep convolutional neural networks (CNNs) have demonstrated strong capabilities for learning discriminative facial embeddings, existing studies have predominantly focused on network architectures, feature representations, and learning strategies, while the influence of distance metric selection remains relatively underexplored. Since recognition decisions are ultimately based on distances between embedding vectors, the choice of similarity metric may affect recognition performance. This study therefore investigates the influence of generalized Minkowski distance order on CSCD-FR using deep embeddings extracted from MobileNetV3-Small, EfficientNet-B2, and DenseNet121. Using the Long-Distance Heterogeneous Face Database (LDHF-DB) at stand-off distances of 1, 60, and 100 m, both ImageNet-pretrained and domain-adapted models were evaluated using -normalized embeddings. Domain adaptation optimized the embedding layer using triplet margin loss while the CNN backbones remained frozen. Minkowski orders from to were evaluated using closed-set identification and verification protocols. ImageNet-pretrained models yielded Rank-1 accuracies below 11%, whereas domain adaptation substantially improved recognition performance. DenseNet121 achieved the highest observed performance, with 93.19% Rank-1 accuracy and 2.16% EER at . The Rank-1-optimal Minkowski distance order varied across architectures, with EfficientNet-B2 and MobileNetV3-Small achieving their highest observed Rank-1 accuracies at and , respectively. These findings show that selecting a similarity metric can provide an additional matching-stage optimization without modifying the CNN backbone. Because the same retained identities were used for domain adaptation and evaluation, the results represent a dataset-specific assessment rather than recognition performance on previously unseen subjects.]]>
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