Contactless 3D finger knuckle is an emerging biometric identifier, which can provide a promising alternative for personal identification. To maximize its potential, feature representation and matching are the two critical components towards high performance. A recent pioneering work is limited by its preliminary design of the feature descriptor and the tailor-made similarity function. Although this method demonstrates decent recognition performance, there is room for improvement. This article advances the state-of-the-art method by introducing a new curvature based feature descriptor and a method to compute the similarity functions based on the statistical distribution of the encoded feature space. Our proposed feature representation utilizes an insight in 3D geometry for accurately encoding the curvature information. When computing the similarity between a pair of templates, we compute the similarity function from the probability mass distributions of the encoded feature space. Our proposed approach is scalable to templates with different sizes, and more importantly outperforms the state-of-the-art methods significantly, which is demonstrated in a publicly available database of 3D finger knuckle. In addition, we also demonstrate the generalizability of our approach by evaluating on other publicly available biometric datasets of similar patterns, i.e., 3D palmprint and finger vein.