Fingerprints have long been recognized as a unique and reliable means of personal identification. Central to the analysis and enhancement of fingerprints is the concept of the fingerprint core. Although the location of the core is used in many applications, to the best of our knowledge, this study is the first to investigate the empirical distribution of the core over a large, combined dataset of rolled, as well as plain fingerprint recordings. We identify and investigate the extent of incomplete rolling during the rolled fingerprint acquisition and investigate the centrality of the core. After correcting for the incomplete rolling, we find that the core deviates from the fingerprint center by 5.7% $\pm$ 5.2% to 7.6% $\pm$ 6.9%, depending on the finger. Additionally, we find that the assumption of normal distribution of the core position of plain fingerprint recordings cannot be rejected, but for rolled ones it can. Therefore, we use a multi-step process to find the distribution of the rolled fingerprint recordings. The process consists of an Anderson-Darling normality test, the Bayesian Information Criterion to reduce the number of possible candidate distributions and finally a Generalized Monte Carlo goodness-of-fit procedure to find the best fitting distribution. We find the non-central Fischer distribution best describes the cores' horizontal positions. Finally, we investigate the correlation between mean core position offset and the NFIQ 2 score and find that the NFIQ 2 prefers rolled fingerprint recordings where the core sits slightly below the fingerprint center.
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