Fingermarks are regarded as reliable evidence in criminal investigation and individual identity; however, their changes with pressure and substrates, which can provide clues for case investigation, remain unknown. To advance fingermark quantification, we propose a systematic mathematical model framework to analyse the quantitative data collected by a non-destructive fingerprint imaging and surface analysis technique, which ensures the primitiveness and integrity of the fingermark and exhibits excellent performance in fingermark imaging, even including latent fingermarks that were aged for 60 days. Based on statistical and modelling analysis, for the first time we discover a logarithmic correlation between friction ridge and pressure. Moreover, smoother substrates generally result in wider ridges and exert more significant impacts on fingermarks, such as transparent glass emerging as the smoothest substrate, with the widest ridges and the highest influence weight at 21.2%, which has been confirmed by surface analysis. Notably, the interaction effect between pressure and substrates on fingermarks is first corroborated. Extensive experiments demonstrate the competitive results based on the mathematical models, and the proposed quantitative relationship among friction ridge, pressure and substrate provides a new perspective for investigating the connection between fingermarks and their influencing factors.

Fingermarks are regarded as reliable evidence in criminal investigation and individual identity; however, their changes with pressure and substrates, which can provide clues for case investigation, remain unknown. To advance fingermark quantification, we propose a systematic mathematical model framework to analyse the quantitative data collected by a non-destructive fingerprint imaging and surface analysis technique, which ensures the primitiveness and integrity of the fingermark and exhibits excellent performance in fingermark imaging, even including latent fingermarks that were aged for 60 days. Based on statistical and modelling analysis, for the first time we discover a logarithmic correlation between friction ridge and pressure. Moreover, smoother substrates generally result in wider ridges and exert more significant impacts on fingermarks, such as transparent glass emerging as the smoothest substrate, with the widest ridges and the highest influence weight at 21.2%, which has been confirmed by surface analysis. Notably, the interaction effect between pressure and substrates on fingermarks is first corroborated. Extensive experiments demonstrate the competitive results based on the mathematical models, and the proposed quantitative relationship among friction ridge, pressure and substrate provides a new perspective for investigating the connection between fingermarks and their influencing factors.