Fingerprints and mathematics
Fingerprints are unique impressions left by the raised portions of the skin on fingers, known as epidermal ridges. These patterns, which include arch, loop, and whorl categories, serve important functions such as enhancing grip and tactile sensitivity. Fingerprint analysis has evolved significantly over the last century, integrating advanced technologies and mathematical techniques for improved accuracy and efficiency in identification. Current systems can rapidly compare fingerprints against vast databases using sophisticated algorithms, drastically reducing the time required for identification compared to traditional manual methods. Despite the effectiveness of fingerprints, other biometric technologies like voiceprints and facial recognition are also employed, each with its own advantages. However, fingerprints remain a popular choice due to their ease of use and high accuracy rate of around 98%. Yet, challenges persist, such as accurately identifying burned or damaged fingerprints, which can complicate forensic investigations. The intersection of mathematics and fingerprint analysis highlights the continuous improvement in forensic science, making it a vital tool in criminal investigations while also emphasizing the importance of careful and accurate analysis to prevent wrongful convictions.
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Fingerprints and mathematics
Summary: Mathematical algorithms help professionals use fingerprints as a means of identification.
The study of fingerprints could be considered both science and art. Fingerprint interpretation and analysis have grown over the twentieth and twenty-first centuries along with the development of new technologies and mathematical tools for imaging processing. Fingerprinting is a recognized method for personal identification and is used worldwide.
A fingerprint is an impression left by the raised portion of the epidermis on the fingers. The epidermal ridges are small corrugations of the skin (with an average of 0.5 mm in breadth) without hair or sebaceous glands but with numerous sweat glands, also found in the toes. The epidermal ridges in a particular area of the inner hands and bottom of the feet have two functions: to provide traction to help people grab objects (the sweat glands moisten the skin, augmenting the security of contact) and to enhance the sense of touch by the stimulation of the underlying nerve. Humans are not the only species with epidermal ridges; some primates, including gorillas and chimpanzees, and koala bears have their own unique prints.
Fingerprint Patterns
There are three general groups of fingerprint patterns: arch, loop, and whorl. They may be divided into subgroups by means of the smaller differences existing between the patterns in the same general group. Fingerprint groups may be also divided into male and female and by age. Historically, the identification of these patterns was done manually in a tedious and time-consuming approach requiring ink, paper, and sufficient knowledge and training of the fingerprint examiner. In the early twenty-first century, automatic fingerprint identification systems can quickly verify a person’s identity by searching millions of records in a matter of seconds. Advanced mathematical algorithms are used in forensic science and other areas such as biometric identification, the science of identifying a person using some unique physical characteristic. Correlation-based methods rely on identifying characteristics of print patterns and positioning those characteristics within the pattern, using what are called “registration points.” Another mathematically interesting problem is to reconstruct a fingerprint from a partial print or a blurred print.
Other Advances
Other methods to identify humans are used in addition to fingerprints: biometric technology voiceprint, retina/iris scan, hand geometry, and facial recognition. However, fingerprinting is the easiest to use and it provides an average accuracy of 98%.
Wavelets have become an important mathematical tool for fingerprint recognition. This method could be an efficient solution for fingerprint recognition systems because it eliminates the necessity of preprocessing the images, reducing the time required for analysis.
Fingerprint identifications play a vital role in many criminal investigations but there are still challenges, such as identifying the body of a victim of a fire with parts of the fingers burned. Mathematical equations and operators have been used for the calculation of fingerprint probabilities based on individual characteristics, such as only a partial print. The use of digital fingerprints requires more work in description and analysis to avoid ambiguities in identification, such as wrongly convicting an innocent person to prison.
Bibliography
Federal Bureau of Investigation. “The Science of Fingerprints (Classification and Uses).” http://ebooks.ebookmall.com/title/science-of-fingerprints-classification-and-uses-hoover-ebooks.htm.
Hawthorne, M. R. Fingerprints: Analysis and Understanding. Boca Raton, FL: CRC Press, 2009.
Komarinski, P. Automated Fingerprint Identification Systems (AFIS). London: Elsevier, 2005.
Orton, William. “The Mathematics of Fingerprints.” School Science and Mathematics 88, no. 1 (1988).