Measuring Information Content in Biometric Features in .NET

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Measuring Information Content in Biometric Features
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In this work, we elaborate an approach to address this question based on de nitions from information theory [6]. We de ne the term biometric information as follows: Biometric information (BI): The decrease in uncertainty about the identity of a person due to a set of biometric features measurements. In order to interpret this de nition, we refer to two instants: (1) before a biometric measurement, t0 , at which time we only know a person p is part of a population q, which may be the whole planet; and (2) after receiving a set of measurements, t1 , we have more information and less uncertainty about the person s identity. BI may be used to answer two different types of questions. First, given a set of measurements from a speci c person, we want to know how identi able that individual is in a population. This is the individual biometric information (IBI). Second, given a system that makes biometric measurements, such as ngerprint minutiae or eigenfaces, we want to know, on average, how distinguishable people are in the population, using those biometric features. This is the system biometric information (SBI). The difference is that IBI is the information of an individual features and SBI is the average information over the population. In order to motivate our approach, we initially consider the properties that such a measure should have. Consider a soft biometric system that measures height and weight; furthermore, assume that all humans are uniformly and independently distributed in height between 100 and 200 cm and in weight between 100 and 200 lb. If a person s features were completely stable and could be measured with in nite accuracy, people could be uniquely identi ed from these measurements, and the biometric features could be considered to yield in nite information. However, in reality, repeated biometric measurements give different results due to measurement inaccuracies and to short- and long-term changes in the biometric features themselves. If this variability results in an uncertainty of 5 cm and 5 lb, one simple model would be to round each measure to 105, 115, . . . , 195. In this case, there are 10 10 equiprobable outcomes and an information content of log2 (100) = 6.6 bits. Such an analysis is intrinsically tied to a choice of biometric features. Thus, our approach does not allow us to answer how much information is in a ngerprint but only how much information is in the position and angle data of ngerprint minutiae Furthermore, for many biometrics, it is not clear what the underlying features are. Face images, for example, can be described by image basis features or landmark based features [7]. To overcome this, we may choose to calculate the information in all possible features. In the example, we may provide height in inches as well as in centimeters; however, in this case, a good measure of information must not increase with such redundant data. This work also develops a new approach to measuring biometric image quality. Biometric sample quality is a measure of the usefulness of a biometric image [8]. One recent development is the signi cant level of interest in standards for measurement of biometric quality. For example, ISO has recently established a biometric sample quality draft standard [8]. According to reference 8, biometric sample quality may be
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23.2 Theoretical Framework
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considered from the point of view of character (inherent features), delity (accuracy of features), or utility (predicted biometrics performance). A general consensus has developed that the most important measure of a quality metric is its utility images evaluated as higher quality must be those that result in better identi cation of individuals, as measured by an increased separation of genuine and impostor match score distributions. The nature of biometric sample delity has seen little investigation, although for speci c biometric modalities, algorithms to measure biometric quality have been proposed. For example, the NFIQ algorithm [9] is a widely used measure for ngerprint image quality. One current dif culty is that there is no consensus as to what a measure of biometric sample delity should give. In this work, we propose a new approach to measure this quantity, based on an information theoretic framework. We begin with the intuitive observation that a high-quality biometric image is more useful to identify the individual than is a low-quality image. This suggests that the quantity of identi able information decreases with a reduction in quality. Given a way to measure the decrease in information caused by a given image degradation, one can measure the associated decrease in biometric information. In this chapter, we develop a mathematical framework to measure biometric feature information in a given system for a set of biometric features. This work is based on the our previous work on this topic [6, 10]. We address ill-conditioning in the measurements using distribution modeling and regularization. We then use this algorithm to analyze the biometric information content of two different face recognition algorithms and then de ne the information loss due to a degradation in image quality.
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