This paper shows that maintaining logical consistency of an iris recognition system is a matter of finding a suitable partitioning of the input space in enrollable and unenrollable pairs by negotiating the user comfort and the safety of the biometric system. In other words, consistent enrollment is mandatory in order to preserve system consistency. A fuzzy 3-valued disambiguated model of iris recognition is proposed and analyzed in terms of completeness, consistency, user comfort and biometric safety. It is also shown here that the fuzzy 3-valued model of iris recognition is hosted by an 8-valued Boolean algebra of modulo 8 integers that represents the computational formalization in which a biometric system (a software agent) can achieve the artificial understanding of iris recognition in a logically consistent manner.
Because the visual acuity of the human agent is doubled by its intelligenceboth of them together ensuring an excellent quality in indentifying the (dis)similarity of iris images, the geometry that illustrates the binary decisions given by the human agent during a Turing test [11] of iris recognition is very simple (Fig. 1.a): it consists of one collection of crisp points (0 and 1) and one histogram that counts how many times a decision of unitary score (1 -for the case of similar irides) or a null decision (0 -for the pairs of non-similar irides) was given by the human agent. Still, the geometry that illustrates the fuzzy binary decisions given by a software agent ( [6]- [8]) during a Turing test of iris recognition is not that simple: in this case, the fuzzy biometric decisions given by the software agent define (draw) a f-geometry [13] in which the intra-and inter-class score distributions could be a little bit confused (Fig. 1.c, Fig. 2.a, Fig. 2.b), or confused much stronger (Fig. 1.b, Fig. 1.c in [6], Fig. 10 in [4]), or not confused at all. (Fig. 1.b from here, and Fig. 4.a, Fig. 4.b, Fig. 4.c in [6]).
In fact, Fig. 1.a illustrates that iris recognition is crisp for a human agent, and consequently, the recognition function R (as it is perceived by the human agent) is a crisp indicator of the imposter (0) and genuine (1) classes of iris pairs (P): R(•,•): P →{0,1}, In concordance with the terminology introduced in [13], the function R (Fig. 1.a) will be referred to as the prototype recognition function and it is a crisp concept. The goal of designing automated iris recognition systems is to find fuzzy approximations f-R for the prototype recognition function R, as close as possible to R. Such an approximation f-R will be further referred to as a fuzzy recognition function. The fuzzy approximations f-R obtained by applying automated iris recognition methods are of the same types as those presented in Fig. 1.b (an excellent approximation, [7]), Fig. 1.c, Fig. 2.a, Fig. 2.b (very good approximations, [8]), Fig. 10 in [4] (good approximation), Fig. 1.b -Fig. 1.c and Fig. 4.a -Fig. 4.c in [6] (good approximations), where the marks (good, very good, excellent) were given using as a reference the result obtained in an approach considered nowadays as being the “state of the art” in iris recognition (and marked here as “good approximation” [4]).
In the case in which the recognition is made using artificial agents and good quality eye images, the fact that the approximations f-R depart from the prototype R (situation illustrated in Fig. 1.b -Fig. 1.b.c and Fig. 4.a -Fig. 4.c from [6] and in Fig. 10 from [4]) can not be caused by the lack of visual acuity of the system, but only by the less intelligent manner in which the system decides (understands) iris similarity or dissimilarity. Practically, the artificial agent fuzzifies the prototype R and the separation between genuine and imposter score distributions. More inadequate and unintelligent the image processing is, much confusion it introduces in the biometric decision model. There are two significant differences between the ways in which the human agent and software agent decide the similarity or dissimilarity of two iris images: -Ordinary people are not aware of the numerical reality of an image but only of certain meanings “decoded” accordingly to their experience from the chromatic variation captured in the image. For the human agent the iris image is not a numerical data but a set of complex knowledge about the iris texture and the image quality (given by the technical acquisition conditions and the posture in which the eye is captured). The similarity/dissimilarity decision given by the human agent for a pair of iris images is based on ad-hoc techniques of comparing two such sets of knowledge, techniques which are adaptive in relation with the pair of images analyzed.
-An artificial agent makes the biometric decision using only numerical support. From its point of view, the iris image is numerical data in the first place. Depending on the intelligence with which it is endowed, the artificial agent can extract (artificial) knowledge about the numerical data, which is usually referred to as “features”, and further encoded in a numeric format. For example, the binary iris code ([1] - [4], [6]) is a binary encoding of the features extracted from a uint8 (8-bit unsigned integer) iris image. The artificial agent performs the comparison of two iris images indirectly, by comparing encoded features of the two iris images. In short, the human agent operates in a rich knowledge space, whereas an artificial agent usually encodes the actual knowledge space in a relatively poor, partial and often imprecise numeric data, in a manner very similar to lossy compression. This is why the fuzzification is almost inherent in the ordinary practice of automated iris recognition.
As it was described above, any simple Turing test of iris recognition undertaken by using good q
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