Feature vector

Expert systems. In situations where the statistical classifiers cannot be used, because of the complexity or inhomogeneity of the data, rule-based expert systems can sometimes be a solution. The complex images can be more readily described by rules than represented as simple feature vectors. Rules can be devised which cope with inhomogeneous data by, for example, triggering some specialised data-processing algorithms. 

We present in this paper an invariant pattern recognition method, applied to radiographic images of welded joints for the extraction of feature vectors of the weld defects and their classification so that they will be recognized automatically by the inspection system. 

An invariant pattern recognition method, based on the Hartley transform, and applied to radiographic images, containing different types of weld defects, is presented. Practical results show that this method is capable to describe weld flaws into a small feature vectors, allowing their recognition automatically by the inspection system we are realizing. 

Table 1 Three Hartley feature vectors of the weld defect of figure 3.b.

Subheading 2.3. describes the last class of finite feature vectors, namely, those with continuous-valued components, where the components (i.e., features) are usually obtained from computed or experimentally measured properties. An often-overlooked aspect of continuous feature vectors is the inherent nonorthogonality of the basis of the feature space. The consequences of this are discussed in Subheading 2.3.2, Similarity measures derived from continuous... 

The components of discrete feature vectors may indicate the presence or absence of a feature, the number of occurrences of a feature, or a finite set of binned values such as would be found in an ordered, categorical variable. 

Each component of an -component binary feature vector, also called bit... 

Binary feature vectors are completely equivalent to sets (see the Appendix for further discussion). Care must be exercised when using them to ensure that appropriate mathematical operations are carried out. The number of components in a bit vector is usually quite large, normally n 100. In some cases n can be orders of magnitude larger, sometimes exceeding a million components... 

Fig. 2. Distance between two binary-valued feature vectors vA and vB is not given by the Euclidean distance but the Hamming distance between the two.

Most similarity measures for binary-valued feature vectors in use today are symmetric Tversky (6), however, has defined an infinite family of asymmetric measures... 

Feature vectors with integer- or categorical-valued components are identical in form to binary-valued vectors (see Eq. 2.16). In contrast, however, each component takes on a finite number of values... 

D information in any substantive way, although they do capture some 3-D information indirectly, and this is why some feature vector procedures are referred to as 2.5-D methods. 

Property-Based Continuous-Valued Feature Vectors... 

Subheading 2.2. describes the properties of discrete-valued feature vectors, with components given by finite, ordered sets of values. The most prevalent class is that of vectors with binary-valued components, which are mathemati-... 

Hamid Muhammed, H. and Larsolle, A. (2003) Feature-vector based analysis of hyperspectral crop reflectance data for discrimination quantification of fungal disease severity in wheat. Biosyst. Eng. 86(2), 125-34. 

Zak-Gabor coefficients calculation and transformation into a features vector 0.06... 

The number of features in the maximal feature vector, of order of hundreds of thousands, is too big to be useful in practice, due to such issues like data transmission through the net, data storage in databases, templates comparison made in smart card processors or biometric standalone devices, etc. To reduce the number of features, we will look for a feature vector that leads to minimum sample equal error rate determined on available iris images database. 

Number of sorted iris feature vector elements... 

One may assume a uniform distribution of the information along the iris and aim into selecting the best frequency-scale pairs (k, D). This can be done by grouping in one class all coefficients of the same frequency-scale pair (k, D), and enlarging the feature vector by all features in a class. In other words, the problem is to find the best frequency-scale pairs. 

Note that the number of features included in the feature vector b is not identical for all classes. The sorting rule for the classes of features mirrors the rule used for features we sort the classes by the decreasing number of elements included into the feature vector. This enables to find the frequency-scale pairs for which the distributions of cb and cw are best separated. In other... 

We calculated both d and s for various numbers of feature classes used in features calculations, and chose classes (scale-frequency pairs) characterized by the maximal d. This leads to the iris feature vector of 1152 bits (144 bytes) containing only four feature classes (Figure 7). Simultaneously, for those four selected feature classes we achieved the maximal non-zero separation s. 

Figure 7. a) Decidability d vs. number of sorted frequency-scale pairs included in the feature vector, b) the separation margin s, c) the length of the iris feature vector, d) distribution of comparison scores for the same and different irises for the best final 144 byte iris feature vector. 

We verified the above feature vector using the iris data for 180 individuals included in BioBase, with four images per volunteer available, three used for template creation and one employed in verification trials (Figure 8). We obtained zero false matches and zero false non-matches. 

Biometrics can be used in granting the remote access to the network. The scenario employs a common client-server network model, thus incorporating standard security mechanisms with biometric enhancements. The client terminal (see Figure 9) is a biometric-based host, equipped with the capturing device and the processing unit that measures the biometric trait and calculates the features vector (biometric template). The client capabilities may be understood in a wider sense, thus enabling the client to be equipped with sensors related to more than one biometric modality. The proposed access scenario enables to include the aliveness detection capability and the biometric replay attack prevention. To insert the necessary elements into the communication flow, capture-dependent parameters will be retrieved by the client terminal prior to the biometric trait measurement. 

The Enrolment Terminal (cf. Figure 12) uses the NASK Iris Module and BioBase Access Module. A separate application is developed that uses common elements of NASK biometrics modules, namely, the device library to control the hardware, and the algorithms library to process iris images and calculate iris features vectors. 

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