Classication experiments

Our rst set of classication experiments is conducted on 100 selected (complete) nger- prints from the FVC2002 Db1a database. The image quality varies. To obtain a perfor- mance benchmark, we inspect each test ngerprint and manually classify them into the ve classes in accordance to the rules laid in Table 4.4.

We then operate the two comparative classiers separately on the test ngerprints. The classication results are summarized respectively into two confusion matrices - one shown in Table 4.5 and the other shown in Table 4.6.

The confusion matrix has a row for each actual class and a column for each hypothetical class estimated from the respective approach. It shows that, as the non-parenthesized number, how many test objects fell into a hypothetical or actual class. The sum of non- parenthesized numbers in each row indicates the total number of test ngerprints belonging

Hypothetical class

Actual class Arch Left Loop Right Loop Tended Arch Whorl

Arch 1(100%) 0(0.0) 0(0.0) 0(0.0) 0(0.0)

Left Loop 0(0.0) 30(96.8%) 0(0.0) 1(3.2) 0(0.0)

Right Loop 0(0.0) 1(3.3) 25(83.3%) 3(10.0) 1(3.3)

Tended Arch 0(0.0) 0(0.0) 2(14.3) 12(85.7%) 0(0.0)

Whorl 0(0.0) 0(0.0) 2(8.3) 0(0.0) _22(91.7%)

Total: 10% error rate with 0% rejection rate. Table 4.5: Confusion matrix from the FOMFE-based classication scheme on the FVC2002 Db1a database

Hypothetical class

Actual class Arch Left Loop Right Loop Tended Arch Whorl

Arch 0(0.0%) 1(100) 0(0.0) 0(0.0) 0(0.0)

Left Loop 0(0.0) 32(97.0%) 1(3.0) 0(0.0) 0(0.0)

Right Loop 0(0.0) 0(0.0) 33(94.3%) 0(0.0) 2(5.7)

Tended Arch 0(0.0) 3(42.9) 4(57.1) _0(0.0%) 0(0.0)

Whorl 0(0.0) 0(0.0) 0(0.0) 0(0.0) 24(100%)

Total: 11% error rate with 0% rejection rate. Table 4.6: Confusion matrix from the PCASYS classication scheme on the FVC2002 Db1a database

Figure 4.15: Classication results from the FVC02 Db1a database: error rates across dif- ferent classes.

to that actual class. Each parenthesized number thus reports the percentage in the actual class that has been (mis)classied into a hypothetical class. For example, among the total 31left loop ngerprints, 30 of them are classied as left loop and 1 of them is misclassied as tended arch using the FOMFE-based approach. That is, 96.8% of the left loop ngerprints in

4.5. APPLICATION TO FINGERPRINT CLASSIFICATION 115 the test were correctly classied as left loop, leaving 3.2% misclassied as tended arch. The diagonal entries shown in boldface correspond to correct classications. The experimental results shown in Table 4.5 and 4.6 are due to zero rejection rates. That is, every ngerprint in the test is classied into a hypothetical class. The total error rate is also reported in the respective table. The error rates for each class using the comparative classiers are plotted in Figure 4.15.

Comparing Table 4.5 and 4.6, we see that the total error rates from the two classiers are very close: 10% for the FOMFE-based classication approach and 11% for the PCASYS approach. However, their error distributions over the ve ngerprint classes possess a sig- nicant dierence. This can be viewed more clearly in Figure 4.15. It can be observed that PCASYS performs well on Left Loop, Right Loop and Whorl ngerprints but shows poor discrimination on Arch and Tended Arch types. We consider it is due to the training pref- erence tuned for PCASYS to favor the three most common classes on the cost of sacricing accuracy for the other ngerprints. This is often the trade-o in the neural network. On the other hand, the rule-based approach does not have this restriction. It can be observed that the error distribution is more even using the FOMFE-based classication approach.

We further operate the classiers on a bigger test set to evaluate the performance. The test set was randomly selected from the NIST SDB14 database [109]. The database contains ink-rolled ngerprint impressions scanned from 10-print cards. Each ngerprint in the database was manually analyzed by a human expert and assigned to one of the ve classes. From each ngerprint class, we randomly select 49 test objects. Thus, the test set contains 49 × 5 = 245 ngerprints. The confusion matrices from the two classiers are shown in Table 4.7 and 4.8, respectively. The error rates of classication are compared in Figure 4.16.

It can be observed from the tables and the gure that the FOMFE-based classication approach outperforms the PCASYS approach with ngerprints uniformly distributed over the ngerprint classes. This is shown signicantly in the total error rate: 19.2% from

Hypothetical class

Actual class Arch Left Loop Right Loop Tended Arch Whorl

Arch 42(85.7%) 1(2.0) 0(0.0) 6(12.3) 0(0.0)

Left Loop 0(0.0) 42(85.7%) 1(2.0) 4(8.2) 2(4.1)

Right Loop 0(0.0) 3(6.1) 38(77.6%) 7(14.2) 1(2.0)

Tended Arch 4(8.2) 2(4.1) 8(16.3) 32(65.3%) 3(6.1)

Whorl 1(2.0) 2(4.0) 2(4.0) 0(0.0) _44(90.0%)

Total: 19.2% error rate with 0% rejection rate. Table 4.7: Confusion matrix from the FOMFE-based classication scheme on the NIST SDB14 database

Hypothetical class

Actual class Arch Left Loop Right Loop Tended Arch Whorl

Arch 10(20.4%) 20(40.8) 18(36.7) 0(0.0) 1(2.4)

Left Loop 0(0.0) 48(98.0%) 0(0.0) 0(0.0) 1(2.4)

Right Loop 0(0.0) 0(0.0) 48(98.0%) 0(0.0) 1(2.4)

Tended Arch 0(0.0) 24(50.0) 24(50) _0(0.0%) 1(2.4)

Whorl 0(0.0) 3(6.1) 1(2.4) 0(0.0) 45(92.0%)

Total: 38.4% error rate with 0% rejection rate. Table 4.8: Confusion matrix from the PCASYS classication scheme on the NIST SDB14 database

Figure 4.16: Classication results from the NIST SDB14 database: error rates across dif- ferent classes

the FOMFE-based classication method compared to 38.4% from PCASYS. The error distribution is similar as that observed in Figure 4.15 where PCASYS performs better for the loops and whorls whereas the FOMFE-based classication approach performs better

4.6. SUMMARY 117 for the arches.

4.6 Summary

Most existing SP detection algorithms operate over ridge orientation elds (ROF), including Poincare Index (PI) based methods that examine high curvature presence and convolution methods based on (symmetric/template) ler designs. Thus, these methods largely depend on the estimation accuracy of ROF. That is, their performance often degrades when the intrinsic features are overwhelmed by noise in the ROF. Moreover, most of them cannot extract multiple features simultaneously: The PI based methods cannot extract rotation information, while the convolution based methods resort to dierent lters for detecting cores and deltas respectively.

On the other hand, we propose a rather dierent approach to conduct singularity anal- ysis based on the FOMFE model. Unlike other model-based methods, the FOMFE-based SP detection approach does not require (prior/coarse) SP detection and does not involve iterative process. In fact, the linearization of FOMFE has enabled a common framework to interpret the local ridge patterns from a new angle. The analysis can be explicitly expressed in terms of dierential geometric operators, which is benecial for both implementation and computation. Accordingly, we facilitate ecient SP detection algorithms based on FOMFE that can simultaneously extract multiple SP features such as location, type, rotation and symmetry. Particularly, we associate delta with asymptote analysis and nd a promising means to dene the orientation of a delta.

We have also applied the FOMFE-based SP detection approach to ngerprint regis- tration and classication. Our experimental results show that the proposed approach is eective and can achieve better performance compared to other existing methods especially for poor quality ngerprints. However, the (exclusive) classication performance is not yet satisfactory due to its intrinsic limitation based on rules (which are sometimes too simple for ambiguous and partial ngerprints). In the next chapter, we will explore more eec-

tive means based on the FOMFE approach to reduce the number of matches and improve detection eciency for automatic ngerprint identication systems.

Chapter 5

Model-based Fingerprint Indexing

This chapter investigates ngerprint indexing schemes based on a new feature representation of model coecients. In particular, we exploit global model representations reconstructed from partial ngerprints to search the database for matching candidates, which, to the best of our knowledge, was not previously available in the literature.

This chapter is organized as follows. Section 5.1 introduces the motivation of nger- print indexing and key issues for developing the technique. Section 5.2 proposes ngerprint indexing based on the FOMFE model coecients, and reports experimental results for ngerprint identication under normal circumstances. Section 5.3 studies partial nger- print identication. In particular, we formulate the reconstruction as solving an inverse problem in Section 5.3.2, and devise two reconstruction algorithms accordingly in Section 5.3.3. Quality of partial ngerprints with respect to the retrieval performance is discussed in Section 5.3.4. Section 5.3.5 performs identication experiments for partial ngerprints after reconstruction. Finally, Section 5.4 provides a summary for the proposed model-based ngerprint indexing schemes.

5.1 Motivation of Indexing

In many applications, it is often required to identify a ngerprint from thousands or mil- lions of records in the database. Although the computation load of identication can be distributed by a network of hardware units, it is undoubtedly more ecient and envi-

ronmentally friendly to develop scalable computing techniques that can break down the number of required matches. Such a ngerprint retrieval process is also called candidate list reduction.

Most current operating automatic ngerprint identication systems (AFIS) facilitate meta data and binning (ngerprint classication) techniques to reduce the candidate list before matching. However, both technologies have their own drawbacks. The exclusive classication, as demonstrated in Section 4.5, can only dene a limited number of pattern classes, and the number of pattern classes is usually much less than the number of individual records in the database. Further, the natural distribution of ngerprints is not even - over 90% of them tend to crowd into only three pattern classes [90]. Thus, the number of ngerprints can still be huge within a single ngerprint class. The meta data, on the other hand, is not always available as in the case of latents. Privacy issues are another concern about the use of meta data: Once the security system is breached, various (sensitive) information regarding the identity will be disclosed at the same time.

Fingerprint indexing is a new technology that is also known as continuous classication [90]. It has a similar idea as content-based image retrieval (CBIR) [91] which aims at fast retrieval of a query image based on the visual content (feature) of the image itself. In fact, ngerprints can be viewed as texture-like images. The key indexing technique does not focus on the classical pattern classication problems but on the retrieval process by sorting the salient (texture) features of those subjects. By this means, the resulting system can avoid the membership problem of ambiguous ngerprints often seen in the binning candidate reduction schemes.

Similar to CBIR [134], there are also three fundamental issues for ngerprint index- ing, namely visual feature extraction, multi-dimensional indexing, and retrieval strategy. Among the three, feature extraction has been widely covered in the literature of ngerprint recognition. To our understanding, the key element here is to identify the distinctive fea- ture and its most suitable representation for indexing, so that the match of an anonymous

5.2. INDEXING BASED ON FOMFE 121