In this chapter we compared dierent local similarity calculation methods (stage 1 strategies) and investigated how many paired minutia points should be used to calculate the nal local similarity score (stage 2 strategies). The results did not point towards a combination of these two strategies that are superior to all the others across all six of the databases considered. However, when strategy 1 of stage 1 was implemented in conjunction with strategies 3 or 4 of stage 2, the lowest EERs were obtained across all the databases considered.
The main conclusion is therefore that the proposed strategy 1 of stage 1 performs signi cantly better than the MCC-based local similarity on the FVC2004 ngerprint databases (i.e. at a signi cance level of 0.05). Although it also produces lower EERs when implemented on the FVC2002 ngerprint databases, there is not su cient evidence to conclude that this strategy gen- erally performs signi cantly better. The above-mentioned improvement may however point towards the fact that the proposed algorithm is more robust with respect to noise as is the case for the MCC-based strategy, since the FVC2004 ngerprint databases contain more low quality ngerprints than is the case for the FVC2002 ngerprint databases (Maltoni et al., 2009), which may result in comparisons with higher noise levels.
These results do not provide clear guidelines on how to calculate the local similarity score, but rather point towards how a similarity score should not be calculated: Firstly, using the similarity between the three best neighbouring minutia points is not distinctive enough for calculating the similarity between descriptors and can therefore not compete with methods that consider all the neighbouring minutia points within a 90-pixel radius. It is interesting to note that the literature states that xed length local descriptors are not accurate because of their sensitivity to noise (Liu and Mago, 2012; Feng, 2008). However, these results demonstrate that even if the pairs are assigned in such a way that they are less sensitive to noise, the use of three neighbouring minutia points is still not distinctive enough to compare favourably with other methods. This study therefore suggests that it is better to consider all the neighbouring minutia points within a xed radius than only a certain percentage of paired minutia pairs.
Secondly, what the local similarity score calculation is concerned, this study suggests that it is better to calculate the average of the neighbouring similarity between all the pairs, than to use a percentage of paired neighbouring minutia points or the MCC-based similarity. Although the performance of the proposed method is only marginally better, cases do exist where the other two methods perform signi cantly worse. The proposed approach is therefore reliable in various scenarios.
When considering how to choose the paired minutia points and how many pairs to use, this study suggests the following. The use of all the minutia points
CHAPTER 5. COMPARING LOCAL SIMILARITY SCORE CALCULATION
METHODS 60
(strategy 2 of stage 2) is highly sensitive to noise, which results in strategies 3 and 4 of stage 2 performing better on comparisons with low noise levels. It is therefore, in the rst place not necessary to include all the paired minutia points. Secondly, the identi cation of minutia points through a tolerance box- based approach performs well on most databases, but produces poor results on DB1_A of FVC2004. The second suggestion is therefore to rather use a percentage of the minutia points within the overlapping region than to incor- porate the tolerance box-based approach, speci cally for the purpose of local similarity score calculation.
In summary, this chapter proposed a new local similarity algorithm based on descriptors that is robust to partial overlap, but still compares individual minutia points in order to be robust with respect to noise. This method per- forms best when the local similarity is based on the average similarity between all the neighbouring pairs. Even though the proposed local similarity method often performs only marginally better than other local similarity methods, it appears to be more stable across all databases. Furthermore, when averaging a percentage (around 50%) of the pairs in the overlap, the local similarity proposed by Cappelli et al. (2010a) produces the best results.
Chapter 6
Combining dierent similarity
score calculation methods
6.1 Introduction
The results in Chapter 3 indicate that the similarity score calculation method based on the Minutia Cylinder Code (MCC) Local Greedy Similarity with Distortion Tolerant Relaxation (LGS_DTR) as proposed by Cappelli et al. (2010b), i.e. S3, achieves the highest performance for most of the databases
considered. However, the performance of this method decreases for databases containing many comparisons with high levels of intra-class variations and/or inter-class similarities, as is the case for the FVC2004 ngerprint databases. Furthermore, this method does not perform the best for all the databases con- sidered. This indicates that said similarity score calculation method is more sensitive to speci c intra-class variations or inter-class similarities than is the case for some of the other similarity score calculation methods. The combi- nation of dierent similarity score calculation methods may therefore improve the performance of existing similarity score calculation methods and is the focus of the current chapter.
The research questions posed in this chapter are as follows:
Firstly, does the combination of the three types of similarity score cal- culation methods (as introduced in Section 2.2) improve the accuracy of the individual similarity score calculation methods?
Secondly, does this improved method also address intra-class variations and inter-class similarities and therefore produce a similar performance when implemented on the FVC2004 and FVC2002 ngerprint databases? Finally, is the performance of this fused similarity score calculation method better than that of the most pro cient existing similarity score calculation method, i.e. LGS_DTR?
CHAPTER 6. COMBINING DIFFERENT SIMILARITY SCORE
CALCULATION METHODS 62 In this chapter, four dierent similarity score calculation methods are com- bined into a new similarity score calculation method. This study suggests that the combined method may better address the dierent types of intra-class variations and inter-class similarities than is the case for existing, individual similarity score calculation methods and may therefore be more accurate. Sec- tion 6.2 explains the methodology, while Sections 6.3.1 and 6.3.2 elaborate on the individual similarity score calculation methods and the fusion process respectively. Section 6.4 presents the results and Section 6.5 provides a dis- cussion and conclusions.
6.2 Methodology
The methods considered here are similar to those discussed in Chapter 4, but for the fact that the similarity score calculation stage dier. Dierent similarity score calculation methods are implemented on six databases with the testing protocol and preprocessing procedures as described in Chapter 3. Section 6.3.1 explains the individual similarity score calculation methods (adjusted versions of existing similarity scores), while section 6.3.2 elaborates on how the fusion process that combines the four individual similarity score calculation meth- ods, works. After the calculation of the similarity score values, the next step is to calculate the EER, FMRzero, FNMRzero, FMR100, FMR1000, FMR10000, and
area under the Receiver Operating Characteristic Curves (AUC) as perfor- mance measures for each similarity score calculation method on the dierent databases considered. These performances are then compared to those of ex- isting similarity score calculation methods as reported in Chapter 4. Finally, should the proposed calculation methods produce better results than exist- ing similarity score calculation methods, the signi cance of this improvement is determined. In order to verify this, we implement the dependent (paired) t-statistic at a signi cance level of 0.05 on the EER.