Handwritten signature comes under the category of behavioural biometric trait and has been used widely especially for financial transactions [48]. However, it is prone to temporal changes and may get affected by the physical and emotional health of the signatory. A signature is composed of characters that may or may not be readable. It has also been observed that the successive signatures of the same person have a significant difference. Due to these reasons, the signature of a person is analysed as a whole image and not as different characters put together. The handwritten signatures can be categorised as online and offline [16]. An offline signature is captured by scanning or taking a photograph of the signature from a paper. On the other hand, online signature is acquired using an electronic tablet and stylus that also records pen positions, elevation, and pressure. Feature extraction plays an important role in signature identification and verification. The features extracted from online signatures can be classified into two categories called functional and parametric features. The functional features consist of information regarding acceleration, position, force, time, etc. w'hile signing, while the parametric features constitute the parameters calculated from the signals captured from the signing device. Signature identification system tries to establish the identity of the input signature by comparing it with all the signature templates stored in the database. The database is indexed with the goal of reducing the time taken for comparison by finding top-& candidates for comparison.

KD-Tree-Based Signature Database Indexing

The technique proposed in Ref. [48] extracts 100 global features for the construction of a feature vector to be used for indexing. Some of the features are total duration of the signature, number of pen-ups, average velocity, velocity correlation, average number of jerks, standard deviation in x- and у-axis, etc. The constructed 100-dimensional feature vectors are then indexed using KD-tree [24]. KD-tree partitions the feature vector space into к sub-spaces, thus forming indexes. During retrieval, the feature vector is obtained for the query signature and the range search is invoked to find the most suitable candidates by considering only those candidates that lie within d distance from the query.

11.6.2 Results

The discussed technique has been tested on MCYT online signature database [51]. It consists of 50 signatures collected from 330 individuals each. Of the 50 signatures, 25 are original and the remaining 25 are forged. However, the authors have used

Sample signature images from MCYT online signature database

FIGURE 11.15 Sample signature images from MCYT online signature database.

TABLE 11.2

Comparison of Time Taken for Recognition for MCYT Database with and without Indexing

Training Partition (%)

Identification Time (in Seconds)

Time Reduction (in %)















only the genuine ones making a database containing 8,250 signatures. Some of the samples from MCYT online signature database are shown in Figure 11.15.

The experimentation has been conducted in three ways, viz., training the model on 40%, 60%, and 80% of the database and then testing on the remaining partition. The identification accuracy (also referred to as Correct Index Power (CIP)) has been reported as 72.59%, 78.03%, and 81.58% when tested on the aforementioned three partitions, respectively. The authors have reported 95.95%, 96.79%, and 96.29% reduction in identification time if indexing is implemented. The time requirement for testing the data set with and without indexing has been shown in Table 11.2. However, it has to be noted that the KD-tree structure depends on the sequence followed to represent the feature vector; therefore, the tree may not always be balanced. A dimensional reduction may further help in the same.


Identification is a compute-intensive task that may take longer time to produce results. Indexing is used to fasten the identification process by quickly producing a list of possible candidates who are likely to be similar to the query biometric sample. It is interesting to note that the retrieval takes constant time and produces a short list. As the list is produced in constant time, we can neglect the time spent in retrieval. Also, the time to search through the candidate list is small as the list is expected it to have few elements only. Both these factors contribute to an efficient identification solution. We have seen CGTC-based method for the fingerprint indexing [2], which achieves 95% hit rate at just 3.57% penetration rate. It needs only 7.86% penetration rate to achieve 100% hit rate on FVC 2004 DBla database [44]. In both scenarios, the system achieves 28 and 13 times speed-up than the non-indexed identification process. For indexing finger-knuckle database, a boosted geometric hashing-based technique is proposed in Ref. [28]. The technique on publicly available (PolyU)FKP data set has achieved 99% hit rate at 10.62% and 94.07% penetration rate when SURF and SIFT features were used, respectively. CRR of the system with SIFT and SURF features is found to be 96.36% and 99.69% on the same database. This technique is robust to occlusion and rotation. To test the same, FKP images are introduced to artificial occlusion of 1%, 4%, 9%, 16%, 25%, and 36%; also for rotation, these images are rotated by 0°, 10°, 50°, 110°, and 150°. It has been observed that not much deterioration is seen in indexing performance. Face is one of the most on-demand biometric traits. There are a large number of facial databases with all kinds of variations such as age, expression, and pose. Many of the face databases have large number of images. PHC was proposed in Ref. [22] for facial image indexing. The technique maps the face images to a hamming space where similar faces could be clustered. The predictability of the hash codes was enhanced by utilising a convolutional neural network. The proposed technique achieved a recognition rate of 83.15% on YouTube Celebrities data set when the length of PHC was 128 bits. It can be observed that with the increase in predictability of the hash codes, the recognition accuracy also improved. Iris is one of the most accurate biometric traits. An indexing system for iris images proposed in Ref. [32] uses three databases, viz. CASIA-IrisV3-Interval [43], the BATH University database, and the НТК database [47] to evaluate its performance. The proposed technique has achieved penetration rates of 0.98%, 0.13%, and 0.12% and bin miss rates of 0.3037%, 0.4226%, and 0.2019% on the three databases CASIA-IrisV3-Interval, BATH University database, and НТК database, respectively. A comparison of the proposed method shows that it has higher penetration rate as compared to other methods on iris database. Signature is a very popular biometric trait in offline use. Many organizations in real world widely use this behavioural trait for financial transactions and document authentication. A KD-tree-based indexing technique has been proposed in Ref. [48] for indexing online signature database. Signature images are represented using a 100-dimensional feature vector. These features are indexed using partitioning with KD-tree. Experimentation has been conducted in three different database split, viz. training the model on 40%, 60%, and 80% of the database and then testing on the remaining data. The identification accuracy (referred to as CIP) has been reported as 72.59%, 78.03%, and 81.58%, respectively, when tested on the aforementioned three partitions.

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