- A novel offline signature modeling is introduced and evaluated which attempts to advance a grid based feature extraction method uniting it with the use of an ordered powerset. Specifically, this work represents the pixel distribution of the signature trace by modeling specific predetermined paths having Chebyshev distance of two, as being members of alphabet subsets-events. In addition, it is proposed here that these events, partitioned in groups, are further explored and processed within an ordered set context. As a proof of concept, this study progresses by counting the events' first order appearance (in respect to inclusion) at a specific powerset, along with their corresponding distribution. These are considered to be the features which will be employed in a signature verification problem. The verification strategy relies on a support vector machine based classifier and the equal error rate figure. Using the new scheme verification results were derived for both the GPDS300 and a proprietary data set, while the proposed technique proved quite efficient in the handling of skilled forgeries as well.
INTRODUCTION
Automated handwritten signature verification systems
(ASVS) remain up to now an accepted way for humans to
declare their identity in many application areas including
civilian ones [
The goal of an offline ASVS is to efficiently transform
an image into a mathematical measurable space where it will
be represented by means of its corresponding features [6].
Next, the features are feeding computational intelligence
techniques and pattern recognition classifiers which will
decide, after appropriate training and testing procedures, if a
signature under query belongs to a claimed writer [7], [8].
According to the experimental protocol followed, there are
two major approaches which have been applied to off-line
ASVS; writer dependent (WD) and writer-independent (WI).
The WD approach uses an atomic classifier for each writer.
The WI approach uses a classifier to match each input
questioned signature to one or more reference signatures, and
a single classifier is trained for all writers [9], [
Feature extraction is considered to be one of the most
challenging tasks when ASVS are designed. An important
feature extraction philosophy which attracts increasing
interest, exploits the signature using a coarse or fine detail
grid which is imposed upon the image. Among others,
examples of grid based feature extraction can be found in the
work provided by references [
In another work provided by Tselios, Zois, Nassiopoulos
and Economou [
The distributions of the now ordered transition paths in the new feature space are used to code the signature image. In the case study presented here a WD verification scheme is followed which comprises of the training and testing phase. Verification results have been drawn with the use of two databases, the GPDS300 and a proprietary one by means of the false acceptance, false rejection and the equal error rate (EER) figure of merit. The rest of this work is organized as follows: Section 2 provides the database details and the description of the feature extraction algorithm. Section 3 presents the experimental verification protocol which has been applied. Section 4 presents the comparative evaluation results while section 5 draws the conclusions.
The proposed feature extraction modeling has been
studied with the use of two databases of 8-bit grey scale
signatures: a Greek signers’ database (CORPUS1) [
In order to produce the binary form of the acquired
signatures the following preprocessing steps have been
carried out: thresholding using Otsu’s method [6],
skeletonization, cropping and segmentation. This procedure
is expected to reduce a number of side effects of the writing
instruments variations. The result is the generation of the
most informative window (MIW) of the image. The features
are extracted either from the whole MIW of the signature or
from segments of signature’s MIW with the use of the
equimass sampling grid method [
Since, in offline signatures, signature-pixel ordering is unknown, the ordered sequence of the pixels cannot be estimated. This note diminish the number of queried FCB2 transition paths, in a 5x5 pixel grid window, with center pixel each black pixel of signature’s image, to the sixteen independent transition paths presented in Fig. 2. In this case study only the FCB2 paths have been taken into account. It is advantageous in our case to explicitly treat the notion of the signature pixels indexes (i,j) as a transformation of sequences produced by the source. As a consequence, the feature extraction grid can be identified as a discrete space – discrete alphabet source.
Let the triad ( , Β, P) indicate the probability space on
which all the potential outcomes are identified. By definition
is the sample space upon which a discrete digital source
transmits alphabet symbols. The source may transmit either
single symbols or sets of them (events) from a 16 symbol
alphabet as figure 2 illustrates. Let B a sigma field (the event
space) that encloses all potential occurrences of symbols
combinations from the FCB2 alphabet. That is, B is the largest
possible -field [
In order to evade the problem of 216 space management is grouped into T subsets {t }t1,,T and we define the sub-s-fields Bt as the power sets for each t . In this work we choose to group the 16-FCB2(i) components into ensembles of four tetrads (call it hereafter F4-collection) thus resulting to an early set of 4 24=64 possible event combinations. From the complete set of all the possible ensembles of the F4 collection only 87 orthogonal cases shall be enabled along with their corresponding probabilities. From a mathematical point of view the signature image is analyzed into four major subspaces where each of them is composed of 16 orthogonal dimensions. The term orthogonal denotes that each symbol in a sub-alphabet space of a F4 tetrad cannot be derived as any combination of the same subspace F4 symbols. This constraint provides each signature with 87 different F4 orthogonal tetrad event sets, found through exhaustive search. Fig. 3 provides the FCB2 alphabet along with a F4 orthogonal collection. As a proof of concept, the orthogonal F4 collection #44, selected randomly is illustrated in figure 3.
Finally, each one of the four F4 power-sets of figure 3b is evaluated by ordering the elements of the powerset with respect to inclusion. Fig. 4 provides a graphical explanation of one powerset in line with the proposed modeling. In order to illustrate the method with clarity, figure 4 has been created which shows the powerset of the #44 F4 collection with respect to inclusion. The indexes x, y, z, w are associated with one tetrad’s elements of the F4 collection. For each arrow in figure 4 there is a corresponding probability evaluated for every segmented image. Thus, the overall dimensionality of the feature vector for one F4 collection is equal to 32 (4+12+12+4) for each image segment.
According to the exposed material, a discrete source,
designated as Sn, can be defined by its transmitted set of
symbols-events which are now members of an ordered F4
collection. This novel modeling of the feature generation
process is an evolution of the previous method as it was
described in [
To make this work robust a short description is provided for generating the ordered feature components. According to the material exposed in sections IIC, IID, each one of the preprocessed image segments is scanned top-down and leftright to identify its signature pixels. Let us denote with the labels One (O) and Two (T) a conjugated pair of 5 5 moving grids with the property that their topological centers are distant by a Euclidean distance of one. Then for each signature pixel the {O, T} grids are imposed. Next, detection of discrete events at both {O, T} grids is performed followed by the evaluation of the corresponding ordered probabilities, as described in fig. 4. In addition, fig. 5 presents in a graphical manner the generation of a feature component namely the {X, XY}. In this work the overall feature dimensionality is 128 due to the selection of the segmentation preprocessing steps.
III.
CLASSIFICATION PROTOCOL
On the grounds of proofing the proposed concept and
according to the discussion exposed in section II the training
phase of the WD verification scheme follows: for each
writer, #nref reference samples of genuine along with an
equal number of simulated-forgery signature samples are
randomly chosen in order to train the classifier. The “S2”
image segmentation scheme combines the features calculated
on the whole signature image as well as the relevant 2x2
equimass segmentation grid [
Evaluation of the verification efficiency of the system is accomplished with the use of a global threshold on the overall SVM output score distribution. This is achieved by providing the system’s False Acceptance Rate (FAR: samples not belonging to genuine writers, yet assigned to them) and the False Rejection Rate (FRR: samples belonging to genuine writers, yet not classified) functions. With these two rates, the receiver operator characteristics (ROC) are drawn by means of their FAR/FRR plot. Then, classification performance is measured with the utilization of the system Equal Error Rate (EER: the point which FAR equals FRR).
According to the discussion presented above, FAR, FRR and the relevant EER rates, are evaluated for (a) CORPUS 1 and and (b) CORPUS 2 with five and twelve reference samples for both genuine and forger class. The corresponding results are presented in Table I by means of the mean FAR, FRR and EER values. The letters G and F in Table I designate the genuine and skilled forgery samples respectively. In addition, the ROC curves are presented for both databases in fig. 6 along with their corresponding EER defined as the cross section of the ROC curves and the diagonal.
Our results are compared to recently published relevant
figures. The reported results for CORPUS 1 are compared
with the results relevant to those reported in [
V.
CONCLUSIONS
In this work a handwritten model based on the powerset
of an ordered event topology with respect to inclusion is
considered as a tool for offline signature verification. A
number of verification experiments based on an SVM
classifier have been carried out in two signature databases
namely the GPDS and a proprietary one. Primary verification
results indicate that the proposed feature extraction method
has an appealing aspect; As a comment on the efficiency of
the method one can state that in the case of the Corpus 1 a
substantial improvement is observed while in the case of
Corpus 2 the results are comparable with those of the
literature. Since the approach described in this case study is
preliminary it is anticipated that further exhaustive research
will unveil important conclusions with respect to the
modeling of handwriting. However a number of various
other models and experimental setups including i.e. the
dissimilarity framework [
Recognition",