Dynamic Time Warping

The format of the extracted features is a set of M state vectors obtained

via frequent measurements of the interaction, whereby M is the number

of simultaneously observed features. Although these state vectors provide

quantitative snapshots of the interaction, only a subset M0 of the total

number of features will contribute towards the users’ final verification. Given that all features, apart from the Spherical Harmonics Coefficients (SHC), exhibit a strong dependence on temporal relations and ordering, it is essential that classification is performed via some appropriate spatiotem- poral means. The Dynamic Time Warping (DTW) algorithm [4] has been utilized as the classifier in the present scheme, since it sufficiently man- ages to capture the spatiotemporal information of the biometric traits. The

SHC-related features are compared with each other via theL1−norm.

Used for calculating a metric about the dissimilarity between two (feature)

matching path computed via dynamic programming, namely the Dynamic

Time Warping (DT W) algorithm. TheDT W algorithm can provide either

a valuable tool for stretching, compressing or aligning time shifted signals ( [4]) or a metric for the similarity between two vectors ( [237]). Specifically, it has been widely used in a series of matching problems, varying from speech processing ( [4]) to biometric recognition applications ( [39]). A possible implementation basis on estimating the closed area formed by the path around the diagonal of the rectangular DTW-grid (Figure 4.14(b)). The

total dissimilarity dDT W between the vectors under comparison is defined

as the product of the areaAc and the minimum difference costDmin(T, T),

that are calculated via dynamic programming [4]. Its main advantages

are its simple implementation and its satisfactory performance given the required processing time.

A short description of the functionality ofDT W algorithm for comparing

two one-dimensional vectors (probe & gallery signal) is presented below:

The probe vector p of length L is aligned along the X-axis while the

gallery vector g of length L0 is aligned along the Y-axis of a rectangular

grid respectively. In our caseL ≡L0 as a result of the preprocessing steps

(Section 4.1.1 or Section 4.1.2). Each node (i,j) on the grid represents a

match of the ith element of p with the jth element of g. The matching

values of eachp(i),g(j) pair are stored in a cost matrixCM associated with

the grid. c(1,1) = 0 by definition and all warping paths are a concatenation

of nodes starting from node (1,1) to node (L, L).

The main task is to find the path for which the least cost is associated. Thus the difference cost between the two feature vectors is provided. In this

respect, let (xk, yk) represent a node on a warping path at the instancekof

matching. The full costD(xk, yk) associated to a path starting from node

(1,1) and ending at node (xk, yk) can be calculated as:

D(xk, yk) =D(x(k−1), y(k−1)) +c(xk, yk) = k X

m=1

c(xm, ym) (4.41)

Accordingly, the problem of finding the optimal path can be reduced to

finding this sequence of nodes (xk, yk), which minimizesD(xk, yk) along the

As stated by Sakoe and Chiba in ( [4]), a good path is unlikely to wander very far from the diagonal. Thus, the path with minimum difference cost, would be the one that draws the thinnest surface around the diagonal as shown by the dashed lines in Figure 4.14(b). In the ideal case of perfect matching between two identical vectors, the area of the drawn surface would be eliminated. The closed area around the diagonal can be calculated by counting the nodes between the path and the diagonal at every row ( [110]) as indicated by the following equation.

V(pi, qj) =                            1 , if (i > j) ofN(pi, qj) forj =j, j+ 1, ..., j+d, whered=i−j 1 , if (i < j) ofN(pi, qj) fori=i, i+ 1, ..., i+d,, whered=i−j 1 , if (i=j) ofN(pi, qj) 0 , otherwise (4.42)

Thus, the value V(pi, qj) = 1 to these nodes. On the contrary, all other

nodes lying outside the closed area will be assigned the valueV(pi, qj) = 0.

Then, the total area S created by the path is mathematically stated as

following: Ac= T X i=1 L X j=1 V(pi, qj) (4.43) whereby

Finally the total dissimilarity measure dDT W between vector p and g

(Equation 4.43) can be computed as the product of area size Ac and the

minimum full costD(T, T) (Equation 4.41):

dDT W =Ac·Dmin(T, T) (4.44)

The general process that is followed is that each “probe” feature vector or feature vector set is compared with the “gallery” template of the claimed ID, that are stored in the database. In order to combine authentication scores from different modalities so as to derive an authentication metric for the full prehension movement, the scores from each tracking device have to be fused.

It should be noted that the camera-based and sensor-based tracking devices are used in turns, in combination with the glove-based tracking device. The fusion of scores from different tracking devices is performed via score-level fusion:

Dtot = X

j∈{C,M,G}

wjdj,DT W (4.45)

whereby dj,DT W stands for the score provided by each tracking device j

(C:Camera; M:Magnetic; G:Glove), while wj is the corresponding weight

coefficient and is proportional to the total number of bits of information of the utilized features.

wj =

bits of inf ormation f or all f eatures of device j

total N umber of bits f or all utilized f eatures (4.46)

4.5. Summary

Summarizing, in the current section a novel biometric module has been pro- posed, exploiting the dynamic characteristics of the movements of the arm and the finger. The feature extraction procedures for each of the two body- parts can be schematically seen in Figure 4.15 and Figure 4.16, respectively.

Figure 4.15.: Flow Chart diagram of the procedure followed for the extrac- tion of dynamic features from the movement of the arm. Specifically, the movement of the arm of the user is initially recorded by two different types of trackers, i.e. an proprietary vision-based tracker that manages to effectively capture the movement of the head and the palm

in the 3D space, and a 4-point wired sensor-based tracker that accurately

detects the location of the head, shoulder, elbow and palm of the user in short timesteps (Figure 4.15). Next, the aforementioned locations are used for the description of the performed movement via generating the so-

Figure 4.16.: Flow Chart diagram of the procedure followed for the extrac- tion of dynamic features from the movement of the fingers.

Figure 4.17.: Flow Chart diagram of the procedure followed for the selection of the most indicative activity related features.

called “Activity Surface” and “Activity Curves” descriptors. Finally, the last building block refers both to the direct processing and the processing via transformations of these descriptors towards the extraction of these activity related features that are indicative for user recognition.

Similarly, the movement of the fingers of the hand of the user are tracked in means of angles between the phalanxes (i.e. via the translation of de- formation of the integrated thin metallic layers on the surface of the glove, into real angle values). In the next step, the so-called “Activity Curves” are generated from the successive tracked angles and are used as the de- scriptors of the movements of the hand. Lastly, the activity related features that are characterized by adequate recognition capacity, are extracted via the corresponding processing.

Following the aforementioned activity-related feature extraction approach, the proposed feature selection methodology is illustrated in Figure 4.17. Ini- tially, each feature is evaluated in terms of its relative entropy value, while the mutual information between all possible pairs of features are estimated in a confusion matrix. Based on these values, an iterative algorithm, run on a training dataset (i.e. a subset of the utilized dataset), is applied, in order to exclude the redundant and noisy features by aiming at the lowest EER value.

for both enrollment (i.e. training) and recognition modes, respectively. In particular, the high level flow chart diagrams of the followed process consist of the aforementioned tracking module (i.e. Figure 4.15 and Figure 4.16) and are followed by the filtering out of the least indicative features for

user recognition, as concluded in the module in Figure 4.17. The final

decision, regarding the validity of the identity of the user is taken in the last building block via the utilization of two efficient classification algorithms that effectively handle the comparison between the incoming signature and the stored template.

Figure 4.18.: High Level flow chart diagram of the procedure followed for the enrollment/training and recognition phase of the novel bio- metric system.

An analytical evaluation of the proposed methodology regarding both the validity of the feature selection methodology and the classification results will be presented in Chapter 6.