ANALISIS DE LOS FACTORES DE ÉXITO EXPORTADOR

In the previous section the research background on gesture recognition system was

presented. In this section, we describe our gesture recognition technique which is

meant to be used as a component of a gesture-based user interface. The input to this

component is the movement trajectory information of the gesture signal. The

assumption is that the movement trajectory is captured by an intermediate device and

presented to the system. Particularly for vision based hand tracking, the trajectory of

the hand is provided by the vision-based hand tracker which can virtually be any

method of tracking. The method for skin blobs tracking which we introduced in the

previous chapter is one of the possible inputs. The gesture signal recognition can be

represented as a classification problem in the feature space. This approach typically

has two major components: Feature selection and classification.

6.3.1 Feature selection

Feature selection can be a challenging task. The number of the selected features should be as small as possible to be efficiently used by a classifier. There are also other issues such as sensitivity to input noise which may be caused by vibrations of the hand, small rotation and scale which may vary from person to person or with different input devices.

The movement trajectory of each gesture signal in two dimensional space can be

represented as a set of (x�> y1) coordinates over time. Therefore, a gesture trajectory

Chapter 6. Modelling and recognition of gesture signals in 2D space

Although this representation makes the reconstruction of the input accurate, it is not invariant to position which makes it not suitable for a general gesture recognizer.

There are other alternatives for representing the shape of a gesture signal . The gesture signal can also be represented as a set of angles over time. The value of the angle sequence can be extracted directly from the set of coordinates using the gradient of

the motion trajectory over time as represented in the following formula.

(6.1)

• where Gm is a gesture signal recorded between time steps 0 to _m. • a1 is the angle at time step t

• (xr. y1) represents the coordinate of the gesture movement trajectory at time-step

t.

To reduce the effect of vibration and also having a smaller number of feature-values, the calculated angle is quantized to values of 1 0°. Thus, each sample after

quantization will have a value between 0 to 35 (Figure 6. 1 a). Hence, the input

gestures can be described as a finite set of integer values.

13 , , - - I • • • ' ' . . . \ 2 17' I \ \ 0 1

s

Figure 6.1. a) Quantized input vectors, b) Gesture vector (0, 13, 0), c) Gesture vector (17, 31, 17)

The advantage of this representation is its invariance to translation. Using this model, a gesture like Figure 6. 1 b will be different from Figure 6. 1c, and the data, implicitly

includes the time and the direction of the movement trajectory . Figure 6.2a shows a

simple hand movement. The density of the arrows in different parts of the movement represents the speed of the hand in those parts. A higher density of arrows represents

slower movement. It is observed that the hand has vibrations in some parts and the

number of samples (arrows) in Figure 6.2a is considerably more than Figure 6.2b, which is the quantized version of the original movement trajectory. With this

approach, a gesture is translated to a gesture signal (Figure 6.2c), which reduces the

gesture recognition problem to a signal matching problem. Figure 6.3 shows that the

proposed modeling of the gesture is invariant against position variation. The

interesting feature of this model is that it transforms rotation in gesture space to a

vertical shift in the angle space.

a)

nme '''P (c)

b)

(d)

Figure 6.2. a) Original gesture trajectory, b) sampling from the gesture trajectory, c) gesture signal of the collected data over time, d) reconstructed gesture using [c].

Chapter _6. Modelling and recognition of gesture signals in 2D space

-+- Gesture � With slight rotation � With different starting point

- 30 " ! 25 " f 20 i 1 5 0 � 10 " g> 5 < 4 7 10 13 16 1 9 22 25 28 31 34 Timpe step

Figure 6.3. Left: Gesture signal, Right: gesture movement trajectories

6.3.2 Gesture Classification

After feature selection, introduced m the previous section, the next step is to implement a tool for recognition of a gesture signal. In this study, we applied a feed-

forward neural network for gesture classification. Applying this classifier requires a

primary training step which we describe in detail in the following sections. Figure 6.4

summarizes the steps involved in gesture recognition based on our technique.

Obviously, the gesture set is application dependent. Hence, some factors like user' s

physical and ergonomical limitations in employing gesture signals should be considered. -t iil :r s· (,Q

Recording the Pre-processing Training the

training data the training data classifier Gesture

recognition

6.3.3 Recording the training data

The data collection for training the classifier was done using the trajectory recoding

software which we implemented for this purpose (Figure 6.5). The program records the movements of a mouse cursor on the "Test canvas" and translates it to a gesture signal . The start and end of each signal is indicated by the user by clicking and

releasing the left mouse button. Hence, input devices such as optical mouse, trackball or digital tablet, which can control the mouse cursor are useable together with this application. Finally, the recorded gesture signals were then stored in a file for further

processing.

l!:i Gesture recorder [Gesturc05.txt] _GJ©Jrg)

o 2 s a 10 121• 16 18 20 22 24 26 28 30 n Time 'Step

Chapter 6. Modelling and recognition of gesture signals in 2D space

6.3.4 Normalizing the data

Although our modeling approach has the mentioned attractive features, because of the nature of the gesture which is the movement trajectory information, the number of samples may vary for each user or even at each time of the gesture input. The varying number of samples on the other hand is not suitable for classifiers. Most classifiers such as Neural-Networks, Support Vector Machines, and Eigen Vector Regression require a certain number of inputs which represents the number of dimensions in the feature space. Therefore, a pre-process is required to equate the size of the input data. Since the effects of the different normalization approaches using this technique are unknown, we designed a set of experiments to study the results of the different normalization techniques to find a realistic approach providing a reasonable accuracy. The details of the experiments and the results of their evaluation are drawn in the following sections.