**6. Performance analysis of wavelets separation technique**

### **6.1 Monte Carlo approach and a signal generator**

The Monte Carlo approach [Metropolis & Ulam (1949)] is applied for the tests of wavelets performance depending on a few conditions. The testing of the algorithms using synthetic EOG and blinking signals generator is necessary. Such approach is very good for the testing of algorithm. The tests based on the analysis of the recorded signal are limited by the number of available samples. The representative set of the real samples is necessary with the man–made description of every example. The synthetic technique needs a good generator, but the tests are much more reliable. The samples obtained by the real measurement process are related to the small set of humans. The EOG and blinking signals generator is described in [Krupi ´nski & Mazurek (2010a)] and used in the papers [Krupi ´nski & Mazurek (2010b;d;e; 2011)] with some additional extensions (the smooth pursuit support). There are two possible techniques

<sup>0</sup> 0.02 0.04 0.06 0.08 0.1 <sup>0</sup>

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Real–Time Low–Latency Estimation of the Blinking and EOG Signals 325

<sup>0</sup> 0.02 0.04 0.06 0.08 0.1 <sup>1</sup>

**std** (c) Mean position error (in the number of samples) of detected

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**std** (f) Mean position error (in the number of samples) of detected

1.5 2 2.5 3 3.5 4 4.5 5 5.5

blinks

saccades

**std** (b) Blinks overdetected

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**std** (e) Saccades overdetected

The 1000 tests were processed. The maximal number of missing blinks is less than 4% for the higher noised samples (Fig. 13a). This figure depicts the reduction of the missed blinks due to the higher probability of assignment the noise peaks to a blink. The amount of overdetected blinks is depicted in Fig. 13b. The estimated position of the blink is disturbed too (Fig. 13c). The noise level does not influence significantly the position error for the standard deviation for about 0.08. The saccade position detector is more sensitive (Fig. 13d). This is expected behavior, because a single noise value may disturb the position of a saccade. The large values of overdetected saccades due to higher standard deviation noise values, creates false saccades (Fig. 13e) or shifts existing ones (Fig. 13f). The curves for the corresponding quality plots are

This is similar test to Test 1. The smooth pursuit signal is added so a trend occurred (Fig. 14). It is expected that the results are similar to the case without smooth pursuit. The wavelets transform does not support very long time scales so the influence of wavelets processing should not be observed. The smooth pursuit is very low frequency signal and should be processed in similar manner like the constant levels of the EOG signals between neighborhood

**6.3 Test 2 – three saccades, three blinks and smooth pursuit**

**std** (a) Blinks missed

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**std** (d) Saccades (in the number of

Fig. 13. Monte Carlo performance Test 1

similar for the blinks and saccades.

samples) missed

saccades.

Fig. 12. Example 2 – two blinks, two saccades, smooth pursuit

for the application of the generator. The generator could be used for any possible values of parameters and also for the limited values of parameters. Additionally, it allows testing the specific cases more deeply.

#### **6.2 Test 1 – three saccades and three blinks**

This test shows the performance of the algorithm depending on the noise (Fig. 13).

The signal consists of three blinks, three saccades, and the smooth pursuit is not applied. The Gaussian additive noise disturbs the signal. There are many sources of the noises in biosignal measurement systems related to the electrical properties of human body, a contact type and the measurement system. The external radio frequency interference is also the important factor of noise.

12 Will-be-set-by-IN-TECH

**Scale**

**Scale**

Fig. 12. Example 2 – two blinks, two saccades, smooth pursuit

**Counted Slopes**

transform

**Time [n]**

**Time [n]**

(e) Lines

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**Time [n]**

(h) Slope Counter

for the application of the generator. The generator could be used for any possible values of parameters and also for the limited values of parameters. Additionally, it allows testing the

The signal consists of three blinks, three saccades, and the smooth pursuit is not applied. The Gaussian additive noise disturbs the signal. There are many sources of the noises in biosignal measurement systems related to the electrical properties of human body, a contact type and the measurement system. The external radio frequency interference is also the important

This test shows the performance of the algorithm depending on the noise (Fig. 13).

100 200 300 400 500 600

(b) Continuous wavelets

100 200 300 400 500 600

**Scale**

−1.5 −1 −0.5 0 0.5 1 1.5 2

transform

**Accumulated Peaks**

**Time [n]**

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>0</sup>

**Time [n]**

(f) Accumulated lines of

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**Time [n]** (i) Detected signals

(c) Peaks

100 200 300 400 500 600

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(a) Original signal

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(d) Accumulated peaks of

**Time [n]**

**Time [n]**

(g) Accumulated transform

specific cases more deeply.

factor of noise.

100 200 300 400 500 600

**6.2 Test 1 – three saccades and three blinks**

**Time [n]**

−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

transform

**Summed along Scale**

**Scale**

**Amplitude**

#### Fig. 13. Monte Carlo performance Test 1

The 1000 tests were processed. The maximal number of missing blinks is less than 4% for the higher noised samples (Fig. 13a). This figure depicts the reduction of the missed blinks due to the higher probability of assignment the noise peaks to a blink. The amount of overdetected blinks is depicted in Fig. 13b. The estimated position of the blink is disturbed too (Fig. 13c). The noise level does not influence significantly the position error for the standard deviation for about 0.08. The saccade position detector is more sensitive (Fig. 13d). This is expected behavior, because a single noise value may disturb the position of a saccade. The large values of overdetected saccades due to higher standard deviation noise values, creates false saccades (Fig. 13e) or shifts existing ones (Fig. 13f). The curves for the corresponding quality plots are similar for the blinks and saccades.

#### **6.3 Test 2 – three saccades, three blinks and smooth pursuit**

This is similar test to Test 1. The smooth pursuit signal is added so a trend occurred (Fig. 14).

It is expected that the results are similar to the case without smooth pursuit. The wavelets transform does not support very long time scales so the influence of wavelets processing should not be observed. The smooth pursuit is very low frequency signal and should be processed in similar manner like the constant levels of the EOG signals between neighborhood saccades.

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Real–Time Low–Latency Estimation of the Blinking and EOG Signals 327

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**std** (c) Mean position error (in the number of samples) of detected

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**std** (c) Mean position error (in the number of samples) of detected

**std** (c) Mean position error (in the number of samples) of detected

 1.5 2.5 3.5 4.5

blinks

 1.5 2.5 3.5 4.5

blinks

saccades

**std** (b) Blinks overdetected

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**std** (b) Blinks overdetected

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**std** (b) Saccades overdetected

**std** (a) Blinks missed

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**std** (a) Blink missed

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**std** (a) Saccades missed

Fig. 17. Monte Carlo performance Test 5

Fig. 16. Monte Carlo performance Test 4

Fig. 15. Monte Carlo performance Test 3

Fig. 14. Monte Carlo performance Test 2

This test confirms that the trend does not affect significantly the results. This is very important for the applications, because no additional processing is necessary related to the smooth pursuit removal during estimation.

#### **6.4 Test 3 – two blinks only**

This test shows the influence of blinks (that are available) and saccades (that are absent) (Fig. 15).

The number of blinks missed is reduced proportionally in comparison to the previous Test 1. There is no influence due to false detected saccades.

#### **6.5 Test 4 – two blinks, smooth pursuit**

This similar test to Test 3 related to the influence of smooth pursuit (Fig. 16).

The results are similar to the previous test. The smooth pursuit does not influence significantly the algorithm.

#### **6.6 Test 5 – two saccades**

This is similar test to Test 3, but here exist only saccades without blinks (Fig. 17).

As expected there is no significant influence of blink detection on saccades.

blinks

blinks

Fig. 15. Monte Carlo performance Test 3

Will-be-set-by-IN-TECH

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**std** (c) Mean position error (in the number of samples) of detected

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**std** (f) Mean position error (in the number of samples) of detected

blinks

saccades

**std** (b) Blinks overdetected

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**std** (e) Saccades overdetected

This test confirms that the trend does not affect significantly the results. This is very important for the applications, because no additional processing is necessary related to the smooth

This test shows the influence of blinks (that are available) and saccades (that are absent)

The number of blinks missed is reduced proportionally in comparison to the previous Test 1.

The results are similar to the previous test. The smooth pursuit does not influence significantly

This similar test to Test 3 related to the influence of smooth pursuit (Fig. 16).

This is similar test to Test 3, but here exist only saccades without blinks (Fig. 17).

As expected there is no significant influence of blink detection on saccades.

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**std** (a) Blinks missed

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**std** (d) Saccades missed

Fig. 14. Monte Carlo performance Test 2

There is no influence due to false detected saccades.

pursuit removal during estimation.

**6.5 Test 4 – two blinks, smooth pursuit**

**6.4 Test 3 – two blinks only**

(Fig. 15).

the algorithm.

**6.6 Test 5 – two saccades**

Fig. 16. Monte Carlo performance Test 4

number of samples) of detected saccades

Fig. 17. Monte Carlo performance Test 5

Fig. 19. Latency area and latency time

**8. Conclusions and further work**

The application of the EOG measurements system has been rising. The EOG systems are used in different and new application areas. The signal processing techniques for real–time processing with high accuracy and low–latency are necessary. There are many processing techniques for the detection and separation of blinking and EOG signals. Most of them are not suitable for more specific cases and new ones are necessary. The recent research shows the

Real–Time Low–Latency Estimation of the Blinking and EOG Signals 329

In this chapter the new wavelets–based technique for the estimation of blinking and saccade time moments using CWT was proposed. The estimation of the blink and EOG signals is important for the real–time HCI systems. Previous work related to the optimization approach [Krupi ´nski & Mazurek (2010b;d;e; 2011)], using the blinking and eye movement model, was not well fitted for the real–time processing. The computation requirements were high and not defined by the number of processing steps due to the applications of the random number generator in the optimization algorithm. The proposed techniques in those papers were based on the evolutionary approach. The reduction of computation time was obtained by the selection of more efficient evolutionary operators. The computation time was also reduced by the reduction of the number of processed samples. The blink and saccade positions were also considered as a starting point for the optimization process near the global minima [Krupi ´nski & Mazurek (2010b)] and the sensitivity of this approach was considered in [Krupi ´nski & Mazurek (2010e)]. Additionally, the estimation of the smooth pursuit movements was observed to improve the results [Krupi ´nski & Mazurek (2010d)].

importance of the wavelets transform with carefully selected wavelets function.

#### **6.7 Test 6 – two saccades, smooth pursuit**

In this test the influence of smooth pursuit on the detection of saccades is tested (Fig. 18).

Fig. 18. Monte Carlo performance Test 6

The plots are similar to the previous Test 5. It means that there is no significant influence of smooth pursuit.

Additionally, in all tests there is no one wrong detection of the saccade slope direction (falling or rising).
