**6. Estimation of the position, distance, and rotation of the markers**

Estimation of the marker is possible using numerous image processing techniques. The feature based techniques or image synthesis, using the model fitting, are possible also. The feature techniques are based on the corners detection. More advanced techniques uses corners detection for further starting point of the line detection. The estimation quality depends on the marker shape and the number of pixels used for the estimation. The larger number of pixels and larger distant between used pixels are important due to noises and possible occlusions, especially.

Proposed technique use a few techniques for the optimization algorithm. Single technique is not feasible for applications due to computation cost and poor results as it is shown by 10 Will-be-set-by-IN-TECH

not well measured, especially for variable light conditions for such configuration. The scale of the larger marker may differ in some direction, so for example the ellipse is observed instead the circle. It gives an ability estimation of full 6 DoF (Degree–of–Freedom) for every large

Correspondence between real and virtual world is used during the calibration of the cameras. Calibrated cameras are used in marker systems or in model fitting approach. The model fitting approach is similar to the calibration process but the instead calibrated object there are two

Vision tracking techniques for robots are based on the numerous approaches: marker based, object features, or even on complete synthesis of the expected object. All of the them are interesting and the selection is application depended. The most valuable techniques for the controlled environment scenarios are marker based. The uncontrolled environments exist if the unexpected situations may occurs, related to the object occlusions, different lighting

The marker based techniques are very interesting, because different markers designs are possible. The light emitting markers are especially useful for poor lighting conditions. They need additional power connections (wires) for the bulbs or LEDs. The retroreflective markers reflect surrounding light and no additional power connection are necessary for them. The retroreflective markers are interesting for small size and small power robots, especially. Controlled environment of the robot's work area gives an ability of the correct light setup for maximization performance of retroreflective markers. Markers may support angular estimation (3DoF) depending on own shape. The simplest matte ball markers are orientation less so only a 3D position (3DoF) is obtained by the triangulation using two or more cameras. The carefully selected set of such markers located at close distance gives ability of estimation of orientation. The larger markers with additional orientation features may

In this paper, the four–sector circle with the boundary ring is used as marker (Fig. 10). Such marker gives an ability of orientation estimation with 180 degree accuracy, position and distance. Complete set of DoF (six of them) is possible to estimate. The estimation of all parameters is limited by the optical visibility of the markers. A low angle case between camera and marker plane are hard to process. This is the reason, why a ball shape markers are preferred, because they have superior visibility. Large markers support estimation of own

The marker uses boundary ring for improving separation between background and marker, what is important for the scale estimation, because estimation process should be related to the

Estimation of the marker is possible using numerous image processing techniques. The feature based techniques or image synthesis, using the model fitting, are possible also. The feature techniques are based on the corners detection. More advanced techniques uses corners detection for further starting point of the line detection. The estimation quality depends on the marker shape and the number of pixels used for the estimation. The larger number of pixels and larger distant between used pixels are important due to noises and possible occlusions,

Proposed technique use a few techniques for the optimization algorithm. Single technique is not feasible for applications due to computation cost and poor results as it is shown by

parameters even for partial occlusions but it is not considered in following tests.

**6. Estimation of the position, distance, and rotation of the markers**

sets of calibrated cameras (real and virtual) and deformable model of the real robot.

marker.

**5. Markers**

conditions, etc.

support estimation of orientation.

marker, not to the background.

especially.

(c) Filtered (blurred) marker before downsampling (d) Example of noised image of marker at low resolution

Fig. 10. Model of marker and noised measurements

the numerical tests. The dedicated renderer of the marker and mask at different positions, scale (distance), 3D rotations, and contrast is used. The contrast fitting is important due to variable light conditions. The white and black points are defined by the two coordinate pairs (Fig. 11). The black (*Xb*,*Yb*) and white point (*Xw*,*Yw*) define simplest contrast, brightness, and saturation parameters of image transformation.

The first optimization phase is quite simple and the exhaustive search is used for a priori defined spatial and angular resolutions. Positions are tested using subpixel resolutions, 10 times higher resolution in both direction, and rotations using 20 deg. angle resolutions. The scale is not tested, because different scales of markers have common central part. Contrast is also not tested and fixed. The advantages of this phase are the fixed computation cost and possibilities in parallel processing.

The best position obtained from first phase due to obtained *l*<sup>2</sup> value is tested using optimization in second phase. The selection is driven by the threshold value for *l*<sup>2</sup> value. Second phase is started in parallel for obtained positions with enough low value of *l*2. Second phase is based on the gradient and non–gradient approaches. The constrained optimization is applied in all optimization phases.

During second phase gradient search algorithm is used and after the optimization is stopped (due to achieving error small changes, or after selected number of iterations) the non–gradient

**START**

265

**Grid based search (position and rotation domains)**

**Gradient search**

**Non-gradient search (evolutionary)**

**iteration**

**=10**

Very interesting are box–plot statistic (Fig. 15), especially the depicted median value of the *l*<sup>2</sup> error. It is shown, that first step (gradient based) reduces error to low–level, but second step (non–gradient) reduces error to much lower level (more then 2 times). The reduction does not occur significantly by the next repetition of the gradient and non–gradient search. It is very important for practical applications. The gradient algorithm fails in local minima and the solution is possible using the non–gradient algorithm. Applications of the non–gradient algorithm only is not shown in this chapter, and the computation cost is very large (the

The position error and following errors are calculated using Euclidean distance formula also. All of them are possible to obtain using the synthetic test using Monte Carlo technique and

First gradient step does not gives good results (Fig. 16). The mean value of the position error is about half of pixel. The next step (non–gradient based) reduces mean error to values about 0.2. It is important quality improvement. The next steps reduces error, but not significantly. After all 20 steps the mean value is reduced, and histogram is little compressed into left direction,

Only z–axis is considered in shown results, that is related to the rotation of the maker around own axis. Rotation errors are reduced significantly (Fig. 17) to the about 0.6 degree (mean

**<10**

**STOP**

Fig. 12. Optimization scheme

Estimation of Position and Orientation

for Non–Rigid Robots Control Using Motion Capture Techniques

computation are very slow, and are omitted).

but the computation cost is quite high.

gives an ability of the algorithm test and configuration.

value). The reduction occurs after 20 iterations but is not so large.

Fig. 11. Contrast curve, with white (*w*) and black (*b*) points

algorithm is started. This process is iterated ten times. Such technique gives abilities of exit from local minimal, that is achieved by the gradient search. The non–gradient algorithm when is used alone, supports exit from local minimum (but the convergence is usually very slow). The gradient algorithm is the minimization procedure from the Matlab Optimization Toolbox (fmincon). The non–gradient algorithm is evolutionary algorithm [ Back (T. et al.;T); Michalewicz (1996)], based on mutation. The single parent and child are used at one time evolutionary step. Mutation operator changes relative values of estimated parameters in specific range [ Spears (2000)].

The non–gradient phase (Fig.13) uses 1000 iterations and during the single iterations modification of the position (2 DoF), scale (2 DoF), rotation (1 DoF), and contrast (4 DoF) are driven by the uniform random noise generator. The probabilities of mutation of parameter is set to the 0.3. More then one parameter may change during the single iteration. Multiple parameters modified during one iterations reduce influence of local minimum.

The number of iterations and number of repetitions is selected after a lot of tests. The convergence to acceptable level of *l*<sup>2</sup> is obtained in most cases, but as it is shown later the better results are obtained, if more such optimization processes are started. In parallel processing devices reduce processing time.

#### **7. Performance of proposed estimation technique**

Monte Carlo approach Fishman (2000) is used for performance analysis. Application of the Monte Carlo method gives an abilities of testing complex system. The 600 tests are applied using pseudo random number generator for parameters setting. Every test uses 20 iterations (gradient and non–gradient). The Gaussian additive noise is applied to the image (0.2 standard deviation). Values that are not fitted into (0 − 1) range are processed by the contrast curve and saturated according this curve.

The *l*<sup>2</sup> error is minimized to low values (Fig. 14) what is a numerical, Monte Carlo test based proof of algorithm. Achieving a zero value of *l*<sup>2</sup> is a very low probable, dependent on the noise level and contrast curve. It means that *l*<sup>2</sup> error is interesting quality of fitness, that is available during optimization process (due to known model) but not necessary a reliable one. 12 Will-be-set-by-IN-TECH

**<sup>1</sup>** (Xw,Yw)

**0 1**

algorithm is started. This process is iterated ten times. Such technique gives abilities of exit from local minimal, that is achieved by the gradient search. The non–gradient algorithm when is used alone, supports exit from local minimum (but the convergence is usually very slow). The gradient algorithm is the minimization procedure from the Matlab Optimization Toolbox (fmincon). The non–gradient algorithm is evolutionary algorithm [ Back (T. et al.;T); Michalewicz (1996)], based on mutation. The single parent and child are used at one time evolutionary step. Mutation operator changes relative values of estimated parameters in

The non–gradient phase (Fig.13) uses 1000 iterations and during the single iterations modification of the position (2 DoF), scale (2 DoF), rotation (1 DoF), and contrast (4 DoF) are driven by the uniform random noise generator. The probabilities of mutation of parameter is set to the 0.3. More then one parameter may change during the single iteration. Multiple

The number of iterations and number of repetitions is selected after a lot of tests. The convergence to acceptable level of *l*<sup>2</sup> is obtained in most cases, but as it is shown later the better results are obtained, if more such optimization processes are started. In parallel processing

Monte Carlo approach Fishman (2000) is used for performance analysis. Application of the Monte Carlo method gives an abilities of testing complex system. The 600 tests are applied using pseudo random number generator for parameters setting. Every test uses 20 iterations (gradient and non–gradient). The Gaussian additive noise is applied to the image (0.2 standard deviation). Values that are not fitted into (0 − 1) range are processed by the

The *l*<sup>2</sup> error is minimized to low values (Fig. 14) what is a numerical, Monte Carlo test based proof of algorithm. Achieving a zero value of *l*<sup>2</sup> is a very low probable, dependent on the noise level and contrast curve. It means that *l*<sup>2</sup> error is interesting quality of fitness, that is available during optimization process (due to known model) but not necessary a reliable one.

parameters modified during one iterations reduce influence of local minimum.

(Xb,Yb)

**y**

**0**

specific range [ Spears (2000)].

devices reduce processing time.

Fig. 11. Contrast curve, with white (*w*) and black (*b*) points

**7. Performance of proposed estimation technique**

contrast curve and saturated according this curve.

**x**

Fig. 12. Optimization scheme

Very interesting are box–plot statistic (Fig. 15), especially the depicted median value of the *l*<sup>2</sup> error. It is shown, that first step (gradient based) reduces error to low–level, but second step (non–gradient) reduces error to much lower level (more then 2 times). The reduction does not occur significantly by the next repetition of the gradient and non–gradient search. It is very important for practical applications. The gradient algorithm fails in local minima and the solution is possible using the non–gradient algorithm. Applications of the non–gradient algorithm only is not shown in this chapter, and the computation cost is very large (the computation are very slow, and are omitted).

The position error and following errors are calculated using Euclidean distance formula also. All of them are possible to obtain using the synthetic test using Monte Carlo technique and gives an ability of the algorithm test and configuration.

First gradient step does not gives good results (Fig. 16). The mean value of the position error is about half of pixel. The next step (non–gradient based) reduces mean error to values about 0.2. It is important quality improvement. The next steps reduces error, but not significantly. After all 20 steps the mean value is reduced, and histogram is little compressed into left direction, but the computation cost is quite high.

Only z–axis is considered in shown results, that is related to the rotation of the maker around own axis. Rotation errors are reduced significantly (Fig. 17) to the about 0.6 degree (mean value). The reduction occurs after 20 iterations but is not so large.

<sup>0</sup> 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 <sup>0</sup>

267

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Optimization step number (a)

Fig. 15. Boxplot statistic for optimization step number – gradient based (odd step numbers),

Known marker size give abilities of distance estimation using single camera. The 24 pixels of diameter correspond to the scale value 0.03. Diameter has variable diameter 24 − 48 pixels in test. The absolute scale error (Fig. 18) is large – 2'nd and 3'rd column preserved about 1/3

Correlation between *l*<sup>2</sup> value and particular error is very interesting. The following values are obtained: *R* = 0.24 for position, *R* = 0.12 for rotation, and *R* = 0.30 for scale. All tested cases

l 2 error (a)

> 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

non–gradient based (even step numbers)

cases for errors about 20% of diameter.

are depicted in Fig. 19 .

l

2 value

Fig. 14. *l*<sup>2</sup> error between image and marker's image model

for Non–Rigid Robots Control Using Motion Capture Techniques

Percents of test

Estimation of Position and Orientation

Fig. 13. Evolutionary optimization

14 Will-be-set-by-IN-TECH

p=0.3

Calculate error basing on the starting parameters

START

p=0.3

p=0.3

p=0.3

p=0.3

p=0.3

p=0.3

Computation of error

Restore previous paramters

current error > previous error Y

Iteration number > 1000

N

STOP

Y

N

Modification of position (X-direction)

Modification of position (Y-direction)

Modification of rotation (Y-axis)

Modification of rotation (X-axis)

Modification of rotation (Z-axis)

> Modification of contrast

> Modification of scale

Fig. 13. Evolutionary optimization

Fig. 14. *l*<sup>2</sup> error between image and marker's image model

Fig. 15. Boxplot statistic for optimization step number – gradient based (odd step numbers), non–gradient based (even step numbers)

Known marker size give abilities of distance estimation using single camera. The 24 pixels of diameter correspond to the scale value 0.03. Diameter has variable diameter 24 − 48 pixels in test. The absolute scale error (Fig. 18) is large – 2'nd and 3'rd column preserved about 1/3 cases for errors about 20% of diameter.

Correlation between *l*<sup>2</sup> value and particular error is very interesting. The following values are obtained: *R* = 0.24 for position, *R* = 0.12 for rotation, and *R* = 0.30 for scale. All tested cases are depicted in Fig. 19 .

<sup>0</sup> 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Rotation error (rad)

<sup>0</sup> 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Rotation error (rad)

<sup>0</sup> 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Rotation error (rad)

(c) Minimal value after 20 steps (10 iteration of gradient and non–gradient interleaved

(b) Step=2 non–gradient based

(a) Step=1 gradient based

Fig. 17. Rotation error (z–axis)

algorithms)

Percents of test

Percents of test

Percents of test

for Non–Rigid Robots Control Using Motion Capture Techniques

Estimation of Position and Orientation

(c) Minimal value after 20 steps (10 iteration of gradient and non–gradient interleaved algorithms)

Fig. 16. Position error

Will-be-set-by-IN-TECH

<sup>0</sup> 0.5 <sup>1</sup> 1.5 <sup>2</sup> 2.5 <sup>3</sup>

Position error (pixels)

(a) Step=1 gradient based

<sup>0</sup> 0.5 <sup>1</sup> 1.5 <sup>2</sup> 2.5 <sup>3</sup>

Position error (pixels)

<sup>0</sup> 0.5 <sup>1</sup> 1.5 <sup>2</sup> 2.5 <sup>3</sup>

Position error (pixels)

(c) Minimal value after 20 steps (10 iteration of gradient and non–gradient interleaved

(b) Step=2 non–gradient based

algorithms)

Fig. 16. Position error

Percents of test

Percents of test

Percents of test

(c) Minimal value after 20 steps (10 iteration of gradient and non–gradient interleaved algorithms)

Fig. 17. Rotation error (z–axis)

<sup>0</sup> 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 <sup>0</sup>

271

<sup>0</sup> 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 <sup>0</sup>

<sup>0</sup> 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 <sup>0</sup>

l 2 error

(c) Correlation between image *l*<sup>2</sup> and scale errors

l 2 error

(b) Correlation between image *l*<sup>2</sup> and rotation

l 2 error

(a) Correlation between image *l*<sup>2</sup> and position

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

errors

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

errors

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Fig. 19. Correlation between image *l*<sup>2</sup> and position, rotation, scale errors

Scale error

Rotation error (rad)

Position error (pixels)

for Non–Rigid Robots Control Using Motion Capture Techniques

Estimation of Position and Orientation

(c) Minimal value after 20 steps (10 iteration of gradient and non–gradient interleaved algorithms)

Fig. 18. Scale (distance) error

18 Will-be-set-by-IN-TECH

<sup>0</sup> 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 <sup>0</sup>

Scale error

<sup>0</sup> 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 <sup>0</sup>

Scale error

<sup>0</sup> 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 <sup>0</sup>

Scale error

(c) Minimal value after 20 steps (10 iteration of gradient and non–gradient interleaved

(b) Step=2 non–gradient based

(a) Step=1 gradient based

Fig. 18. Scale (distance) error

algorithms)

Percents of test

Percents of test

Percents of test

(a) Correlation between image *l*<sup>2</sup> and position errors

(b) Correlation between image *l*<sup>2</sup> and rotation errors

(c) Correlation between image *l*<sup>2</sup> and scale errors

Fig. 19. Correlation between image *l*<sup>2</sup> and position, rotation, scale errors

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Estimation of Position and Orientation

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Come discussion is necessary, because correlation coefficients are quite low. there is not direct relation between both errors, like *R* = 1/4, but correlation is high. Most cases create concentration cloud around expected minimal values of both errors. It is well visible for position errors, and if very small *l*<sup>2</sup> error is measured it is expected that position error is very small also. It looks that position error gives quite large number of pixels used during estimation and the number of pixels influence on the optimization results. The number of pixels for rotation influenced by the rotation probably is lower. This hypothesis should be considered in further works. Improvement of correlation gives abilities of error estimation. This is very important for the tracking algorithms (e.g. Kalman filter) and validation of the measurements. The scale is quite specific, because difference between different scales is defined by the marker's ring. Applications of larger chessboard marker should give better results, but the large markers are not feasible to use.

#### **8. Conclusion**

Non–rigid robots are important design for the future robots and different vision based techniques should be applied for the state estimation. Considered technique, based on the larger marker, is promising for state estimation measurements. Estimation of all parameters is possible but the position, rotation, and scale are considered only. The low values of *l*<sup>2</sup> error corresponds to the low values of the position, rotation and scale errors, and it is a useful estimator of the fitness, but not ideal. The most interesting result is the search scheme, based on the subpixel testing (0.1 pixel accuracy), gradient search and non–gradient search. The next repetition of gradient and non–gradient algorithm does not reduce error so much. Estimation of the parameters (meta level optimization) of non–gradient algorithm is interesting. The 1000 steps are used and reduction of the number of steps is important for the real–time processing. Validation of the proposed algorithm is important for the further optimization and in parallel processing. At this moment, processing time is quite long using Matlab. Optimization of the algorithm and code is necessary together. The visual servoing applications need fast, low latency and computation cost effective solutions. Application of the GPGPU or FPGA are promising computation devices for considered algorithm.

#### **9. Acknowledgments**

This work is supported by the UE EFRR ZPORR project Z/2.32/I/1.3.1/267/05 "Szczecin University of Technology – Research and Education Center of Modern Multimedia Technologies" (Poland).

#### **10. References**


20 Will-be-set-by-IN-TECH

Come discussion is necessary, because correlation coefficients are quite low. there is not direct relation between both errors, like *R* = 1/4, but correlation is high. Most cases create concentration cloud around expected minimal values of both errors. It is well visible for position errors, and if very small *l*<sup>2</sup> error is measured it is expected that position error is very small also. It looks that position error gives quite large number of pixels used during estimation and the number of pixels influence on the optimization results. The number of pixels for rotation influenced by the rotation probably is lower. This hypothesis should be considered in further works. Improvement of correlation gives abilities of error estimation. This is very important for the tracking algorithms (e.g. Kalman filter) and validation of the measurements. The scale is quite specific, because difference between different scales is defined by the marker's ring. Applications of larger chessboard marker should give better

Non–rigid robots are important design for the future robots and different vision based techniques should be applied for the state estimation. Considered technique, based on the larger marker, is promising for state estimation measurements. Estimation of all parameters is possible but the position, rotation, and scale are considered only. The low values of *l*<sup>2</sup> error corresponds to the low values of the position, rotation and scale errors, and it is a useful estimator of the fitness, but not ideal. The most interesting result is the search scheme, based on the subpixel testing (0.1 pixel accuracy), gradient search and non–gradient search. The next repetition of gradient and non–gradient algorithm does not reduce error so much. Estimation of the parameters (meta level optimization) of non–gradient algorithm is interesting. The 1000 steps are used and reduction of the number of steps is important for the real–time processing. Validation of the proposed algorithm is important for the further optimization and in parallel processing. At this moment, processing time is quite long using Matlab. Optimization of the algorithm and code is necessary together. The visual servoing applications need fast, low latency and computation cost effective solutions. Application of the GPGPU or FPGA are

This work is supported by the UE EFRR ZPORR project Z/2.32/I/1.3.1/267/05 "Szczecin University of Technology – Research and Education Center of Modern Multimedia

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results, but the large markers are not feasible to use.

promising computation devices for considered algorithm.

Academic Press, ISBN 9780123746337.

**8. Conclusion**

**9. Acknowledgments**

Technologies" (Poland).

International.

**10. References**


**14** 

Metin Aydin

*Turkey* 

**Brushless Permanent Magnet Servomotors** 

Electrical motors drive a variety of loads in today's world. Almost every industrial process relies on some kind of electrical motors and generators. There exist billions electric motors used in different applications all over the world. Majority of them are small fractional HP motors use in household appliances. However, they used about 5% of the electricity used by the motors. Three phase motors are used in heavier applications and consume substantial amount of electricity. These electric motors operate long hours and consume more than half

The oldest type of electric motor, wound field DC motor, was the most popular motor for years and easiest for speed control. Although they are replaced by adjustable AC drives in many applications, they are still used in some low power and cost effective applications. The main reason why DC drives faded away over the last decade is that they require converters and maintenance, not to mention their lower torque densities compared to AC motors. Induction motors are also one of the most widely used motors in AC drive applications. They are reliable and don't require maintenance due to the absence of brushes and slip rings. The availability of single phase power is another big plus for these motors. The fact that the rotor windings are present makes the induction motors less efficient and creates cooling problems of the rotor. One crucial drawback of the induction motors is the

Variable reluctance motors are also frequently used in the industry and robotics. It's simple and robust stator and rotor structures reduce the cost dramatically compared to other types of motors. The converter requirement is also not very severe. A simple half bridge converter can easily be used to drive the motor. On the other hand, variation of reluctance does also

As for the synchronous motors, they have benefits and drawbacks of both DC and induction motors. The synchronous motors with field winding can be more efficient than a DC or induction motors and are used in relatively large loads such as generating electricity in power plants. If the rotor winding in synchronous motors is replaced by permanent magnets, another variation of synchronous motors is obtained. These motors are called permanent magnet motors which can be supplied by sinusoidal or trapezoidal currents. These motors have three major types based on their magnet structures as

The lack of slip rings and rotor windings as well as high power density, high efficiency and small size make these motors very attractive in the industrial and servo applications. In

parameter variation due to the heat caused by the rotor winding.

create significant cogging, vibration and audible noise.

**1. Introduction** 

displayed in Fig. 1.

of the electricity used by motors.

*Kocaeli University, Department of Mechatronics Engineering, Kocaeli* 

Vol. 5337 (Computer Vision and Graphics International Conference ICCVG 2008), Springer Verlag, 451–460, ISBN 978-3-642-02344-6.

