pattern recognition of human gait signatures

8/2/2019 Pattern Recognition of Human Gait Signatures

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PATTERN RECOGNITION

OF

HUMAN GAIT SIGNATURES

Author: Elizabeth I. Maduko


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ABSTRACT

Pattern recognition is the classification of data into predetermined categories, usually

using statistical methods. Gait recognition is an area of application of pattern recognition

because it classifies and identifies an individual by their gait signatures. Gait recognition

offers the possibility of identifying individuals at a distance, or in video sequences

without any interaction or co-operation from the subject.

This project aims at developing a system capable of gait classification and recognition. A

gait signature has many features which make it an attractive proposition as a method of

identification. Such features include variation in angles of the parts of the body like the

hip, knee, ankle, etc, and variation of the amplitude of the gait pattern.

The experiment phase of the project was conducted on five subjects of three males and

two females, and features of their gait pattern extracted with the help of a video sequence.

The variation of the 2-dimensional angles of the hip, knee, torso and ankles were of

particular interest in this project. The angles obtained from the experiment known as the

crisp data were fuzzified using the Gaussian membership function and the resulting fuzzy

data stored in a knowledge base. Inferences on gait signature(s) under test were madeusing the fuzzy data stored in the knowledge base.

The gait recognition system was built using a high level language C++ as shown in

appendix iv and v, and the output of the system is the membership function of the gait

signature under test with that of each of the five subjects which must vary between 0 and

1. A membership function of 1 indicates total or complete membership with the gait

signature of the corresponding subject while a membership function less than 1 indicates

partial or incomplete membership with the gait signature of the corresponding subject.


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INTRODUCTION

Pattern recognition (also known as classification, pattern classification or statistical

classification) is a field within the area of machine learning, and can be defined as "theact of taking in raw data and taking an action based on the category of the data" [Fau94].

As such, it is a collection of methods for supervised learning. Pattern recognition aims to

classify data (patterns) based on either a priori knowledge or on statistical information

extracted from the patterns. The patterns to be classified are usually groups of

measurements or observations, defining points in an appropriate multidimensional space.

Each individual has a unique gait; hence, the variations in styles and positions of human

gait signatures make it possible for them to be classified and recognized as patterns using

Fuzzy Logic and Artificial Neural Networks (ANN). Fuzzy Logic refers to a logical

system that generalizes classical two-valued logic for reasoning under uncertainty

[Yen99], while an Artificial Neural Network is an information-processing system that has

certain performance characteristics in common with biological neural networks [Nav95].

This project aims at developing a program capable of semi-automatic gait recognition i.e.

developing a system capable of performing recognition of individuals derived from a

video sequence of their pattern of walking. The program should be able to store the

derived gait signature in a knowledge base for comparison at a later stage. The project

was conducted in three phases as described below and as shown in the block diagram.

1. Experiment: The acquisition of thegait pattern of the various subjects used in the

experiment, through a video sequence.

2. Feature Extraction: This phase of the project involves the extraction of the

features (crisp data) of the gait pattern or signature from the video sequence.


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3. Inference: This phase of the project makes the decision on the fuzzified data

acquired from the previous phase, based on a test sample.

The output from the inference phase is in from of a membership function with the

subjects of the experiment, where a membership function of 1 indicates full membership

with that subject and a membership function less than 1 indicates partial membership

with the subject.

The following sections describe the experimental procedure of the project in detail, and

discuss the fuzzification of the acquired crisp data, the fuzzy rules applied to the fuzzified

data, the deffuzification of the output, the final results obtained and recommendations for

future enhancements.

Experiment

Data Data Response

Knowledge

Base

InferenceFeature

Extraction

Figure 1: Block diagram showing the various phases of the project


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EXPERIMENTAL PROCEDURE

The experiment involves capturing subtle changes in an individuals walk, taking into

consideration the variation in angles of the various parts of the body or the amplitude of

the persons walking pattern. The experiment was conducted with five subjects (two

females and three males) in three different stages.

Stage 1: Video Sequence

Stage 2: Points Digitization

Stage 3: Points Processing

Video Sequence

Each subject had a total of five markers (objects capable of reflecting light over a

camera) attached to the following parts of their body:

1. The Shoulder

2. The Hip

3. The Knee

4. The Ankle

5. The Toe

The video of each subjects gait pattern was captured randomly using the installed

camera. For each captured gait pattern, a mark-in point and mark-out point was chosen

arbitrarily. The mark-in point represents the first point in the captured gait video where

all the markers were visible, while the mark out point represents the last point in the

video where the five markers were visible. These mark-in points and mark-out points

were arbitrary in the sense that different points were chosen for each subjects captured

gait video.

Points Digitization

After the mark-in and mark-out points were chosen for each captured gait video, the data

points were cropped between the start and finish markers. Whenever the markers

exceeded the softwares default minimum and maximum outline, the setup was changed


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to accommodate the excesses. The cropped data points were digitized automatically by

the software using the centriod of each marker. For points like those of the hips which

could not be digitized automatically by the software, as a result of the obstruction caused

by the arm during the gait, the cursor location was used to digitize the points instead. This

is known as guessing since the marker centriod was determined by the cursor location

input by the user.

Points Processing

The digitized points were processed by the process wizard in the software. The 2-

dimensional angles of rotation of the marked parts of the body were saved in a

predetermined format using a spline filter and a frequency of 60Hz. Reflex angles were

recorded for the hip, torso and ankle movement, while obtuse angles were recorded for

the knee movement as shown in the stick diagram below.

< 360

< 360

< 180< 360

Figure 2: Stick diagram of the gait pattern showing the recorded angles


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DATA ACQUISITION (CRISP)

The 2-dimensional angles of the hip, knee, torso and ankle movement obtained from the

above described experiment for each subject differed in size and number. For the first

subject (Subject 1), a total of 172 angles were obtained for the movement of each of the

four above named body part. For the second subject (Subject 2), a total of 128 angles

each were obtained. A total 170 angles each were obtained for the third subject (Subject

3), 152 angles each obtained for the fourth subject (Subject 4) and 138 angles each for the

last subject (Subject 5). The angles obtained for each subject in 3 places of decimal is

tabulated and attached in appendix i.

Because of the way the video of the gait patterns were captured and data acquired, the

gait patterns or signatures for the 5 subjects were not in sync as shown in figure 3.1(a)

through 3.1(d).

Hip Pattern

0

50

100

150

200

250

1 11 21 31 41 51 61 71 81 91 101 111121131141151161171

Angl

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Figure 3.1(a): Out of Sync Hip Movement for the Subjects


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Knee Pattern

0

20

40

60

80

100

120140

160

180

200

1 11 21 31 41 51 61 71 81 91 101 111121131141151161171

Angl

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Torso Pattern

240

245

250

255

260

265

270275

280

285

290

1 11 21 31 41 51 61 71 81 91 101 111121131141151161171

Angl

Subject 1Subject 2

Subject 3

Subject 4

Subject 5

Figure 3.1(c): Out of Sync Torso Movement for the Subjects

Figure 3.1(b): Out of Sync Knee Movement for the Subjects


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Ankle Pattern

0

50

100

150

200

250

300

350

1 11 21 31 41 51 61 71 81 91 101 111121131141151161171

Angl

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

As a result of this out of sync data, the acquired data for each subject was synchronized

and trimmed down to 106 for each pattern. These modified angles, which represent the

crisp data to be fuzzified and stored in the knowledge base, are tabulated and attached in

appendix ii. Figures 3.2(a) through 3.2(d) show the graphical representation of the angles

(in sync) for the Hip, Knee, Torso and Ankle movement respectively.

Hip Pattern

0

50

100

150

200

250

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105

Angles

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Figure 3.2 (a) Hip Movement for the Subjects in Sync

Figure 3.1(d): Out of Sync Ankle Movement for the Subjects


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Knee Pattern

0

20

40

60

80

100

120

140

160

180

200

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105

Angle

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Figure 3.2 (b) Knee Movement for the Subjects in Sync

Torso Pattern

240

245

250

255

260

265

270

275

280

285

290

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105

Angle

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Figure 3.2 (c) Torso Movement for the Subjects in Sync


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Ankle Pattern

0

50

100

150

200

250

300

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105

Angle

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Figure 3.2 (d) Ankle Movement for the Subjects in Sync

The next section describes the fuzzification of the modified angles, and the type of

membership function used for the fuzzification.


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FUZZIFICATION

The Gaussian membership function was used to fuzzify all the crisp data obtained as

described in the previous section.

The Gaussian Membership Function

The Gaussian Membership function was chosen because of its popularity and simplicity.

The formula is given below

A(x) = -exp (x m)2/22

Where x represents the crisp data (angles),

represents the membership function of x,

m represents the mean of all the crisp data x in the distribution and

represents the variance of all the crisp data in the distribution.

The variance can be represented mathematically as

= ((x m)2/n)

Where n is the number of angles in the distribution,

x represents the crisp data (angles) and

m represents the mean of all the crisp data x in the distribution.

Figure 4.1(a) and (b) displays the general structure of the membership functions

associated with all the inputs and output variables for the entire fuzzy inference system.

A four input variable and a one output variable membership function is shown. The input

variables include HIP, KNEE, TORSO and ANKLE, while the output variable is the

SUBJECT.


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The obtained Gaussian membership function (the result of the fuzzification) for the crisp

data was tabulated and attached in appendix iii. The data for each subject was stored in

the knowledge base and used for the inference when a gait pattern or signature is to be

tested, classified and recognized. The actual Gaussian membership function obtained for

the crisp data for all the four patterns associated with the five subjects are shown in figure

4.2(a) to 4.2(d) below.

Hip Knee Torso AnkleA(X)

1

X

Figure 4.1(a): Input Variables Membership Function

Subject 1 Subject 2 Subject 3 Subject 4 Subject 5

A(X)1

X

Figure 4.1(b): Output Variable Membership Function


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Memebership Function for Hip Pattern

0

0.2

0.4

0.6

0.8

1

1.2

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

Membershipfu

n Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Membership Function for Knee Pattern

0

0.2

0.4

0.6

0.8

1

1.2

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

MemebershipFun

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Figure 4.2(a): Membership Function for the Hip Pattern of the Subjects

Figure 4.2(b): Membership Function for the Knee Pattern of the Subjects


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Membersip Function for Torso Pattern

0

0.2

0.4

0.6

0.8

1

1.2

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

MemebershipF

un

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Membership Function for Ankle Pattern

0

0.2

0.4

0.6

0.8

1

1.2

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

MemebershipFun

Subject 1

Subject 2

Subject 3

Subject 4

Subject 5

Figure 4.2(d): Membership Function for the Ankle Pattern of the Subjects

Figure 4.2(d): Membership Function for the Ankle Pattern of the Subjects


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RULE-BASED SYSTEM (IF THEN)

Fuzzy if-then rules play a critical role in pattern recognition. They associate a condition

described using linguistic variables and fuzzy sets to a conclusion even when the

condition is only partially satisfied [Yen99].

The Mamdani fuzzy Model [Matlab] was used as the fuzzy if-then rules in this project,

the rules are in the form

Ri: IF x1 is A1 and and xj is Aj THEN y is Bi

Where thexs are the inputs,A1 andBi the fuzzy sets andy is the output. The and in the

rule denotes the min operator. For the gait signature recognition, the inputs used to

construct the fuzzy if-then rules are the hip membership function, knee membership

function, torso membership function and the ankle membership function of the gait

pattern to be detected, while the output is the subject. The min operator was used in

all the rules.

The gait pattern under test is also fuzzified as described in the previous section and

compared with that already stored in the knowledge base, and an inference is made basedon the constructed fuzzy if-then rules. The fuzzy if-then rules were constructed on two

levels as will be described below. As an example of the first level of the fuzzy if-then

rules, we have the following rules

R1: IF hip membership function is 0.977136 and knee membership function is

0.776425 and torso membership function is 0.829157 and ankle membership

function is 0.979104 THEN the gait signature is for subject 5.





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If the conditions for the first level of the fuzzy if-then rules as shown in the example

above are fully satisfied, a membership function of 1 is obtained for subject 5, but when

the conditions are partially or not satisfied, a membership function less than 1 is returned

for subject 5. For the second level of the fuzzy if-then rules, with the above rules already

applied for all the membership functions, the following if-then rule makes the final

decision on the gait pattern under test

IF membership function for subject 5 in R1 is 1 and membership function for subject 5 in

R2 is 1 and and membership function for subject 5 in R106is 1 THEN the gait signature

is for subject 5.

If the conditions for this second level of the fuzzy if-then rules as shown in the example

above are fully satisfied, then the obtained membership function is 1 which indicates full

membership with subject 5. If the conditions are partially or not satisfied, a membership

function less than 1 is returned for subject 5, and this indicates a resemblance with the

gait signature of the subject in question (subject 5 in this case) with a membership

function as obtained by the system.

Using the above examples as a yard stick, it means that in the first level, a total of 106

fuzzy if-then rules were constructed by the system for each subject, and 1 fuzzy if-then

rule constructed in the second level for each subject. This gives a total of 535 fuzzy if-

then rules used in the system for all the five subjects.


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RESULTS (SIMULATION)

The result of the system is the output or response of the inference made from the

comparison of the membership functions of the gait signature to be detected with the

membership functions of the five gait signatures already stored in the knowledge base as

described in the previous section.

The result of the program written for the system displays the resemblance of the gait

signature under test with those of the five subjects already stored in the knowledge base.

The membership functions associated with each resemblance is also displayed. A

membership function of 1 indicates a total or full resemblance of the gait signature under

test with that of the corresponding subject stored in the knowledge base. A membership

function less than 1 indicates partial resemblance of the gait signature under test with that

of the corresponding subject stored in the knowledge base.


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CONCLUSION

The ability to classify and recognize a gait signature from a distance or from a video

sequence makes it a very attractive area of human identification. This can be used in a

number of different scenarios. One example would be to analyze the video stream from

surveillance systems and identify a target individual based on his or her gait signature.

Such systems have a large amount of potential application domains, such as airports,

banks and general high security areas.

It can be concluded from the results of the designed system, that fuzzy reasoning

provides an efficient way of pattern classification and recognition of non-classical sets.


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RECOMMENDATIONS FOR FUTURE ENHANCEMENTS

I believe a lot of improvements can be made to this system in the future in order to

achieve greater pattern recognition results. Some of the improvements can be made in the

following areas:

Digitizing all the cropped data points of the markers automatically by the use of

software using the centriod of each marker instead of guessing some of the points

with the position of the mouse.

Gait signature of individuals is susceptible to factors like the height and size of

the individual, the mood of the individual, the clothes worn by the individual and

a lot of other factors. Taking these factors into consideration when the data is

extracted or when the inference is made can improve the effectiveness of gait

recognition.

Making provision for the subjects to walk in other directions apart from the usual

direction perpendicular to the camera can make a lot of positive difference

because in a real life situation, the gait signature under test probably have walkedin many directions other than that perpendicular to the camera.

Other parameters apart from the angle of the body parts such as angular velocity

can be taken into consideration to increase the variation of the data to be classified

and recognized.

Classifying the acquired data into different known categories or classes (such as

males and females) using classifiers such as the back propagation neural net

before the gait pattern recognition can begin can help to narrow down the number

of gait signature to compare the test gait signature against.


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Having different cameras in different positions take the video coverage of the gait

of the subjects would give the advantage of being able to recognize a particular

gait signature from numerous angles, rather than just from one angle or position.

Lastly, using a larger number of subjects for the experiment would make a good

improvement for this project because a recognized gait signature would be more

accurate when ascertained from a larger data set.


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REFERENCES CITED

[Daw04] Dawson M. R., Gait Recognition Final Thesis Report, Department of

Computing, Imperial College of Science, Technology & Medicine, London, 2002.

[Fau94] Fausset, Laurene, Fundamentals of Neural Networks: Architectures,

Algorithms, and Applications, Prentice Hall, pp1-96,289-324, 1994.

[Matlab] Matlab Fuzzy Logic Toolbox.

[Nav95]Nava A. P., New Paradigms for Fuzzy Neural Networks Ph.D. Dissertation,

New Mexico State University, Las Cruces, New Mexico, 1995.

[Yen99] Yen John, Langari Reza, Fuzzy Logic Intelligence, Control, and Information,

Center forFuzzy Logic, Robotics, and Intelligent Systems, Texas A&M University.

Pearson Education Pte. Ltd.,Delhi, India, 1999.


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APPENDIX I: 2-Dimensional Angles Obtained for the Subjects

SUBJECT 1

HIPANGLE KNEE ANGLE TORSO ANGLE ANKLE ANGLE

202.958 160.094 270.015 252.978

202.044 159.304 269.806 253.733

201.096 158.721 269.673 254.593

200.122 158.334 269.616 255.548

199.140 158.115 269.636 256.591

198.178 158.029 269.729 257.704

197.263 158.042 269.893 258.848

196.416 158.130 270.123 259.969

195.643 158.286 270.411 261.013194.934 158.508 270.746 261.944

194.269 158.801 271.117 262.752

193.623 159.169 271.512 263.445

192.973 159.615 271.918 264.031

192.297 160.148 272.327 264.516

191.585 160.769 272.731 264.891

190.837 161.467 273.128 265.145

190.066 162.214 273.517 265.278

189.288 162.967 273.897 265.316

188.524 163.677 274.270 265.309

187.790 164.303 274.637 265.323

187.092 164.824 274.996 265.417186.424 165.249 275.349 265.624

185.771 165.606 275.692 265.945

185.111 165.929 276.023 266.344

184.430 166.240 276.340 266.773

183.717 166.542 276.638 267.187

182.973 166.822 276.914 267.559

182.199 167.058 277.165 267.889

181.403 167.221 277.390 268.208

180.591 167.287 277.585 268.549

179.770 167.245 277.749 268.915

178.945 167.093 277.878 269.278

178.124 166.821 277.971 269.592177.314 166.406 278.021 269.810

176.533 165.804 278.026 269.888

175.809 164.945 277.978 269.770

175.191 163.734 277.875 269.375

174.744 162.072 277.713 268.596

174.541 159.874 277.490 267.315

174.643 157.104 277.208 265.400

175.088 153.783 276.868 262.726


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175.876 149.984 276.473 259.233

176.981 145.801 276.026 255.004

178.359 141.331 275.531 250.317

179.955 136.675 274.993 245.660

181.712 131.944 274.416 241.641

183.572 127.277 273.807 238.809

185.478 122.836 273.172 237.516

187.386 118.785 272.520 237.811

189.266 115.266 271.863 239.440

191.108 112.384 271.213 241.962

192.916 110.203 270.587 244.912

194.701 108.751 270.000 247.921

196.467 108.025 269.467 250.769

198.208 108.018 269.001 253.365

199.903 108.722 268.612 255.667

201.517 110.141 268.302 257.646

203.000 112.280 268.068 259.294

204.287 115.151 267.903 260.600

205.301 118.782 267.794 261.548

205.966 123.223 267.725 262.102

206.217 128.525 267.680 262.196

206.026 134.687 267.643 261.757

205.412 141.583 267.599 260.769

204.454 148.899 267.537 259.341

203.27 156.135 267.451 257.725

202.005 162.691 267.336 256.233

200.804 168.015 267.195 255.091

199.784 171.723 267.032 254.344

199.017 173.662 266.856 253.879

198.528 173.908 266.678 253.533

198.304 172.741 266.513 253.197

198.297 170.570 266.373 252.864

198.426 167.853 266.271 252.632

198.583 165.011 266.216 252.659

198.647 162.387 266.215 253.082

198.515 160.217 266.275 253.958

198.132 158.615 266.398 255.239

197.500 157.577 266.586 256.800

196.666 157.030 266.838 258.484

195.702 156.870 267.153 260.133

194.680 156.984 267.524 261.633

193.661 157.270 267.944 262.926

192.683 157.640 268.397 263.998

191.756 158.043 268.868 264.869

190.862 158.465 269.339 265.577

189.964 158.920 269.793 266.165

189.028 159.434 270.218 266.681

188.029 160.019 270.608 267.175

186.960 160.674 270.960 267.688

185.832 161.376 271.276 268.238


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184.670 162.091 271.563 268.817

183.501 162.782 271.826 269.400

182.343 163.429 272.075 269.952

181.211 164.021 272.316 270.452

180.115 164.544 272.552 270.898

179.065 164.977 272.787 271.310

178.072 165.283 273.021 271.735

177.141 165.431 273.248 272.218

176.275 165.406 273.462 272.776

175.465 165.208 273.654 273.397

174.694 164.849 273.815 274.038

173.951 164.330 273.934 274.624

173.239 163.619 274.000 275.069

172.586 162.634 274.005 275.279

172.048 161.254 273.945 275.149

171.706 159.344 273.817 274.557

171.652 156.783 273.622 273.362

171.972 153.509 273.363 271.405

172.726 149.549 273.046 268.571

173.928 145.023 272.679 264.866

175.545 140.115 272.27 260.499

177.501 135.036 271.829 255.831

179.704 129.972 271.364 251.234

182.064 125.060 270.884 247.029

184.506 120.390 270.395 243.594

186.963 116.035 269.905 241.397

189.377 112.081 269.420 240.789

191.701 108.626 268.947 241.739

193.906 105.770 268.493 243.725

195.978 103.593 268.067 245.913

197.912 102.141 267.678 247.632

199.704 101.418 267.335 248.769

201.355 101.388 267.044 249.769

202.858 102.003 266.811 251.257

204.202 103.246 266.638 253.557

205.362 105.157 266.523 256.421

206.302 107.828 266.465 259.248

206.970 111.367 266.454 261.517

207.308 115.858 266.481 263.015

207.266 121.338 266.530 263.755

206.811 127.780 266.586 263.803

205.947 135.054 266.632 263.197

204.725 142.86 266.655 261.980

203.253 150.707 266.639 260.285

201.682 157.964 266.576 258.387

200.174 164.008 266.458 256.667

198.861 168.371 266.281 255.469

197.807 170.839 266.047 254.979

197.004 171.478 265.761 255.173

196.385 170.618 265.433 255.848


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195.847 168.793 265.080 256.714

195.288 166.594 264.723 257.519

194.633 164.490 264.386 258.154

193.850 162.730 264.096 258.673

192.939 161.385 263.882 259.208

191.913 160.455 263.765 259.864

190.792 159.914 263.763 260.684

189.614 159.713 263.885 261.665

188.429 159.769 264.134 262.788

187.293 159.992 264.502 264.021

186.254 160.308 264.979 265.300

185.342 160.665 265.546 266.533

184.569 161.030 266.181 267.620

183.920 161.390 266.861 268.494

183.363 161.750 267.560 269.150

182.847 162.135 268.256 269.628

182.322 162.576 268.929 269.984

181.750 163.091 269.568 270.279

181.112 163.678 270.166 270.567

180.408 164.313 270.721 270.884

179.651 164.954 271.234 271.252

178.859 165.560 271.707 271.68

178.045 166.103 272.143 272.165

177.225 166.559 272.547 272.707

176.415 166.902 272.919 273.306

175.631 167.107 273.262 273.958

174.885 167.151 273.575 274.648

174.184 167.019 273.857 275.354

173.528 166.708 274.106 276.036

172.916 166.233 274.323 276.648

172.343 165.605 274.505 277.156

SUBJECT 2


200.348 157.361 265.613 254.181

200.225 155.418 265.569 254.314

200.035 153.711 265.607 254.750

199.784 152.215 265.726 255.512

199.481 150.909 265.924 256.568

199.136 149.795 266.198 257.824

198.750 148.882 266.541 259.182

198.314 148.198 266.943 260.544

197.808 147.791 267.394 261.811

197.208 147.688 267.877 262.918

196.499 147.889 268.380 263.842

195.681 148.364 268.891 264.585


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27

194.766 149.068 269.400 265.164

193.773 149.946 269.901 265.613

192.721 150.945 270.390 265.975

191.621 152.030 270.868 266.280

190.476 153.190 271.335 266.528

189.286 154.426 271.793 266.718

188.055 155.725 272.244 266.864

186.787 157.055 272.688 267.009

185.491 158.374 273.126 267.208

184.174 159.655 273.555 267.477

182.846 160.878 273.972 267.809

181.521 162.020 274.371 268.184

180.214 163.045 274.744 268.591

178.946 163.897 275.084 269.033

177.739 164.502 275.380 269.533

176.613 164.791 275.623 270.106

175.589 164.707 275.802 270.741

174.696 164.192 275.910 271.397

173.975 163.176 275.940 271.997

173.489 161.570 275.889 272.413

173.318 159.271 275.761 272.484

173.551 156.191 275.561 272.025

174.274 152.285 275.302 270.868

175.536 147.592 274.999 268.885

177.338 142.237 274.671 266.020

179.622 136.425 274.336 262.316

182.280 130.420 274.011 257.962

185.179 124.505 273.708 253.439

188.191 118.942 273.436 249.59

191.225 113.931 273.203 247.366

194.232 109.611 273.012 247.217

197.198 106.078 272.862 248.682

200.116 103.392 272.751 250.708

202.967 101.577 272.674 252.412

205.716 100.628 272.622 253.565

208.307 100.521 272.585 254.387

210.671 101.238 272.550 255.103

212.733 102.763 272.505 255.753

214.413 105.083 272.436 256.302

215.642 108.179 272.334 256.742

216.363 112.047 272.192 257.059

216.538 116.723 272.008 257.195

216.152 122.266 271.785 257.084

215.218 128.712 271.533 256.696

213.791 136.017 271.262 256.078

211.976 143.956 270.983 255.410

209.933 152.054 270.704 254.939

207.870 159.634 270.431 254.824

206.005 165.951 270.166 255.053

204.521 170.348 269.909 255.507


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28

203.515 172.460 269.656 256.018

202.971 172.377 269.407 256.371

202.787 170.636 269.159 256.343

202.824 168.004 268.916 255.817

202.951 165.146 268.684 254.885

203.064 162.374 268.471 253.906

203.086 159.736 268.288 253.339

202.959 157.270 268.148 253.449

202.636 155.086 268.059 254.220

202.098 153.28 268.03 255.499

201.352 151.88 268.065 257.105

200.425 150.878 268.166 258.853

199.358 150.261 268.33 260.569

198.193 150.019 268.555 262.113

196.972 150.123 268.838 263.410

195.731 150.514 269.175 264.463

194.496 151.114 269.563 265.328

193.284 151.858 269.999 266.056

192.107 152.700 270.476 266.674

190.972 153.611 270.990 267.202

189.879 154.563 271.531 267.671

188.824 155.525 272.091 268.116

187.798 156.481 272.661 268.556

186.787 157.427 273.230 269.006

185.774 158.364 273.789 269.476

184.741 159.287 274.328 269.985

183.678 160.185 274.839 270.548

182.576 161.050 275.313 271.162

181.437 161.867 275.746 271.811

180.267 162.608 276.130 272.491

179.077 163.238 276.461 273.204

177.878 163.722 276.732 273.950

176.693 164.007 276.937 274.729

175.557 164.020 277.072 275.525

174.525 163.667 277.131 276.282

173.663 162.837 277.110 276.924

173.055 161.405 277.010 277.359

172.793 159.243 276.83 277.485

172.971 156.244 276.575 277.177

173.665 152.361 276.252 276.268

174.914 147.635 275.872 274.566

176.700 142.211 275.447 271.911

178.941 136.332 274.99 268.220

181.500 130.302 274.515 263.546

184.216 124.427 274.034 258.281

186.935 118.970 273.553 253.289

189.541 114.131 273.081 249.717

191.980 110.040 272.620 248.385

194.249 106.773 272.174 249.158

196.374 104.363 271.744 251.094


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29

198.381 102.804 271.332 253.145

200.280 102.067 270.941 254.683

202.062 102.102 270.572 255.628

203.701 102.869 270.229 256.216

205.165 104.347 269.913 256.690

206.409 106.536 269.630 257.160

207.390 109.434 269.382 257.620

208.064 113.029 269.176 258.033

208.398 117.329 269.016 258.325

208.371 122.390 268.908 258.376

207.988 128.278 268.857 258.052

207.285 134.957 268.868 257.346

206.318 142.255 268.943 256.422

205.151 149.923 269.084 255.578

203.833 157.732 269.292 255.155

202.395 165.564 269.567 255.447

SUBJECT 3


194.519 167.186 278.151 254.862

193.740 168.044 278.671 255.461

192.912 168.912 279.167 255.985

192.041 169.779 279.642 256.455

191.141 170.621 280.097 256.898

190.227 171.412 280.535 257.341

189.311 172.132 280.959 257.795

188.403 172.770 281.373 258.264

187.519 173.305 281.779 258.744

186.689 173.698 282.181 259.233

185.947 173.902 282.580 259.721

185.312 173.888 282.975 260.186

184.782 173.654 283.364 260.604

184.332 173.226 283.738 260.957

183.922 172.639 284.088 261.238

183.516 171.912 284.400 261.453

183.085 171.045 284.657 261.609

182.609 170.017 284.839 261.695

182.085 168.789 284.925 261.677

181.527 167.297 284.896 261.476

180.971 165.466 284.735 260.969

180.470 163.216 284.429 260.008

180.085 160.485 283.974 258.439

179.883 157.237 283.373 256.16

179.926 153.473 282.638 253.189


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30

180.265 149.245 281.791 249.711

180.914 144.668 280.861 246.085

181.846 139.923 279.882 242.784

183.001 135.224 278.889 240.272

184.308 130.789 277.917 238.840

185.713 126.802 276.994 238.538

187.191 123.395 276.140 239.215

188.735 120.652 275.368 240.592

190.340 118.621 274.676 242.341

191.995 117.318 274.057 244.183

193.668 116.738 273.497 245.963

195.309 116.867 272.978 247.633

196.851 117.694 272.485 249.174

198.232 119.210 272.010 250.527

199.418 121.389 271.556 251.595

200.409 124.188 271.133 252.291

201.219 127.561 270.759 252.562

201.861 131.48 270.449 252.407

202.332 135.941 270.215 251.885

202.617 140.947 270.061 251.080

202.710 146.467 269.984 250.077

202.622 152.405 269.974 248.973

202.386 158.579 270.014 247.898

202.054 164.717 270.088 247.008

201.688 170.482 270.173 246.436

201.347 175.535 270.249 246.229

201.076 179.574 270.298 246.333

200.908 182.373 270.305 246.612

200.844 183.835 270.261 246.911

200.846 184.023 270.161 247.113

200.846 183.155 270.009 247.177

200.772 181.542 269.814 247.122

200.593 179.497 269.592 247.011

200.332 177.226 269.365 246.951

200.067 174.783 269.159 247.088

199.869 172.173 269.001 247.553

199.723 169.517 268.920 248.381

199.521 167.095 268.939 249.479

199.144 165.196 269.078 250.697

198.555 163.943 269.348 251.903

197.824 163.252 269.750 253.018

197.082 162.908 270.279 254.017

196.441 162.715 270.924 254.897

195.939 162.596 271.668 255.644

195.537 162.597 272.489 256.242

195.163 162.801 273.362 256.690

194.754 163.253 274.260 257.011

194.279 163.927 275.154 257.245

193.735 164.746 276.021 257.432

193.136 165.621 276.846 257.609


31/72

31

192.493 166.487 277.618 257.802

191.809 167.301 278.330 258.039

191.088 168.036 278.980 258.351

190.336 168.665 279.569 258.762

189.568 169.168 280.102 259.281

188.799 169.529 280.584 259.895

188.043 169.743 281.024 260.578

187.317 169.805 281.430 261.310

186.634 169.709 281.812 262.08

186.001 169.462 282.174 262.886

185.414 169.080 282.524 263.729

184.864 168.597 282.864 264.601

184.337 168.042 283.192 265.475

183.815 167.440 283.506 266.310

183.273 166.822 283.796 267.056

182.681 166.215 284.053 267.666

182.012 165.627 284.262 268.093

181.250 165.041 284.409 268.276

180.398 164.418 284.478 268.143

179.473 163.703 284.455 267.601

178.516 162.827 284.329 266.557

177.601 161.69 284.092 264.935

176.844 160.149 283.743 262.687

176.379 158.048 283.286 259.814

176.326 155.265 282.73 256.395

176.751 151.767 282.089 252.656

177.644 147.639 281.377 248.994

178.920 143.070 280.611 245.918

180.448 138.322 279.810 243.887

182.095 133.67 278.986 243.152

183.773 129.343 278.151 243.714

185.451 125.493 277.315 245.361

187.121 122.228 276.483 247.732

188.761 119.645 275.660 250.415

190.326 117.836 274.848 253.066

191.768 116.866 274.050 255.468

193.044 116.768 273.271 257.510

194.134 117.541 272.520 259.159

195.042 119.146 271.811 260.435

195.798 121.514 271.163 261.365

196.440 124.573 270.602 261.945

196.994 128.271 270.149 262.140

197.470 132.572 269.822 261.902

197.862 137.447 269.630 261.22

198.149 142.868 269.569 260.137

198.307 148.779 269.624 258.769

198.331 155.052 269.772 257.273

198.248 161.457 269.985 255.823

198.107 167.692 270.234 254.572

197.964 173.424 270.489 253.612


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32

197.862 178.35 270.726 252.970

197.832 182.211 270.923 252.64

197.893 184.804 271.064 252.613

198.052 186.007 271.138 252.880

198.273 185.851 271.139 253.422

198.453 184.585 271.069 254.174

198.450 182.637 270.933 255.018

198.132 180.511 270.745 255.784

197.427 178.662 270.522 256.278

196.357 177.348 270.286 256.356

195.053 176.530 270.061 256.04

193.735 175.878 269.875 255.558

192.619 174.978 269.750 255.247

191.792 173.629 269.706 255.365

191.174 171.963 269.756 255.977

190.591 170.329 269.909 256.969

189.898 169.064 270.168 258.129

189.058 168.327 270.535 259.256

188.138 168.082 271.009 260.221

187.240 168.202 271.59 260.969

186.453 168.556 272.275 261.494

185.833 169.029 273.055 261.831

185.393 169.541 273.915 262.039

185.112 170.043 274.830 262.179

184.936 170.527 275.774 262.298

184.798 171.009 276.719 262.430

184.629 171.523 277.645 262.597

184.371 172.104 278.535 262.808

183.996 172.765 279.378 263.066

183.517 173.460 280.170 263.383

182.981 174.100 280.908 263.787

182.445 174.591 281.594 264.301

181.941 174.886 282.230 264.929

181.487 174.970 282.819 265.654

181.093 174.842 283.365 266.456

180.762 174.511 283.872 267.306

180.496 173.981 284.344 268.181

180.30 173.249 284.786 269.059

180.164 172.337 285.200 269.905

180.065 171.298 285.591 270.674

179.976 170.195 285.958 271.323

179.879 169.079 286.303 271.816

179.769 167.973 286.627 272.132

179.648 166.882 286.928 272.255

179.522 165.799 287.208 272.175


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33

SUBJECT 4


196.965 171.428 273.638 249.514

196.622 171.169 274.345 250.635

196.231 170.951 275.028 251.685

195.804 170.756 275.681 252.678

195.355 170.547 276.288 253.619

194.895 170.272 276.821 254.525

194.418 169.893 277.254 255.438

193.910 169.413 277.584 256.402

193.366 168.884 277.856 257.433

192.798 168.370 278.140 258.542

192.239 167.908 278.501 259.709

191.733 167.490 278.968 260.905

191.288 167.095 279.516 262.092

190.845 166.726 280.070 263.245

190.295 166.407 280.543 264.329

189.551 166.161 280.886 265.327

188.582 165.988 281.101 266.263

187.411 165.857 281.216 267.188

186.088 165.728 281.260 268.116

184.665 165.554 281.245 269.009

183.185 165.271 281.167 269.809

181.689 164.782 281.018 270.493

180.228 163.969 280.79 271.072

178.876 162.702 280.482 271.533

177.735 160.860 280.104 271.766

176.919 158.340 279.670 271.514

176.540 155.073 279.198 270.390

176.681 151.047 278.702 267.953

177.382 146.328 278.197 263.860

178.631 141.062 277.694 258.137

180.371 135.454 277.199 251.358

182.513 129.734 276.717 244.523

184.960 124.134 276.250 238.740

187.618 118.878 275.801 234.891

190.398 114.185 275.372 233.411

193.212 110.265 274.963 234.261

195.974 107.299 274.576 236.952

198.605 105.415 274.209 240.602

201.045 104.669 273.862 244.210

203.269 105.027 273.535 247.105

205.294 106.372 273.227 249.165

207.160 108.548 272.943 250.630

208.883 111.427 272.691 251.787

210.417 114.971 272.477 252.769

211.658 119.235 272.308 253.524

212.475 124.331 272.184 253.866


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34

212.774 130.353 272.098 253.624

212.534 137.295 272.041 252.835

211.814 144.987 272.000 251.858

210.734 153.018 271.964 251.367

209.442 160.748 271.920 252.089

208.076 167.456 271.861 254.251

206.748 172.564 271.783 257.129

205.522 175.805 271.685 259.264

204.418 177.281 271.568 259.319

203.413 177.408 271.434 256.896

202.462 176.753 271.286 252.736

201.513 175.777 271.127 248.291

200.522 174.703 270.961 244.915

199.45 173.602 270.795 243.294

198.263 172.513 270.638 243.446

196.941 171.507 270.504 244.913

195.49 170.688 270.409 247.026

193.948 170.141 270.372 249.187

192.379 169.891 270.414 251.067

190.852 169.897 270.549 252.613

189.430 170.077 270.79 253.909

188.161 170.341 271.139 255.058

187.080 170.602 271.596 256.127

186.210 170.784 272.155 257.156

185.562 170.833 272.807 258.162

185.130 170.726 273.541 259.159

184.889 170.467 274.340 260.156

184.789 170.091 275.183 261.162

184.761 169.655 276.038 262.172

184.727 169.211 276.872 263.191

184.612 168.801 277.656 264.217

184.356 168.455 278.364 265.232

183.920 168.187 278.980 266.216

183.285 167.994 279.495 267.151

182.447 167.862 279.901 268.028

181.415 167.756 280.190 268.858

180.204 167.620 280.358 269.663

178.840 167.397 280.401 270.456

177.363 167.026 280.319 271.216

175.836 166.433 280.117 271.898

174.340 165.513 279.804 272.448

172.969 164.146 279.390 272.762

171.839 162.214 278.893 272.649

171.081 159.609 278.338 271.814

170.823 156.259 277.755 269.867

171.155 152.165 277.172 266.370

172.114 147.411 276.609 261.040

173.678 142.142 276.086 254.089

175.788 136.545 275.615 246.334

178.362 130.832 275.206 238.929


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35

181.314 125.220 274.864 232.968

184.558 119.923 274.595 229.228

188.006 115.139 274.398 228.094

191.572 111.050 274.269 229.532

195.165 107.812 274.203 233.086

198.689 105.542 274.188 237.872

202.047 104.316 274.211 242.758

205.144 104.168 274.253 246.812

207.892 105.090 274.291 249.659

210.223 107.024 274.299 251.445

212.096 109.868 274.244 252.544

213.479 113.512 274.097 253.274

214.335 117.895 273.837 253.752

214.615 123.029 273.459 253.945

214.262 128.981 272.971 253.816

213.222 135.813 272.397 253.419

211.501 143.449 271.758 253.041

209.213 151.54 271.079 253.237

206.567 159.464 270.384 254.610

203.803 166.474 269.698 257.32

201.127 171.928 269.046 260.649

198.676 175.497 268.449 263.214

196.523 177.259 267.922 263.78

194.692 177.644 267.471 261.936

193.181 177.219 267.098 258.228

191.965 176.403 266.804 253.892

191.003 175.347 266.589 250.285

190.233 174.065 266.457 248.269

189.574 172.591 266.416 248.046

188.947 171.040 266.472 249.270

188.303 169.584 266.636 251.311

187.621 168.392 266.913 253.552

186.911 167.557 267.304 255.601

186.193 167.088 267.800 257.324

185.486 166.933 268.382 258.748

184.805 167.000 269.027 259.967

184.158 167.183 269.710 261.083

183.546 167.393 270.405 262.158

182.953 167.560 271.092 263.229

182.357 167.646 271.751 264.311

181.739 167.644 272.368 265.382

181.082 167.578 272.935 266.39

180.375 167.491 273.450 267.285

179.604 167.424 273.914 268.059

178.754 167.396 274.326 268.768

177.807 167.412 274.69 269.503

176.754 167.465 275.009 270.320

175.603 167.527 275.286 271.237

174.377 167.558 275.523 272.234

173.115 167.501 275.723 273.275


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36

171.867 167.304 275.884 274.290

170.675 166.934 276.004 275.174

169.569 166.378 276.080 275.805

168.566 165.628 276.107 276.136

167.676 164.671 276.085 276.182

166.900 163.495 276.012 275.969

SUBJECT 5


192.122 112.787 265.667 238.458

193.810 113.478 265.146 241.162

195.430 114.821 264.710 243.617

196.948 116.833 264.352 245.825

198.313 119.514 264.056 247.742199.471 122.840 263.807 249.277

200.364 126.777 263.592 250.291

200.943 131.281 263.400 250.655

201.169 136.303 263.220 250.305

201.025 141.778 263.047 249.302

200.523 147.605 262.878 247.882

199.703 153.623 262.710 246.420

198.639 159.595 262.541 245.349

197.425 165.203 262.371 245.072

196.165 170.094 262.197 245.813

194.951 173.945 262.015 247.492

193.841 176.559 261.822 249.699

192.845 177.919 261.611 251.838

191.929 178.194 261.375 253.366

191.025 177.703 261.112 253.967

190.060 176.834 260.827 253.593

188.981 175.921 260.532 252.447

187.780 175.141 260.245 250.885

186.497 174.501 259.992 249.297

185.205 173.913 259.800 248.036

183.973 173.293 259.695 247.357

182.840 172.615 259.697 247.346

181.807 171.935 259.819 247.911

180.836 171.363 260.062 248.840

179.873 171.028 260.424 249.898

178.875 171.027 260.893 250.934

177.831 171.388 261.461 251.888

176.766 172.072 262.117 252.729

175.734 172.978 262.856 253.458

174.807 173.979 263.668 254.088

174.041 174.943 264.544 254.648

173.457 175.774 265.462 255.172


37/72

37

173.030 176.418 266.392 255.682

172.700 176.870 267.302 256.175

172.402 177.159 268.170 256.631

172.082 177.335 268.981 257.028

171.706 177.455 269.738 257.375

171.258 177.565 270.446 257.705

170.734 177.696 271.116 258.047

170.134 177.861 271.755 258.413

169.458 178.055 272.364 258.799

168.706 178.267 272.945 259.197

167.882 178.484 273.49 259.583

166.989 178.688 273.992 259.92

166.036 178.845 274.438 260.170

165.039 178.902 274.816 260.300

164.020 178.791 275.114 260.270

163.007 178.444 275.319 260.065

162.028 177.801 275.423 259.682

161.115 176.815 275.422 259.096

160.308 175.442 275.313 258.238

159.662 173.635 275.098 256.972

159.247 171.338 274.784 255.125

159.156 168.486 274.384 252.484

159.484 165.016 273.916 248.878

160.306 160.902 273.398 244.268

161.654 156.181 272.849 238.88

163.506 150.968 272.285 233.374

165.794 145.444 271.722 228.835

168.44 139.812 271.178 226.325

171.381 134.266 270.671 226.329

174.584 128.975 270.223 228.499

178.028 124.084 269.856 231.916

181.684 119.717 269.584 235.619

185.494 115.989 269.416 239.053

189.353 113.021 269.338 242.160

193.120 110.935 269.323 245.095

196.631 109.849 269.326 247.926

199.710 109.856 269.287 250.561

202.192 111.012 269.147 252.849

203.944 113.320 268.853 254.680

204.894 116.719 268.377 256.011

205.060 121.086 267.724 256.833

204.549 126.248 266.936 257.113

203.524 132.022 266.079 256.802

202.152 138.252 265.22 255.866

200.568 144.809 264.414 254.344

198.879 151.544 263.694 252.442

197.167 158.239 263.069 250.581

195.500 164.572 262.531 249.309

193.93 170.161 262.056 249.083

192.481 174.667 261.617 250.029


38/72


39/72

39

177.292 122.568 267.411 232.397


40/72

40

APPENDIX II: Modified 2-Dimensional Angles of Subjects

SUBJECT 1


190.066 164.303 273.517 265.316

189.288 164.824 273.897 265.309

188.524 165.249 274.27 265.323

187.79 165.606 274.637 265.417

187.092 165.929 274.996 265.624

186.424 166.24 275.349 265.945

185.771 166.542 275.692 266.344

185.111 166.822 276.023 266.773

184.43 167.058 276.34 267.187183.717 167.221 276.638 267.559

182.973 167.287 276.914 267.889

182.199 167.245 277.165 268.208

181.403 167.093 277.39 268.549

180.591 166.821 277.585 268.915

179.77 166.406 277.749 269.278

178.945 165.804 277.878 269.592

178.124 164.945 277.971 269.81

177.314 163.734 278.021 269.888

176.533 162.072 278.026 269.77

175.809 159.874 277.978 269.375

175.191 157.104 277.875 268.596174.744 153.783 277.713 267.315

174.541 149.984 277.49 265.4

174.643 145.801 277.208 262.726

175.088 141.331 276.868 259.233

175.876 136.675 276.473 255.004

176.981 131.944 276.026 250.317

178.359 127.277 275.531 245.66

179.955 122.836 274.993 241.641

181.712 118.785 274.416 238.809

183.572 115.266 273.807 237.516

185.478 112.384 273.172 237.811

187.386 110.203 272.52 239.44189.266 108.751 271.863 241.962

191.108 108.025 271.213 244.912

192.916 108.018 270.587 247.921

194.701 108.722 270 250.769

196.467 110.141 269.467 253.365

198.208 112.28 269.001 255.667

199.903 115.151 268.612 257.646

201.517 118.782 268.302 259.294


41/72

41

203 123.223 268.068 260.6

204.287 128.525 267.903 261.548

205.301 134.687 267.794 262.102

205.966 141.583 267.725 262.196

206.217 148.899 267.68 261.757

206.026 156.135 267.643 260.769

205.412 162.691 267.599 259.341

204.454 168.015 267.537 257.725

203.27 171.723 267.451 256.233

202.005 173.662 267.336 255.091

200.804 173.908 267.195 254.344

199.784 172.741 267.032 253.879

199.017 170.57 266.856 253.533

198.528 167.853 266.678 253.197

198.304 165.011 266.513 252.864

198.297 162.387 266.373 252.632

198.426 160.217 266.271 252.659

198.583 158.615 266.216 253.082

198.647 157.577 266.215 253.958

198.515 157.03 266.275 255.239

198.132 156.87 266.398 256.8

197.5 156.984 266.586 258.484

196.666 157.27 266.838 260.133

195.702 157.64 267.153 261.633

194.68 158.043 267.524 262.926

193.661 158.465 267.944 263.998

192.683 158.92 268.397 264.869

191.756 159.434 268.868 265.577

190.862 160.019 269.339 266.165

189.964 160.674 269.793 266.681

189.028 161.376 270.218 267.175

188.029 162.091 270.608 267.688

186.96 162.782 270.96 268.238

185.832 163.429 271.276 268.817

184.67 164.021 271.563 269.4

183.501 164.544 271.826 269.952

182.343 164.977 272.075 270.452

181.211 165.283 272.316 270.898

180.115 165.431 272.552 271.31

179.065 165.406 272.787 271.735

178.072 165.208 273.021 272.218

177.141 164.849 273.248 272.776

176.275 164.33 273.462 273.397

175.465 163.619 273.654 274.038

174.694 162.634 273.815 274.624

173.951 161.254 273.934 275.069

173.239 159.344 274 275.279

172.586 156.783 274.005 275.149

172.048 153.509 273.945 274.557

171.706 149.549 273.817 273.362


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42

171.652 145.023 273.622 271.405

171.972 140.115 273.363 268.571

172.726 135.036 273.046 264.866

173.928 129.972 272.679 260.499

175.545 125.06 272.27 255.831

177.501 120.39 271.829 251.234

179.704 116.035 271.364 247.029

182.064 112.081 270.884 243.594

184.506 108.626 270.395 241.397

186.963 105.77 269.905 240.789

189.377 103.593 269.42 241.739

191.701 102.141 268.947 243.725

193.906 101.418 268.493 245.913

195.978 101.388 268.067 247.632

197.912 102.003 267.678 248.769

SUBJECT 2


197.808 149.068 269.4 265.164

197.208 149.946 269.901 265.613

196.499 150.945 270.39 265.975

195.681 152.03 270.868 266.28

194.766 153.19 271.335 266.528

193.773 154.426 271.793 266.718

192.721 155.725 272.244 266.864

191.621 157.055 272.688 267.009

190.476 158.374 273.126 267.208

189.286 159.655 273.555 267.477

188.055 160.878 273.972 267.809

186.787 162.02 274.371 268.184

185.491 163.045 274.744 268.591

184.174 163.897 275.084 269.033

182.846 164.502 275.38 269.533

181.521 164.791 275.623 270.106

180.214 164.707 275.802 270.741

178.946 164.192 275.91 271.397

177.739 163.176 275.94 271.997

176.613 161.57 275.889 272.413

175.589 159.271 275.761 272.484

174.696 156.191 275.561 272.025

173.975 152.285 275.302 270.868

173.489 147.592 274.999 268.885

173.318 142.237 274.671 266.02

173.551 136.425 274.336 262.316

174.274 130.42 274.011 257.962

175.536 124.505 273.708 253.439

177.338 118.942 273.436 249.59

179.622 113.931 273.203 247.366

182.28 109.611 273.012 247.217


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43

185.179 106.078 272.862 248.682

188.191 103.392 272.751 250.708

191.225 101.577 272.674 252.412

194.232 100.628 272.622 253.565

197.198 100.521 272.585 254.387

200.116 101.238 272.55 255.103

202.967 102.763 272.505 255.753

205.716 105.083 272.436 256.302

208.307 108.179 272.334 256.742

210.671 112.047 272.192 257.059

212.733 116.723 272.008 257.195

214.413 122.266 271.785 257.084

215.642 128.712 271.533 256.696

216.363 136.017 271.262 256.078

216.538 143.956 270.983 255.41

216.152 152.054 270.704 254.939

215.218 159.634 270.431 254.824

213.791 165.951 270.166 255.053

211.976 170.348 269.909 255.507

209.933 172.46 269.656 256.018

207.87 172.377 269.407 256.371

206.005 170.636 269.159 256.343

204.521 168.004 268.916 255.817

203.515 165.146 268.684 254.885

202.971 162.374 268.471 253.906

202.787 159.736 268.288 253.339

202.824 157.27 268.148 253.449

202.951 155.086 268.059 254.22

203.064 153.28 268.03 255.499

203.086 151.88 268.065 257.105

202.959 150.878 268.166 258.853

202.636 150.261 268.33 260.569

202.098 150.019 268.555 262.113

201.352 150.123 268.838 263.41

200.425 150.514 269.175 264.463

199.358 151.114 269.563 265.328

198.193 151.858 269.999 266.056

196.972 152.7 270.476 266.674

195.731 153.611 270.99 267.202

194.496 154.563 271.531 267.671

193.284 155.525 272.091 268.116

192.107 156.481 272.661 268.556

190.972 157.427 273.23 269.006

189.879 158.364 273.789 269.476

188.824 159.287 274.328 269.985

187.798 160.185 274.839 270.548

186.787 161.05 275.313 271.162

185.774 161.867 275.746 271.811

184.741 162.608 276.13 272.491

183.678 163.238 276.461 273.204


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44

182.576 163.722 276.732 273.95

181.437 164.007 276.937 274.729

180.267 164.02 277.072 275.525

179.077 163.667 277.131 276.282

177.878 162.837 277.11 276.924

176.693 161.405 277.01 277.359

175.557 159.243 276.83 277.485

174.525 156.244 276.575 277.177

173.663 152.361 276.252 276.268

173.055 147.635 275.872 274.566

172.793 142.211 275.447 271.911

172.971 136.332 274.99 268.22

173.665 130.302 274.515 263.546

174.914 124.427 274.034 258.281

176.7 118.97 273.553 253.289

178.941 114.131 273.081 249.717

181.5 110.04 272.62 248.385

184.216 106.773 272.174 249.158

186.935 104.363 271.744 251.094

189.541 102.804 271.332 253.145

191.98 102.067 270.941 254.683

194.249 102.102 270.572 255.628

196.374 102.869 270.229 256.216

198.381 104.347 269.913 256.69

200.28 106.536 269.63 257.16

SUBJECT 3


194.519 167.186 278.151 254.862

193.74 168.044 278.671 255.461

192.912 168.912 279.167 255.985

192.041 169.779 279.642 256.455

191.141 170.621 280.097 256.898

190.227 171.412 280.535 257.341

189.311 172.132 280.959 257.795

188.403 172.77 281.373 258.264

187.519 173.305 281.779 258.744

186.689 173.698 282.181 259.233

185.947 173.902 282.58 259.721

185.312 173.888 282.975 260.186

184.782 173.654 283.364 260.604

184.332 173.226 283.738 260.957

183.922 172.639 284.088 261.238

183.516 171.912 284.4 261.453


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45

183.085 171.045 284.657 261.609

182.609 170.017 284.839 261.695

182.085 168.789 284.925 261.677

181.527 167.297 284.896 261.476

180.971 165.466 284.735 260.969

180.47 163.216 284.429 260.008

180.085 160.485 283.974 258.439

179.883 157.237 283.373 256.16

179.926 153.473 282.638 253.189

180.265 149.245 281.791 249.711

180.914 144.668 280.861 246.085

181.846 139.923 279.882 242.784

183.001 135.224 278.889 240.272

184.308 130.789 277.917 238.84

185.713 126.802 276.994 238.538

187.191 123.395 276.14 239.215

188.735 120.652 275.368 240.592

190.34 118.621 274.676 242.341

191.995 117.318 274.057 244.183

193.668 116.738 273.497 245.963

195.309 116.867 272.978 247.633

196.851 117.694 272.485 249.174

198.232 119.21 272.01 250.527

199.418 121.389 271.556 251.595

200.409 124.188 271.133 252.291

201.219 127.561 270.759 252.562

201.861 131.48 270.449 252.407

202.332 135.941 270.215 251.885

202.617 140.947 270.061 251.08

202.71 146.467 269.984 250.077

202.622 152.405 269.974 248.973

202.386 158.579 270.014 247.898

202.054 164.717 270.088 247.008

201.688 170.482 270.173 246.436

201.347 175.535 270.249 246.229

201.076 179.574 270.298 246.333

200.908 182.373 270.305 246.612

200.844 183.835 270.261 246.911

200.846 184.023 270.161 247.113

200.846 183.155 270.009 247.177

200.772 181.542 269.814 247.122

200.593 179.497 269.592 247.011

200.332 177.226 269.365 246.951

200.067 174.783 269.159 247.088

199.869 172.173 269.001 247.553

199.723 169.517 268.92 248.381

199.521 167.095 268.939 249.479

199.144 165.196 269.078 250.697

198.555 163.943 269.348 251.903

197.824 163.252 269.75 253.018


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46

197.082 162.908 270.279 254.017

196.441 162.715 270.924 254.897

195.939 162.596 271.668 255.644

195.537 162.597 272.489 256.242

195.163 162.801 273.362 256.69

194.754 163.253 274.26 257.011

194.279 163.927 275.154 257.245

193.735 164.746 276.021 257.432

193.136 165.621 276.846 257.609

192.493 166.487 277.618 257.802

191.809 167.301 278.33 258.039

191.088 168.036 278.98 258.351

190.336 168.665 279.569 258.762

189.568 169.168 280.102 259.281

188.799 169.529 280.584 259.895

188.043 169.743 281.024 260.578

187.317 169.805 281.43 261.31

186.634 169.709 281.812 262.08

186.001 169.462 282.174 262.886

185.414 169.08 282.524 263.729

184.864 168.597 282.864 264.601

184.337 168.042 283.192 265.475

183.815 167.44 283.506 266.31

183.273 166.822 283.796 267.056

182.681 166.215 284.053 267.666

182.012 165.627 284.262 268.093

181.25 165.041 284.409 268.276

180.398 164.418 284.478 268.143

179.473 163.703 284.455 267.601

178.516 162.827 284.329 266.557

177.601 161.69 284.092 264.935

176.844 160.149 283.743 262.687

176.379 158.048 283.286 259.814

176.326 155.265 282.73 256.395

176.751 151.767 282.089 252.656

177.644 147.639 281.377 248.994

178.92 143.07 280.611 245.918

180.448 138.322 279.81 243.887

182.095 133.67 278.986 243.152

183.773 129.343 278.151 243.714

SUBJECT 4


195.804 170.756 273.638 253.619


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47

195.355 170.547 274.345 254.525

194.895 170.272 275.028 255.438

194.418 169.893 275.681 256.402

193.91 169.413 276.288 257.433

193.366 168.884 276.821 258.542

192.798 168.37 277.254 259.709

192.239 167.908 277.584 260.905

191.733 167.49 277.856 262.092

191.288 167.095 278.14 263.245

190.845 166.726 278.501 264.329

190.295 166.407 278.968 265.327

189.551 166.161 279.516 266.263

188.582 165.988 280.07 267.188

187.411 165.857 280.543 268.116

186.088 165.728 280.886 269.009

184.665 165.554 281.101 269.809

183.185 165.271 281.216 270.493

181.689 164.782 281.26 271.072

180.228 163.969 281.245 271.533

178.876 162.702 281.167 271.766

177.735 160.86 281.018 271.514

176.919 158.34 280.79 270.39

176.54 155.073 280.482 267.953

176.681 151.047 280.104 263.86

177.382 146.328 279.67 258.137

178.631 141.062 279.198 251.358

180.371 135.454 278.702 244.523

182.513 129.734 278.197 238.74

184.96 124.134 277.694 234.891

187.618 118.878 277.199 233.411

190.398 114.185 276.717 234.261

193.212 110.265 276.25 236.952

195.974 107.299 275.801 240.602

198.605 105.415 275.372 244.21

201.045 104.669 274.963 247.105

203.269 105.027 274.576 249.165

205.294 106.372 274.209 250.63

207.16 108.548 273.862 251.787

208.883 111.427 273.535 252.769

210.417 114.971 273.227 253.524

211.658 119.235 272.943 253.866

212.475 124.331 272.691 253.624

212.774 130.353 272.477 252.835

212.534 137.295 272.308 251.858

211.814 144.987 272.184 251.367

210.734 153.018 272.098 252.089

209.442 160.748 272.041 254.251

208.076 167.456 272 257.129

206.748 172.564 271.964 259.264

205.522 175.805 271.92 259.319


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48

204.418 177.281 271.861 256.896

203.413 177.408 271.783 252.736

202.462 176.753 271.685 248.291

201.513 175.777 271.568 244.915

200.522 174.703 271.434 243.294

199.45 173.602 271.286 243.446

198.263 172.513 271.127 244.913

196.941 171.507 270.961 247.026

195.49 170.688 270.795 249.187

193.948 170.141 270.638 251.067

192.379 169.891 270.504 252.613

190.852 169.897 270.409 253.909

189.43 170.077 270.372 255.058

188.161 170.341 270.414 256.127

187.08 170.602 270.549 257.156

186.21 170.784 270.79 258.162

185.562 170.833 271.139 259.159

185.13 170.726 271.596 260.156

184.889 170.467 272.155 261.162

184.789 170.091 272.807 262.172

184.761 169.655 273.541 263.191

184.727 169.211 274.34 264.217

184.612 168.801 275.183 265.232

184.356 168.455 276.038 266.216

183.92 168.187 276.872 267.151

183.285 167.994 277.656 268.028

182.447 167.862 278.364 268.858

181.415 167.756 278.98 269.663

180.204 167.62 279.495 270.456

178.84 167.397 279.901 271.216

177.363 167.026 280.19 271.898

175.836 166.433 280.358 272.448

174.34 165.513 280.401 272.762

172.969 164.146 280.319 272.649

171.839 162.214 280.117 271.814

171.081 159.609 279.804 269.867

170.823 156.259 279.39 266.37

171.155 152.165 278.893 261.04

172.114 147.411 278.338 254.089

173.678 142.142 277.755 246.334

175.788 136.545 277.172 238.929

178.362 130.832 276.609 232.968

181.314 125.22 276.086 229.228

184.558 119.923 275.615 228.094

188.006 115.139 275.206 229.532

191.572 111.05 274.864 233.086

195.165 107.812 274.595 237.872

198.689 105.542 274.398 242.758

202.047 104.316 274.269 246.812

205.144 104.168 274.203 249.659


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49

207.892 105.09 274.188 251.445

210.223 107.024 274.211 252.544

212.096 109.868 274.253 253.274

213.479 113.512 274.291 253.752

214.335 117.895 274.299 253.945

SUBJECT 5


176.766 176.418 264.544 254.088

175.734 176.87 265.462 254.648

174.807 177.159 266.392 255.172

174.041 177.335 267.302 255.682

173.457 177.455 268.17 256.175

173.03 177.565 268.981 256.631

172.7 177.696 269.738 257.028

172.402 177.861 270.446 257.375

172.082 178.055 271.116 257.705

171.706 178.267 271.755 258.047

171.258 178.484 272.364 258.413

170.734 178.688 272.945 258.799

170.134 178.845 273.49 259.197

169.458 178.902 273.992 259.583

168.706 178.791 274.438 259.92

167.882 178.444 274.816 260.17

166.989 177.801 275.114 260.3

166.036 176.815 275.319 260.27

165.039 175.442 275.423 260.065

164.02 173.635 275.422 259.682

163.007 171.338 275.313 259.096

162.028 168.486 275.098 258.238

161.115 165.016 274.784 256.972

160.308 160.902 274.384 255.125

159.662 156.181 273.916 252.484

159.247 150.968 273.398 248.878

159.156 145.444 272.849 244.268

159.484 139.812 272.285 238.88

160.306 134.266 271.722 233.374

161.654 128.975 271.178 228.835

163.506 124.084 270.671 226.325

165.794 119.717 270.223 226.329

168.44 115.989 269.856 228.499

171.381 113.021 269.584 231.916

174.584 110.935 269.416 235.619

178.028 109.849 269.338 239.053


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50

181.684 109.856 269.323 242.16

185.494 111.012 269.326 245.095

189.353 113.32 269.287 247.926

193.12 116.719 269.147 250.561

196.631 121.086 268.853 252.849

199.71 126.248 268.377 254.68

202.192 132.022 267.724 256.011

203.944 138.252 266.936 256.833

204.894 144.809 266.079 257.113

205.06 151.544 265.22 256.802

204.549 158.239 264.414 255.866

203.524 164.572 263.694 254.344

202.152 170.161 263.069 252.442

200.568 174.667 262.531 250.581

198.879 177.877 262.056 249.309

197.167 179.753 261.617 249.083

195.5 180.432 261.183 250.029

193.93 180.189 260.733 251.816

192.481 179.366 260.25 253.76

191.148 178.28 259.729 255.128

189.891 177.129 259.179 255.44

188.65 175.961 258.618 254.638

187.364 174.757 258.074 253.075

185.988 173.515 257.582 251.313

184.515 172.299 257.179 249.871

182.979 171.23 256.903 249.089

181.446 170.432 256.786 249.101

179.986 169.999 256.854 249.855

178.649 169.969 257.123 251.152

177.453 170.325 257.596 252.717

176.387 171.002 258.264 254.264

175.429 171.908 259.102 255.575

174.559 172.947 260.07 256.536

173.764 174.028 261.115 257.152

173.034 175.075 262.173 257.513

172.356 176.018 263.187 257.749

171.703 176.805 264.111 257.988

171.037 177.419 264.932 258.331

170.312 177.874 265.667 258.835

169.499 178.205 266.351 259.493

168.611 178.457 267.018 260.237

167.702 178.67 267.693 260.982

166.832 178.873 268.387 261.663

166.039 179.073 269.098 262.256

165.328 179.259 269.81 262.765

164.679 179.404 270.503 263.221

164.054 179.457 271.158 263.656

163.413 179.346 271.756 264.075

162.731 178.993 272.28 264.456

161.992 178.323 272.715 264.764


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51

161.197 177.266 273.043 264.959

160.36 175.76 273.248 264.985

159.503 173.762 273.313 264.771

158.651 171.248 273.225 264.239

157.831 168.201 272.979 263.3

157.072 164.624 272.581 261.853

156.409 160.547 272.053 259.783

155.886 156.046 271.428 256.952

155.562 151.237 270.75 253.205

155.51 146.26 270.066 248.433

155.809 141.248 269.417 242.734

156.527 136.311 268.837 236.663

157.704 131.527 268.348 231.231

159.343 126.939 267.96 227.467

161.418 122.568 267.676 225.891

163.892 122.034 267.494 226.415

166.731 121.476 267.411 228.673

169.912 120.663 267.395 232.397

173.431 120.057 267.399 232.423

177.292 119.321 267.421 232.665


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52

APPENDIX III: Fuzzified Data for the angles of the Body Parts of the

Subjects

SUBJECT 1

HIP KNEE TORSO ANKLE

171.652 0.300197 101.388 0.117584 266.215 0.329034 237.516 0.077974

171.706 0.302691 101.418 0.117911 266.216 0.329167 237.811 0.08324

171.972 0.315151 102.003 0.124421 266.271 0.336456 238.809 0.103189

172.048 0.318764 102.141 0.125996 266.275 0.336989 239.44 0.117612

172.586 0.34499 103.593 0.143492 266.373 0.350203 240.789 0.153554

172.726 0.351998 105.770 0.173007 266.398 0.353620 241.397 0.172164

173.239 0.378297 108.018 0.207794 266.513 0.369543 241.641 0.180069

173.928 0.415049 108.025 0.20791 266.586 0.379833 241.739 0.183315

173.951 0.416303 108.626 0.217972 266.678 0.392997 241.962 0.190856

174.541 0.448982 108.722 0.219609 266.838 0.416379 243.594 0.252589

174.643 0.45473 108.751 0.220105 266.856 0.419043 243.725 0.258045

174.694 0.457613 110.141 0.244766 267.032 0.445499 244.912 0.310799

174.744 0.460447 110.203 0.245906 267.153 0.464046 245.66 0.346995

175.088 0.480104 112.081 0.282044 267.195 0.470545 245.913 0.359724

175.191 0.486042 112.28 0.286053 267.336 0.492582 247.029 0.418556

175.465 0.501944 112.384 0.288162 267.451 0.510774 247.632 0.451965

175.545 0.506614 115.151 0.347589 267.524 0.522411 247.921 0.468321

175.809 0.522105 115.266 0.350192 267.537 0.524490 248.769 0.517373

175.876 0.526053 116.035 0.367858 267.599 0.534432 250.317 0.609433

176.275 0.549695 118.782 0.434349 267.643 0.541510 250.769 0.636473

176.533 0.565077 118.785 0.434424 267.678 0.547153 251.234 0.664161

176.981 0.591898 120.390 0.475377 267.680 0.547473 252.632 0.745354

177.141 0.601496 122.836 0.53996 267.725 0.554744 252.659 0.746875

177.314 0.611876 123.223 0.55035 267.794 0.565917 252.864 0.758358

177.501 0.623093 125.060 0.600007 267.903 0.583621 253.082 0.770416

178.072 0.657238 127.277 0.659983 267.944 0.590289 253.197 0.776709

178.124 0.660334 128.525 0.693342 268.067 0.610314 253.365 0.785813

178.359 0.674287 129.972 0.731282 268.068 0.610478 253.533 0.794805

178.945 0.70871 131.944 0.78107 268.302 0.64852 253.879 0.812944

179.065 0.715675 134.687 0.845016 268.397 0.663884 253.958 0.817009

179.704 0.75215 135.036 0.852599 268.493 0.679331 254.344 0.836437

179.77 0.755851 136.675 0.88624 268.612 0.698331 255.004 0.867808

179.955 0.766144 140.115 0.944586 268.868 0.738472 255.091 0.871754

180.115 0.77495 141.331 0.960666 268.947 0.7506 255.239 0.878359

180.591 0.800564 141.583 0.963676 269.001 0.758811 255.667 0.896665

181.211 0.832428 145.023 0.993035 269.339 0.808403 255.831 0.903352

181.403 0.841908 145.801 0.996524 269.42 0.819762 256.233 0.918938

181.712 0.856742 148.899 0.998485 269.467 0.826244 256.8 0.938861

182.064 0.872965 149.549 0.996468 269.793 0.868823 257.646 0.963764


53/72

53

182.199 0.878986 149.984 0.994651 269.905 0.882391 257.725 0.965779

182.343 0.885279 153.509 0.966471 270 0.893432 258.484 0.982304

182.973 0.911169 153.783 0.963311 270.218 0.917033 259.233 0.993406

183.501 0.930662 156.135 0.930849 270.395 0.934298 259.294 0.994077

183.572 0.93312 156.783 0.920309 270.587 0.950962 259.341 0.994569

183.717 0.938017 156.87 0.918844 270.608 0.952648 260.133 0.999657

184.43 0.959597 156.984 0.916907 270.884 0.972221 260.499 0.99995

184.506 0.961645 157.03 0.91612 270.96 0.976738 260.6 0.999802

184.67 0.965891 157.104 0.914847 271.213 0.988957 260.769 0.99933

185.111 0.976128 157.27 0.911962 271.276 0.991311 261.548 0.993578

185.478 0.983302 157.577 0.906519 271.364 0.994133 261.633 0.992597

185.771 0.988131 157.64 0.905385 271.563 0.998486 261.757 0.991043

185.832 0.989035 158.043 0.897995 271.826 0.999879 262.102 0.985954

186.424 0.995964 158.465 0.890011 271.829 0.999866 262.196 0.984373

186.96 0.999319 158.615 0.887115 271.863 0.999675 262.726 0.97394

186.963 0.99933 158.92 0.881132 272.075 0.996609 262.926 0.969343

187.092 0.999716 159.344 0.872612 272.27 0.990958 263.998 0.938807

187.386 0.999986 159.434 0.870773 272.316 0.989234 264.866 0.907312

187.79 0.998979 159.874 0.861642 272.52 0.979823 264.869 0.907193

188.029 0.997632 160.019 0.858581 272.552 0.978088 265.309 0.889128

188.524 0.993083 160.217 0.85436 272.679 0.970529 265.316 0.888829

189.028 0.986039 160.674 0.844446 272.787 0.963264 265.323 0.888531

189.266 0.981881 161.254 0.831528 273.021 0.944979 265.4 0.885228

189.288 0.981471 161.376 0.828765 273.046 0.942827 265.417 0.884493

189.377 0.979763 162.072 0.812715 273.172 0.931411 265.577 0.877489

189.964 0.966693 162.091 0.812271 273.248 0.924082 265.624 0.8754

190.066 0.964109 162.387 0.805298 273.363 0.912375 265.945 0.860773

190.862 0.940876 162.634 0.799418 273.462 0.901729 266.165 0.850396

191.108 0.93264 162.691 0.798053 273.517 0.895595 266.344 0.841753

191.701 0.910859 162.782 0.795869 273.622 0.883463 266.681 0.825018

191.756 0.908707 163.429 0.780136 273.654 0.879662 266.773 0.820349

192.683 0.8693 163.619 0.775452 273.807 0.860822 267.175 0.799486

192.916 0.858531 163.734 0.772604 273.815 0.859809 267.187 0.79885

193.661 0.822048 164.021 0.765453 273.817 0.859557 267.315 0.792051

193.906 0.80943 164.303 0.758369 273.897 0.849261 267.559 0.778905

194.68 0.76786 164.33 0.757687 273.934 0.844411 267.688 0.771861

194.701 0.766699 164.544 0.752271 273.945 0.842956 267.889 0.760767

195.702 0.709817 164.824 0.745141 274 0.835621 268.208 0.742886

195.978 0.693692 164.849 0.744502 274.005 0.834947 268.238 0.741189

196.467 0.664798 164.945 0.742044 274.27 0.797994 268.549 0.723443

196.666 0.652949 164.977 0.741224 274.416 0.776656 268.571 0.722178

197.5 0.602998 165.011 0.740352 274.637 0.743259 268.596 0.720739

197.912 0.578296 165.208 0.735285 274.993 0.687345 268.817 0.707958

198.132 0.565139 165.249 0.734227 274.996 0.686867 268.915 0.702254

198.208 0.560602 165.283 0.733349 275.349 0.62986 269.278 0.680973

198.297 0.555295 165.406 0.730169 275.531 0.60023 269.375 0.675251

198.304 0.554878 165.431 0.729522 275.692 0.574044 269.4 0.673774

198.426 0.547617 165.606 0.72498 276.023 0.520665 269.592 0.6624

198.515 0.542329 165.804 0.719823 276.026 0.520188 269.77 0.65182

198.528 0.541558 165.929 0.716558 276.34 0.470711 269.81 0.649437


54/72

54

198.583 0.538297 166.24 0.7084 276.473 0.450234 269.888 0.644788

198.647 0.534505 166.406 0.704029 276.638 0.425308 269.952 0.64097

199.017 0.512705 166.542 0.700438 276.868 0.391564 270.452 0.61107

199.784 0.468302 166.821 0.693051 276.914 0.384968 270.898 0.584373

199.903 0.461528 166.822 0.693024 277.165 0.349941 271.31 0.559786

200.804 0.411465 167.058 0.686752 277.208 0.344112 271.405 0.554135

201.517 0.373617 167.093 0.68582 277.39 0.320022 271.735 0.53458

202.005 0.348738 167.221 0.682409 277.49 0.307202 272.218 0.506224

203 0.300845 167.245 0.681769 277.585 0.295299 272.776 0.473989

203.27 0.288541 167.287 0.680648 277.713 0.279698 273.362 0.440901

204.287 0.244972 167.853 0.665493 277.749 0.275404 273.397 0.438953

204.454 0.238245 168.015 0.66114 277.875 0.26069 274.038 0.403908

205.301 0.205997 170.57 0.592009 277.878 0.260347 274.557 0.376487

205.412 0.202002 171.723 0.560826 277.971 0.249817 274.624 0.373015

205.966 0.182865 172.741 0.533482 277.978 0.249037 275.069 0.350359

206.026 0.180872 173.662 0.508984 278.021 0.244272 275.149 0.346364

206.217 0.17463 173.908 0.502489 278.026 0.243722 275.279 0.339923

SUBJECT 2

HIP KNEE TORSO ANKLE

172.793 0.336542 100.521 0.163648 268.03 0.220558 247.217 0.182196

172.971 0.343593 100.628 0.16513 268.059 0.224796 247.366 0.188269

173.055 0.346948 101.238 0.173762 268.065 0.225682 248.385 0.233591

173.318 0.357563 101.577 0.178696 268.148 0.238148 248.682 0.248052

173.489 0.364554 102.067 0.186002 268.166 0.240905 249.158 0.272396

173.551 0.367105 102.102 0.186532 268.288 0.260166 249.59 0.295717

173.663 0.371737 102.763 0.196737 268.33 0.267013 249.717 0.302791

173.665 0.371819 102.804 0.197382 268.471 0.290815 250.708 0.361246

173.975 0.384789 102.869 0.198409 268.555 0.305572 251.094 0.385483

174.274 0.397499 103.392 0.206801 268.684 0.32906 252.412 0.473477

174.525 0.408315 104.347 0.222742 268.838 0.358358 253.145 0.525135

174.696 0.415757 104.363 0.223016 268.916 0.373685 253.289 0.535441

174.914 0.425328 105.083 0.235574 269.159 0.423411 253.339 0.53903

175.536 0.45312 106.078 0.253674 269.175 0.42678 253.439 0.546219

175.557 0.454071 106.536 0.262295 269.4 0.475264 253.449 0.54694

175.589 0.45552 106.773 0.266827 269.407 0.476806 253.565 0.555302

176.613 0.502703 108.179 0.294702 269.563 0.511465 253.906 0.579984

176.693 0.506447 109.611 0.324789 269.63 0.526555 254.22 0.602789

176.7 0.506775 110.04 0.334125 269.656 0.532436 254.387 0.614926

177.338 0.536889 112.047 0.379663 269.901 0.588372 254.683 0.636416

177.739 0.555996 113.931 0.424972 269.909 0.590208 254.824 0.64663

177.878 0.562644 114.131 0.429913 269.913 0.591126 254.885 0.65104

178.941 0.613709 116.723 0.495849 269.999 0.610882 254.939 0.654941

178.946 0.613949 118.942 0.55443 270.166 0.64918 255.053 0.663163


55/72

55

179.077 0.62025 118.97 0.555177 270.229 0.663559 255.103 0.666762

179.622 0.646414 122.266 0.643623 270.39 0.699944 255.41 0.688751

180.214 0.674656 124.427 0.70096 270.431 0.709098 255.499 0.695084

180.267 0.677171 124.505 0.703001 270.476 0.719091 255.507 0.695653

181.437 0.731841 128.712 0.807971 270.572 0.740152 255.628 0.704226

181.5 0.734727 130.302 0.843929 270.704 0.76847 255.753 0.713035

181.521 0.735687 130.42 0.846493 270.868 0.802363 255.817 0.717526

182.28 0.769826 136.017 0.947246 270.941 0.816911 256.018 0.731535

182.576 0.782796 136.332 0.951517 270.983 0.825113 256.078 0.735686

182.846 0.794434 136.425 0.952747 270.99 0.826466 256.216 0.745179

183.678 0.829003 142.211 0.998506 271.262 0.87609 256.302 0.751052

184.174 0.848564 142.237 0.998569 271.332 0.887811 256.343 0.753839

184.216 0.850181 143.956 0.999743 271.335 0.888301 256.371 0.75574

184.741 0.869839 147.592 0.983242 271.531 0.918457 256.69 0.777105

185.179 0.885411 147.635 0.982896 271.533 0.918741 256.696 0.777503

185.491 0.896013 149.068 0.969409 271.744 0.94645 256.742 0.780537

185.774 0.905261 149.946 0.959323 271.785 0.951227 257.059 0.801112

186.787 0.935279 150.019 0.958424 271.793 0.952134 257.084 0.802709

186.787 0.935279 150.123 0.957127 272.008 0.973501 257.105 0.804047

186.935 0.93924 150.261 0.955377 272.091 0.980137 257.16 0.807536

187.798 0.960031 150.514 0.952085 272.174 0.985843 257.195 0.809747

188.055 0.965436 150.878 0.94716 272.192 0.986954 257.962 0.855948

188.191 0.968146 150.945 0.94623 272.244 0.989918 258.281 0.873755

188.824 0.979359 151.114 0.943849 272.334 0.994157 258.853 0.903306

189.286 0.986054 151.858 0.932819 272.436 0.99758 260.569 0.97035

189.541 0.989200 151.88 0.932479 272.505 0.999055 262.113 0.998182

189.879 0.992759 152.03 0.930143 272.55 0.999650 262.316 0.999352

190.476 0.997324 152.054 0.929766 272.585 0.999913 263.41 0.995489

190.972 0.999427 152.285 0.926091 272.62 1.000000 263.546 0.993816

191.225 0.999905 152.361 0.924865 272.622 1.000000 264.463 0.975815

191.621 0.999845 152.700 0.919284 272.661 0.999878 265.164 0.954471

191.98 0.998938 153.190 0.910914 272.674 0.999789 265.328 0.948579

192.107 0.998424 153.280 0.909338 272.688 0.999666 265.613 0.937563

192.721 0.994516 153.611 0.903443 272.751 0.998765 265.975 0.922204

193.284 0.988882 154.426 0.888274 272.862 0.995799 266.02 0.920192

193.773 0.982424 154.563 0.885635 273.012 0.989023 266.056 0.918566

194.232 0.975065 155.086 0.875339 273.081 0.984852 266.28 0.908132

194.249 0.974769 155.525 0.866429 273.126 0.98178 266.528 0.895964

194.496 0.970274 155.725 0.862291 273.203 0.975888 266.674 0.888511

194.766 0.964961 156.191 0.852468 273.23 0.973634 266.718 0.886225

195.681 0.943947 156.244 0.851335 273.436 0.95332 266.864 0.878501

195.731 0.942669 156.481 0.846229 273.553 0.93942 267.009 0.870634

196.374 0.925087 157.055 0.833608 273.555 0.93917 267.202 0.85987

196.499 0.92143 157.27 0.828791 273.708 0.918535 267.208 0.85953

196.972 0.906911 157.427 0.825244 273.789 0.906563 267.477 0.843982

197.198 0.899608 158.364 0.803578 273.972 0.877042 267.671 0.832406

197.208 0.89928 158.374 0.803342 274.011 0.870334 267.809 0.823997

197.808 0.878777 159.243 0.782542 274.034 0.866312 268.116 0.804804

198.193 0.864836 159.271 0.781861 274.328 0.811085 268.184 0.800467

198.381 0.857818 159.287 0.781472 274.336 0.809493 268.22 0.798159


56/72

56

199.358 0.819316 159.634 0.772985 274.371 0.802474 268.556 0.776239

200.116 0.787375 159.655 0.772468 274.515 0.772798 268.591 0.773918

200.28 0.780258 159.736 0.770473 274.671 0.739408 268.885 0.754173

200.425 0.77391 160.185 0.759328 274.744 0.723412 269.006 0.745924

201.352 0.732239 160.878

pattern recognition of human gait signatures

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