Wall-Corner Classification. A New Ultrasonic Amplitude Based Approach Lisboa, 6 July 2004 M....

Wall-Corner Classification. A New Wall-Corner Classification. A New Ultrasonic Amplitude Based ApproachUltrasonic Amplitude Based Approach

Lisboa, 6 July 2004Lisboa, 6 July 2004

M. Martínez, G. Benet, F.Blanes, P. Pérez, J.E. Simó, J.L.Poza

Universidad Politécnica de ValenciaDep. Informática de Sistemas y Computadores

Camino de Vera s/n Valencia (SPAIN){mimar, gbenet , pblanes, pperez, jsimo, jopolu @disca.upv.es}

Contens

2

• IntroducctionIntroducction

• Amplitude ModelAmplitude Model

• Geometric FeaturesGeometric Features

• Classification AlgorithmsClassification Algorithms

• Experimentals ResultsExperimentals Results

• ConclusionsConclusions

3

ExperimentalResults

IntroducctionAmplitude

ModelGeometric Features

Classification Algorithms

ConclusionsIntroducction

Contens• Introducction

• Amplitude Model

• Geometric Features

• Classification Algorithms

• Experimental Results

• Conclusions

4

ExperimentalResults




Conclusions

Ultrasonic SignalUltrasonic Signal

Introducction

Sonar sensing is one of the most useful and cost-effective methods of environment perception in autonomous robots.

Ultrasonic transducers are light, robust, and inexpensive devices.

The figure plots the envelope of a received echo.

Each peak is matched with a detected object.

5

ExperimentalResults




Conclusions

The Classification Problem (Wall/Corner)The Classification Problem (Wall/Corner)

In order to classify the targets most sonar systems employ only time of fly(ToF) information. Planes are differentiated from corners by taking two

measurements from two or more separate locations.

All these techniques have in common the extreme precision required in the ToF estimation.

Several authors have used the amplitude of the received echo to enhance their classification results. But, The amplitude is a parameter very sensitive:

to environmental conditions, and to the surface characteristics of each reflector

There is not a model of the amplitude reflected of an object.

Introducction

6

ExperimentalResults




Conclusions

The purpose of this paper is to present a method of classify between Walls and Corners, using:

Only one rotating ultrasonic sensor, which is composed of Piezo-ceramic ultrasonic sensors.

A simple but effective amplitude model, and

Information on “ghosts peaks”, which are previous to the main peak from the object to be classified.

Introducction

The Classification Problem (Wall/Corner)The Classification Problem (Wall/Corner)

7

ExperimentalResults




Conclusions


• Amplitude Model




• Conclusions

AmplitudeModel

8

ExperimentalResults




Conclusions

In a previous paper, a theoretical model for the amplitude of received ultrasonic echoes has been presented.

This model can be used to predict the expected amplitude of echoes from simple reflectors, like planes or right corners.

Also, this model can be used to classify the received echoes from bewteen two types of reflectors, following a statistical approach.

(1)

AmplitudeModel

20

242

0 2),(

ex

eCAxA

xNr

9

ExperimentalResults




Conclusions

Main parameters of the model:

Cr is the reflection coefficient.

It is a number between 0 and 1.

It represents the ratio between the intensity returned back to the transducer and the incident intensity of the acoustic beam.

N is a parameter which can take two values:

N = 1 wall target

N = 2 corner target

(1)

AmplitudeModel

20

242

0 2),(

ex

eCAxA

xNr

10

ExperimentalResults




Conclusions

How to apply the amplitude model to classification problem:• An entire circular scan from the scene is performed, and the peak

amplitude values of echoes are obtained (=0º)

• In order to classify each located peak only one parameter of the model is necessary: the value of the Cr of the surface.

— x it is the distance to the object, obtained from the echo (ToF)— it is not necessary, since the ‘mountain peak’ always correspond with

=0º— and A0 are constants well-known at the calibration stage.

AmplitudeModel

11

ExperimentalResults




Conclusions

Under these conditions, the value of N can be derived from equation (1):

• The value of N obtained from this equation can be used for target classification purposes:

N = 1 wall target

N = 2 corner target

AmplitudeModel

rC

xA

Ax

Nln

22

ln0

(2)

How to apply the amplitude model to classification problem (II):

12

ExperimentalResults




Conclusions


• Amplitude Model




• Conclusions

GeometricFeatures

13

ExperimentalResults




ConclusionsGeometricFeatures

Differences in the echoes from corners and wallsDifferences in the echoes from corners and walls

14

ExperimentalResults




ConclusionsGeometricFeatures


15

ExperimentalResults




Conclusions

The ghost peaks previous to the corner’s main peak, must accomplish the following relationships:

)1

(cos 11 dc

dw )2

(cos 12 dc

dw

The angles 1 and 2 are complementary, and will be calculated as follows:

The distance to the corner, dc, will agree with :

22 21 dwdwdc

GeometricFeatures

(3)

(4)


16

ExperimentalResults




Conclusions

The amplitude of the ghost peaks can be also predicted using the amplitude model.

1),1(1 1 awdwAAw

2),2(2 2 awdwAAw

GeometricFeatures


17

ExperimentalResults




Conclusions


• Amplitude Model




• Conclusions

ClassificationAlgorithms

18

ExperimentalResults




Conclusions

By direct application of the amplitude model:

A.C.A. (for Amplitude Classification Algorithm)

By adaptation of a classic algorithm in the recognition of patterns:

K-nearest neighbours method (k-nn)

Classification Algorithms Classification Algorithms


19

ExperimentalResults




Conclusions

A.C.A. (Amplitude Classification Algorithm)A.C.A. (Amplitude Classification Algorithm)

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.2

1.4

Computed values of N

De

nsi

ty o

f p

rob

abili

ty

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Value of NP

rob

abili

ty

Example of normal distributions of parameter N for Walls and Corners

Membership probability of Walls(blue) and Corners(red)

CornersWalls


The parameter N obtained from equation (1) has a quasi normal distribution around the value 1 in the case of walls, and 2 for corners:

If P(W) > P(C) then Detected Object is a Wall, else a Corner

P(C)

P(W)

20

ExperimentalResults




Conclusions

Classic algorithm in pattern recognition:

A training set of patterns for each class is used: Wall and Corner.

Each pattern is composed of one set of characteristicspi= (x1,x2,x3,....,xn)

Given an object to classify oi= (x1,x2,x3,....,xn) the algorithm is as follows:

• The Euclidean distance to each pattern of each class is calculated.

• The k patterns with smaller distances are choosed.

• The obstacle will be classified into the class with more occurrences into the k set of patterns.

K-nearest neighbours method (k-nn)K-nearest neighbours method (k-nn)


21

ExperimentalResults




Conclusions

Some details are given on the application of the algorithm:

The feature vector has four parameters:

A set of 400 patterns for the Wall class, and other 400 for the Corners are used.

The value of the parameter k is 10

this value demonstrated to be a good compromise

aw1 and aw2 are real amplitudes

Aw1 and Aw2 are theorethical amplitudes from eq. (1)

N is obtained from the eq. (2)

1 and 2 are angles calculated from eq. (3)


K-nearest neighbours method (k-nn)K-nearest neighbours method (k-nn)

2

22

1

1121 ,,90

90,

Aw

Awaw

Aw

AwawNoi

22

ExperimentalResults




Conclusions


• Amplitude Model




• Conclusions

ExperimentalResults

23

ExperimentalResults




Conclusions

Four data sets have been used for the experiments with the two classification algorithms:

Materials Orientations Distances(m) Walls Corners

1 Cement, Pladur 20º a 70º 0.5 a 4 1279 650

2 Cement, Pladur 20º a 70º 0.5 a 4 855 309

3 Cement 20º a 70º 0.5 a 4 650 321

4 Cement, Melamine 20º a 70º 0.5 a 4 600 354

Experimental Results in classificationExperimental Results in classification

ExperimentalResults

24

ExperimentalResults




Conclusions

1 2 3 4 1 2 3 4

Wall 88% 79% 92% 61% 88% 79% 92% 61%

Corner 85% 83% 87% 19% 91% 91% 90% 84%

A.C.A. Algorithm (Cr =0.6, N0 = 1.5) K-nn Algorithm (k = 10)

ExperimentalResults


Wall Sucess Percentage(under 1.5 meters)

0

20

40

60

80

100

1 2 3 4

Proof number

Su

cess

Per

cen

tag

e

ACA

knn

Corner Sucess Percentage(under 1.5 meters)

0

20

40

60

80

100

1 2 3 4

Proof number

Su

cess

P

erce

nta

ge

ACA

knn

25

ExperimentalResults




Conclusions

1 2 3 4 1 2 3 4

Wall 88% 82% 90% 67% 88% 79% 92% 61%

Corner 68% 46% 67% 13% 91% 91% 90% 84%

A.C.A. Algorithm (Cr =0.6, N0 = 1.5) K-nn Algorithm (k = 10)

ExperimentalResults


Wall Sucess Percentage(under 4 meters)

0

20

40

60

80

100

1 2 3 4

Proof number

Su

cess

Per

cen

tag

e

ACA

knn

Corner Sucess Percentage(under 4 meters)

0

20

40

60

80

100

1 2 3 4

Proof number

Su

cess

Per

cen

tag

e

ACA

knn

26

ExperimentalResults




Conclusions


• Amplitude Model




• ConclusionsConclusions

Conclusions

27

ExperimentalResults




ConclusionsConclusions

• In this work, a simple model of the amplitude response of the ultrasonic echoes has been used to classify between walls and corners.

— The ultrasonic signal comes from a unique pair of rotating emitter/receiver transducers.

• The amplitude of the echoes together with their time of flight(ToF) can be used in a simple data fusion process.

— geometric features of the two main types of reflectors has been exploited.

• The showed results yield very satisfactory success percentages: Taking into account that the measurements were exclusively data taken from

only one scan and from only one position, as well as the distances up to 4m, and

k-nn algorithm yields the best results in all the situations, but its higher computational cost must also be considered when real time response is required.

Wall-Corner Classification. A New Wall-Corner Classification. A New Ultrasonic Amplitude Based ApproachUltrasonic Amplitude Based Approach

Lisboa, 6 July 2004Lisboa, 6 July 2004

M. Martínez, G. Benet, F.Blanes, P. Pérez, J.E. Simó, J.L.Poza

Universidad Politécnica de ValenciaDep. Informática de Sistemas y Computadores

Camino de Vera s/n Valencia (SPAIN){mimar, gbenet , pblanes, pperez, jsimo, jopolu @disca.upv.es}

Wall-Corner Classification. A New Ultrasonic Amplitude Based Approach Lisboa, 6 July 2004 M....

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