Wall-Corner Classification. A New Ultrasonic Amplitude Based Approach Lisboa, 6 July 2004 M....
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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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
Conclusions
Contens• Introducction
• Amplitude Model
• Geometric Features
• Classification Algorithms
• Experimental Results
• Conclusions
AmplitudeModel
8
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
Conclusions
Contens• Introducction
• Amplitude Model
• Geometric Features
• Classification Algorithms
• Experimental Results
• Conclusions
GeometricFeatures
13
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
ConclusionsGeometricFeatures
Differences in the echoes from corners and wallsDifferences in the echoes from corners and walls
14
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
ConclusionsGeometricFeatures
Differences in the echoes from corners and wallsDifferences in the echoes from corners and walls
15
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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)
Differences in the echoes from corners and wallsDifferences in the echoes from corners and walls
16
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
Differences in the echoes from corners and wallsDifferences in the echoes from corners and walls
17
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
Conclusions
Contens• Introducction
• Amplitude Model
• Geometric Features
• Classification Algorithms
• Experimental Results
• Conclusions
ClassificationAlgorithms
18
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
ClassificationAlgorithms
19
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
ClassificationAlgorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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)
ClassificationAlgorithms
21
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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)
ClassificationAlgorithms
K-nearest neighbours method (k-nn)K-nearest neighbours method (k-nn)
2
22
1
1121 ,,90
90,
Aw
Awaw
Aw
AwawNoi
22
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
Conclusions
Contens• Introducction
• Amplitude Model
• Geometric Features
• Classification Algorithms
• Experimental Results
• Conclusions
ExperimentalResults
23
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
Experimental Results in classificationExperimental Results in classification
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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
Experimental Results in classificationExperimental Results in classification
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
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
Conclusions
Contens• Introducction
• Amplitude Model
• Geometric Features
• Classification Algorithms
• Experimental Results
• ConclusionsConclusions
Conclusions
27
ExperimentalResults
IntroducctionAmplitude
ModelGeometric Features
Classification Algorithms
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}