POSSIBILISTIC MODELING OF ULTRASONIC SIGNAL FOR FLOOR STATE RECOGNITION

Sonda Ammar Bouhamed1, Imene Khanfir Kallel1, Dorra Sellami Masmoudi1, Basel Solaiman2

1Engineering School of the University of Sfax, BP W, 3038 Sfax, Tunisia.

2TELECOM-Bretagne, ITI laboratory, France.

ABSTRACT The process of staircases detection and recognition is complex for blinds. Therefore, an intelligent and real time system is required to help them. In this paper, we investigate using only one ultrasonic sensor and few samples with small size to represent floor and staircases. The performance of such system depend on object representation, data modeling and finally classification algorithm. A simple wave analysis have shown that frequency components are the most affected in stair case context. Accordingly, we have used frequency representation of ultrasonic signal, namely the smoothed periodogram. Then, we model model several extracted features based on Masson possibility approach. Finally, similarity measure is used in the classification algorithm. A training process is under taken on a local database of 500 signal simples is used. An accuracy rate of 94% has been achieved.

Index Terms— Ultrasonic signal processing, Possibility theory, Similarity, Uncertainty information, Floor state recognition

1. INTRODUCTION Floor state recognition under different viewing conditions is a big challenge in electronic white cane. A successful recognition is intended to enhance visually impaired people security. Until now, all proposed systems aiming at floor state recognition are often essentially based on a Laser sensor, infrared sensor or monocular camera. In [1], Yuan and Manduchi have proposed a floor state recognition system in their virtual white cane based on two sensors : Laser and camera. The performances of this system are considered acceptable, but it is costly. In [2], Adams introduced a new concept to identify the floor state, (even surface, ascending and descending staircases) combining three infrared range sensors. In [3], Lee and Lee used also the three infrared range system for detecting ascending and descending stairs. In [4], Se and Brady deal with a distant staircase detection system, which is based on vision system camera outdoor

environment perception. Consequently, floor state detection based only on ultrasonic sensor remains a bog challenge. In this paper, we aim at designing floor state recognition white cane based on only one ultrasonic sensor with few signal samples. Such applications must be generally a real time. In this case, processed data set should be preferably small leading to an incomplete data. Moreover, these data set are generally constructed using signals issued from different sensors making performances mostly affected by the environmental context. Therefore, collected data obtained from these sensors are uncertain. This problem is widely met by human. So, it is interesting to know the principal of human reasoning for modeling and analyzing of collected data in order to solve encountered limitations. In robotic domain, human reasoning can be formulated using various theories, methods and strategies able to follow the same analytical human mind rules. Numerous previous works have proposed various sets of ultrasonic signal processing. The majority of these strategies integrate one or more of classical methods such as Fourier transform, wavelet transform and so on. In [5], artificial neural network is used to recognize two or three-dimensional shapes based on three types of representation which are time domain, frequency domain (power spectrum), and time frequency representation (spectrogram). In [6], Oria et al. was proposed a new approach to detect and classify simply shaped objects. This approach used temporal representation of ultrasonic sensor echo. In [7], Bozma and Kuc introduce a concept for interpreting sonar TOF (Time Of Flight) data in order to classify the environment in three types: corner, plane and edge. The proposed system uses a single mobile sensor for generating a sonar map. In [8], Ihsan and Paolo present a novel approach to recognize objects using neural network classification system. In this system, the sonar echo was treated in frequency and time domain to extract relevant information to present five objects at different distances. In [13], we have proposed a new approach to detect and classify floor state using ultrasonic signal. Our approach is based on temporal and a combination of various frequency representations. The majority of works listed above use large datasets to conduct an exhaustive study of population.

1st International Conference on Advanced Technologies for Signal and Image Processing - ATSIP'2014 March 17-19, 2014, Sousse, Tunisia IFI-148

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Indeed, these approaches integrate more than one ultrasonic representation, to extract relevant information, to represent perfectly the different considered objects. The classical methods of signal processing are not ideal when data are affected by various uncertainty forms. These methods are based on a statistical analysis of data, which consists on ignoring data uncertainty like using the means of measurement. Instead, it is more important if this uncertainty is treated and analyzed. This can be often solved by using other theories able to process the uncertainty of data such as probability theory, possibility theory and so on. The probabilistic approach is valid only when the available data is precise and contains very large samples which is not the case of real time applications. However, human reasoning doesn't operate in a classical way [9-10] and probabilistic approach requires a rough modeling, very similar to the possibilistic reasoning [11]. For this, possibility theory is the most used in different real time applications integrating small datasets where data is affected by different uncertainty forms. In this paper, a new method of uncertainty data based on possibility theory is developed to treat and analyze ultrasonic signal for floor state recognition. This method integrates Masson approach which is proposed in [12]. The remainder of this paper is organized as follows : In section 2, we present the background of the issue, where we describe ultrasonic signal processing for feature extraction. Then, probability distribution estimation for possibility distribution inferring are detailed. Similarity measure operator is also presented in this section as decision criteria. The proposed strategy, based on theories and methods defined in last section, is detailed in section 3. Section 4 gives the performances evaluation of our approach. Finally, we conclude and give some perspective in section 5.

2. BACKGROUND OF THE ISSUE

2.1. Ultrasonic signal processing Ultrasonic signal is mostly affected by environmental phenomena such as temperature, object material, covered distance, and so on. This leads to an induced noise affecting the data. Accordingly, enhancement of this signal becomes mandatory. In this case, a low pass filter is used to reduce noise effect. The resulting filtered signal is used to extract features which are able to describe perfectly the different considered objects. For more opportunity to extract relevant information, smoothed periodogram is used. In fact, frequency representation is very important, especially, when specific information are integrated in frequency components. The periodogram representation estimates the spectral density of ultrasonic signal. Smoothed periodogram

consists on calculating several periodograms based on single signal and using a sliding window.

2.2. Feature extraction Feature extraction is a procedure dedicated to extract relevant information to represent objects. Various information were extracted from signal magnitude and from frequency representations calculated previously. In the following, we show the extracted features from each time and Smoothed periodogram representation. Let xi, i=1, ...,N, be N samples of the filtered ultrasonic signal x. a. Time domain feature 1: mean of the signal.

N

iix

Nx

1

1 (1)

feature 2: Sample standard deviation , a measure that is used to know how spread out the signal:

N

ii xx

N 1

2)(1

1 (2)

feature 3: The largest value of the signal: )(max

,...,1 iNixmx

(3)

feature 4: The smallest value of the signal: )(min

,...,1 iNixmn

(4)

feature 5: Skewness 3 , a measure of signal symetry:

N

ii xx

N 1

33 )(1

(5)

feature 6: Kurtosis 4 , a measure of signal flatness.

N

ii xx

N 1

44 )(1

(6)

feature 7: Root Mean Square (RMS),R, a measure of the magnitude of deviation from the mean

N

ii xx

NV

1

)(1 (7)

VR (8) feature 8: The margin between the maximum and the minimum of signal magnitude : mnmxm (9) b. Frequency domain : smoothed periodogram Features calculated from the filtered signal, were also extracted from the periodogram, as follows: feature 9: the variance performed according to Eq. (7). feature 10: the biais:

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N

ii xx

NB

1

)(1

(10)

2.3. Estimation of possibility distribution Possibilistic data modeling, based on distribution of possibilities, requires reliable method to estimate the different distributions. In this paper, these distributions are calculated from the above computed features. This process needs a compromise step to convert each feature into possibility distribution. Several methods was proposed in literature [14][15]. In [16]and [17], it is established that the transformation of probability distribution to possibility distribution p is the best one. Accordingly, these transformations start by the estimation of probability distribution based on features. 2.3.1. Estimation of probability distribution Consider a finite universe of discourse

MCCC ,...,, 21 . Each class mC of , Mm ,...,1 ,is ”observed” through K information sources,

}S ,...,S ,{S=S K21 . For a given class mC and a given

source kS , Kk ,...,1 , N(k) features are extracted. They are

denoted mkNk

mk

mkkm fffF )(,2,1,, ,...,, .

Assuming that all classes involve all the K information sources, the set of attributes associated with the kth information source, can be rewritten as follows

)(,2,1, ,...,, kNkkkk fffF , k=1,...K. Feature processing and conversion into probability distributions is presented in figure 1. The procedure of the estimation of probability distribution

nkp , from feature n and source Sk is based on histogram

computing. The algorithm of nkp , estimation is described

with algorithm 1. In this paper, three classes defining floor state was considered, even surface, ascending staircase and descending one. Each class is represented by ten features extracted from only one information source. So, in this context, M=3, K=1 and N=10.

Figure 1. The process of the estimation of probability

distribution from source Sk Algorithm 1 : Estimation of probability distribution from extracted features Given a matrix E(T,N) for each class Cm, where N is the number of features and T is the number of observation of feature n.

Note that, if K>1, N is obtained by )(1

kNsumNK

k , with

K is the number of information source. For n=1 to N a. Normalize the data E(1:T, n) = E(1:T, n) - mean(E(1:T, n)) E(1:T, n) = E(1:T, n / std(E(1:T, n)) E(1:T, n) = E(1:T, n) - min(E(1:T, n)) E(1:T, n) = E(1:T, n / max(E(1:T, n)) so that E(1:T,n) is normalized and its values are included in the interval [0,1]. b. Calculate the histogram of normalized data represented by H class. Hg(1:H, n) = hist (E(1:T, n), H) c. Probability distribution is calculated by dividing the number of observation in Hg(h,n), h=1, ...,H, by the number of observations, T, of feature n. For h=1, to H p(h, n) = Hg(h, n) / T End For End For

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2.3.2. Probability-possibility transformation using probability intervals In our system, we use a few sample to estimate probability distribution. For that reason, probability is not precise enough to be used in inferring a possibility distribution. In fact, histogram can be considered as an efficient estimator of probability distribution only when the dataset size is sufficiently large. To solve such limitation, several methods was proposed in [18] and [12]. These methods use confidence intervals of probability to define possibility distributions. Here, we use the method proposed by Masson in [12]. This method consists on characterizing the probabilities of the different classes by defining simultaneous confidence intervals (CIs) of probability represented by [p-, p+]. Masson applies Goodman strategy [19] to calculate the CIs, which contain necessarily the reel probability value, with a joint confidence level, equal to ( 1 ). All proposed methods consider that possibility distribution dominates the true probability distribution, in at least 100( 1 )% of the cases. In [23], May and Johnson stated that the best performances of Goodman's intervals in terms of confidence region volume and coverage probability are obtained when the number of classes, M, is greater than 2 and that each number of samples T, in each class, is greater than 5. 2.3.3 Construction of possibility conditional map to each class In our approach, a conditional possibilistic card is created, in training step, in order to associate a specific signature for each class Cm. The construction of possibilistic card is based on the different possibility distributions, corresponding to all extracted features. Resulted card have as dimension H rows and N columns. 2.3.4 Classification process and Similarity measure In classification process, a new possibilistic card must be created for each new arrived sample, which must be classified in one of the trained classes. Then a similarity measure operator is used. Consider two normalized possibility distributions 1 and

2 , defined in the universe of discourse

Hxxx ,...,, 21 . In literature, different similarity measure operators are proposed [20]. We consider here among these methods, three measures, namely Manhattan distance, Information Affinity and Information closeness. Manhattan distance is calculated as follows :

H

hhhH

d1

2121 )()(1

),( (11)

Information Affinity is a new possibilistic similarity measure proposed by I. Jenhani [20]. It is defined as follows:

2)(),(1),( 2121

21

IncdInfoAff (12)

where : ),( 21 d represents the Manhattan distance

between 1 and 2 .

)( 21 Inc defines the degree of conflict between 1

and 2 and is taken as the maximum operator. This degree is obtained as follows : )max(1)( 2121 Inc (13) Note that the more InfoAff measure is strong the more possibility distributions 1 and 2 are similar. Information closeness method, denoted by G, proposed by Highashi and Klir in 1983 [21], measures similarity between two possibility distributions. This method computes similarity using their U-uncertainty measure [22]. The information closeness ),( 21 G is defined as :

),(),(),( 21221121 ggG (14)

where )()(),( ijji UUg . is taken as the

maximum operator and U is the non-specificity measure defined as:

H

hhh nhU

22)1(2)1()( log)1(log)()(

with 0)1( H . Note that the less the value of G is, the more the possibility distributions are similar.

EXPERIMENTS AND RESULTS In this paper, our experiments are developed using ultrasound signal dataset, which is constructed using only one sensor, attached to the white cane. This dataset is constructed in different conditions and from various shape of staircases. It contains 1500 samples (500 samples for each class). The used signal to create this dataset have a very small size (20 measures). In the first step of our experiments, we employ this dataset with Masson approach to generate the specific possibility distributions from the probability distributions using different dataset sizes. The size which, are used are 500 samples, 200 samples, and 25 samples for each class. In the following, we consider in each experiment the probability distribution and the corresponding possibility distribution for each class. These distributions are estimated using skewness feature, extracted from the filtered signal and using the parameter values, defined in Table 1.

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Table 1. Details of considered parameters for estimation of probability distributions and inferring possibility distributions

Parameters Value Information source Filtered signal Feature number Feature 5 (Skewness) H define the distributions size

H = 10

T T=500, T=200 and T=25

Figure 2. Example of probability and possibility distributions obtained for different sample sizes : (a)

T=500, (b) T=200 and (c) T=25

The use of different dataset sizes for inferring possibility distributions, using Goodman confidence probability intervals show that : The possibility distribution dominates the true probability distribution in all cases.

The highest the size of dataset, the more the possibility distribution is specific. In fact, when T=25, the possibility distribution, corresponding to the first class (C1), represents a total ignorance. Possibility distributions of C2 and C3, lost the specificity and becomes close to total ignorance case. The Goodman confidence interval presents good possibility distribution inferring with high dataset size. To evaluate this method in the application of staircase recognition, the developed dataset is divided into two raw datasets. The first one is used to construct possibility card, representing each class Cm, m=1, ...,3, which defines the floor state. It contains 300 samples, for each class. The second dataset is used for generalization and contains 200 samples for each class. In the generalization step, we use 30 samples to infer possibility distributions for seek of performances. Table 2. Classification rates obtained by InfoAff, manhattan and G similarity measure operator

similarity measure operator

InfoAff Manhattan distance

G : InfoCloseness

Smoothed periodogram

66,6 % 50 % 94,4 %

Filtered signal 55,5 % 55,5 % 55,5 %

Table 2 shows classification performances, obtained for each similarity measure operator obtained by use of smoothed periodogram features and by use of filtered signal features in order to compare temporal and frequency representation performances. Results show the importance of frequency domain, to represent ultrasound signal. Comparison between similarity measure operator, demonstrates that the use of information closeness, based on non-specificity measure, gives the best performance rate. In fact, using Manhattan distance and information Affinity, based on Manhattan distance and possibility distribution inconsistence measure, are not able to discriminate perfectly between classes.

The next experiment consists on evaluating Masson method in small sample size classification. We consider in the following different sample size, which are T=30, T=20, T=10 and T=5. The obtained results are presented in figure 3. Figure 3 shows the classification performances, obtained by different similarity measure operators, for different sample size. We notice that the accuracy rate becomes significantly important for high sample size. These results confirm the Goodman's principles which need a large dataset to define correctly CIs [23].

The curves, obtained for each similarity measure operator, prove the importance of information closeness method. Indeed, these results show the necessity to include the possibility distributions characteristic into similarity operator definition.

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Figure 3. Performance based on Masson method for

different sample size

5. CONCLUSION This paper focuses on possibility modeling of ultrasound signals in the application of staircase detection and recognition. This application is integrated in electronic white cane system, which requires a real time system. The proposed approach uses a few samples with small size, to classify floor state into three classes, even surface, ascending and descending staircases. In this context, frequency representation is employed to extract relevant features. Feature measurement are used to estimate probability distributions, based on histogram method. Then, Masson method that integrates Goodman's intervals, is used to infer possibility distributions from probability distributions. Based on obtained results, the proposed method of floor state recognition provides good performances especially when information closeness is used in similarity measure.

6. REFERENCES [1] D. Yuan and R. Manduchi, “Dynamic Environment Exploration Using a Virtual White Cane,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), Vol. 1, 2005, pp. 243–249. [2]M. D. Adams, “On-Line Gradient Based Surface Discontinuity Detection for Outdoor Scanning Range Sensors,” IEEE/RSJ International Conference on Intelligent Robots and Systems, 2001, pp. 1726–1731. [3]M. Lee and S. Lee, “Design and analysis of an infrared range sensor system for floor-state estimation,” Journal of Mechanical Science and Technology, 2011, pp. 1043–1050. [4] S. Se and M. Brady, “Vision-based Detection of Stair-cases,” Fourth Asian conference on computer Vision, Vol. I, 2000, pp. 535–540. [5] I. E. Dror, M. Zagaeski and C. F. Moss, “Three-dimensional target recognition via sonar: a neural network model,” Neural Networks, Vol. 8, No. 1, 1995, pp. 149–160. [6] J. M. Oria and A. M. G. Gonzalez, “Object recognition using ultrasonic sensors in robotic application,” IECON, 19th Annual Conference of IEEE Industrial Electronics, 1993, pp. 1927–1931.

[7] O. Bozma and R.Kuc, “Building a sonar map in a specular environment using a single Mobile sensor,” IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE. Vol. 13, No. 12, 1991, pp. 1260–1269. [8] M. I. Ecemis and P. Gaudiano, "Object recognition with ultrasonic sensors", IEEE International Symposium on Computational Intelligence in Robotics and Automation, (CIRA '99), pp. 250-255, Monterey, CA, 1999. [9] R. Kohavi and G. H. John, "Wrappers for feature subset selection",Artif.Intell., pp. 273--324, 1997. [10] N. Sokolovska, O. Cappé and F. Yvon, "Sélection de caractéristiques pour les champs aléatoires conditionnels par pénalisation L1", Vol 50, N°3, pp. 139--171, 2009. [11] W. Ezzidine, " Segmentation itérative d'images par propagation de connaissances dans le domaine possibiliste : Application à la détection de tumeurs en imagerie mammographique", Thèse de Doctorat d'université européenne de Bretagne : Télécom Bretagne, pp. 77, 2012. [12] M. H. Masson and T. Denoeux, "Inferring a possibility distribution from empirical data", Fuzzy Sets and Systems, Vol. 157, N°. 3, pp. 319--340, 2006. [13] S.A. Bouhamed, I.K. Kallel, D.S. Masmoudi, "Stair Case Detection And Recognition Using Ultrasonic Signal", 36th International Conference on Telecommunications and Signal Processing (TSP), pp. 672--676, Rome, 2013, [14] D. Dubois, H. Prade, and S. Sandri, "On Possibility/Probability transformations", dans le livre FuzzyLogic, R.Lowen and M. Roubens (eds.), Kluwer AcademicPublishers, pp. 103--112, 1993. [15] G. J. KLIR, "Information-preserving probability-possibility transformations: recent developments", Fuzzy Logic, pp. 417--428, 1993. [16] M. R. Civanlar, H. J. Trussell, "Constructing membership functions using statistical data", Fuzzy Sets and Systems, Vol. 18, pp. 1--13, 1986. [17] S. Sandri, "La combinaison de l'information incertaine et ses aspects algorithmiques", Thèse de Doctorat,Université P. Sabatier, Toulouse, pp . 254, 1991. [18] D. Dubois, H. Prade, and S. Sandri. "On possibility/probability transformations", In Proceedings of the Fourth Int. Fuzzy Systems Association World Congress (IFSA’91), Brussels, Belgium, pp. 50--53, 1991. [19] L.A. Goodman, "On simultaneous confidence intervals for multinomial proportions", Technometrics, Vol. 7, N°. 2, pp. 247--254, 1965. [20] I. Jenhani, N. Ben Amor, Z. Elouedi, S. Benferhat and K. Mellouli, "Information Affinity : A New Similarity Measure for Possibilistic Uncertain Information", 9th ECSQARU, Hammamet, Tunisia, Vol. 4724, pp. 840-852, 2007. [21] M. Higashi, G.J. Klir, "On the notion of distance representing information closeness: Possibility and probability distributions". Int. J. General Systems, Vol. 9, pp. 103--115, 1983. [22] M. Higashi, G.J. Klir, "Measures of uncertainty and information based on possibility distributions", Int. J. General Systems, Vol. 9, N°. 1, pp. 43--58, 1983. [23] W.L. May and W.D. Johnson. A SAS macro for constructing simultaneous confidence intervals for multinomial proportions. Computer Methods and Programs in Bio medecine, Vol. 53, pp. 153--162, 1997.

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