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International Journal of Scientific and Research Publications, Volume 3, Issue 2, February 2013 701 ISSN 2250-3153 Proof: Let F be a fuzzy closed fuzzy open set of the subspace f(X) of Y. Then X x F is fuzzy closed fuzzy open set of the subspace X x f(X) of the fuzzy product space X x Y. Since g(X) is a subset of X x f(X), (X x F) ∩ g(X) is a fuzzy closed fuzzy open set of the subspace g(X) of X x Y. By theorem 3.1,g -1 ((Xx F) ∩ g(X)) = g -1 ((XxF) = f -1 (F) that f -1 (F) is a fuzzy g-closed fuzzy g-open set of X .Hence by the theorem 3.1, f is fuzzy set GO-connected. Theorem 3.8: Let f: (X,τ) → (Y,σ) be a fuzzy weakly g-continuous surjective mapping, and then f is fuzzy set GO-connected. Proof: Let V be any fuzzy closed open set of Y. Since f is fuzzy weakly g-continuous, f -1 (V) ≤ gint (f -1 (cl(V))) = gint(f -1 (V)).And so f - 1 (V) is fuzzy g-open set of X. Moreover we have gcl(f -1 (V)) ≤ gcl(f -1 (int(V))) ≤ f -1 (V).This shows that f -1 (V) is fuzzy g-closed set of X. Since f surjective by the theorem 3.1, f is fuzzy set GO-connected mapping. Defination3.2: A fuzzy topological space (X,τ) is said to fuzzy extremely disconnected if the closure of every fuzzy open set of X is fuzzy open in X. Theorem 3.9: Let (Y,σ) be a fuzzy extremely disconnected space. If a mapping f: (X,τ) → (Y,σ) is fuzzy set GO-connected then f is fuzzy almost g-continuous. Proof: Let V is a fuzzy open set of Y .Then gcl(V) is a fuzzy closed open set in Y. Since f is fuzzy set GO-connected f -1 (cl(V)) is fuzzy g-closed g-open set of X. Therefore f -1 (V)≤ f -1 (cl(V))≤gint f -1 (cl(V))≤ f -1 (gint(cl(V))).Hence f is fuzzy almost g-continuous. Corollary3.1: Let (Y,σ) be a fuzzy GO- extremely disconnected space. If a mapping f: (X,τ) → (Y,σ) is fuzzy set GO-connected then f is fuzzy weakly g-continuous. REFERENCES [1] Azad K.K. , on fuzzy semi continuity fuzzy almost continuity and fuzzy weakly continuity, J. Math. .Anal. Appl. 82(1981),14-32. [2] Chae G.I., Thakur S.S. and Malviya R. Fuzzy set connected functions, East Asian Math. J. 23(1)(2007),103-110. [3] Chang C.L. Fuzzy topological spaces. J. Math. Anal. Appl. 24 (1968), 182-190. [4] Fateh D.S. and Bassan D.D. Fuzzy connectedness and its stronger forms J. Math.. Anal. Appl. 111 (1985)449-464. [5] Kwak J.H. set connected mappings Kyungbook Math. J. 11(1971), 169-172. [6] Maheshwari S .N., Thakur S. S. and Malviya R. Connectedness between fuzzy sets, J. Fuzzy Math 1 (4) (1993),757-759. [7] Mishra M.K. ,et all on “ Fuzzy super closed set” International Journal International Journal of Mathematics and applied Statistics Vol-3,no-2(2012)143-146. [8] Mishra M.K. ,et all on “ Fuzzy super continuity” International Review in Fuzzy Mathematics ISSN : 0973-4392 July –December2012Accepted. [9] Mishra M.K., Shukla M. “Fuzzy Regular Generalized Super Closed Set” Accepted for publication in International Journal of Scientfic and Research Publication ISSN2250-3153.December 2012.(Accepted). [10] Noiri T. On set connected mappings Kyungpook Math. J. 16(1976), 243-246. [11] Pu. P.M. and Liu Y.M. Fuzzy topology I. Neighborhood structure of a fuzzy point Moore-Smith convergence.J.Math.Anal.Appl.76 (1980), 571-599. [12] Pu. P.M. and Liu Y.M. Fuzzy topology II. Product and Quotient spaces. J. Math. Anal. Appl.77(1980) 20-37. [13] Thakur S. S. and Malviya R. Generalized closed sets in fuzzy topology, Math. Notae 38(1995) 137-140 [14] Thakur S. S. and Malviya R. Fuzzy gc-Irresolute Mappings , Proc. Math. Soc. BHU 11(1995),184-186 [15] Yalvac T.H. Fuzzy sets and functions in fuzzy spaces J. Math. Anal. Appl. 126 (1987), 409-423 [16] Zadeh L. A. Fuzzy sets Inform and control 6 (1965), 339-8-358. www.ijsrp.org
International Journal of Scientific and Research Publications, Volume 3, Issue 2, February 2013 702 ISSN 2250-3153 Image Filtering Techniques Used for Monitoring Driver Fatigue: A Survey Abhishek Bhardwaj, Pareesha Aggarwal, Rishi Kumar, Nidhi Chandra Amity School of Engineering and Technology, Amity University, Noida, U.P, India Abstract- Driver fatigue is one of the important factors that cause traffic accidents, and the increasing number of accidents due to lessened driver’s acuity and diligence level has become a problem of serious concern. Therefore, how to avoid this problem has become a topic of discussion. In order to detect and remove this cause of road accident many driver fatigue detection methods have been proposed which can detect the mind state of driver such as drowsiness or inattention, for generating some warning alarms to alert the driver. In this paper we have discussed some of the method that can be used to detect the driver’s fatigue. And on the basis of our study, we have proposed a new technique that can improve the results of the earlier discussed methods. Index Terms- Driver Fatigue Detection; kalman Filter; Uncented Kalman Filter; PERCLOS I I. INTRODUCTION n the last 10 years to avoid many accidents due to driver’s fatigue many countries all over the world have begun to pay attention to driver safety problem and to investigate the mental state of driver relating to driver safety. Driver’s state of mind and fatigue is one of the most important reasons of traffic accidents. Drivers with a lessened diligence level suffer from a marked decline in their abilities of perception, recognition, and vehicle control, which poses serious danger to their own life and the lives of other people. The study says that in France, the National Police Administration concludes that 14.9 percent of accidents causing human hurt and 20.6 percent of accidents causing death are fatigue related. According to statistics the leading cause of fatal or injury-causing traffic accidents is driver fatigue. Therefore, how to avoid fatigue driving efficiently can help prevent many accidents, and also save money and reduce personal suffering. Without any solution this problem will increase with time. So, there is a need of designing some systems that can detect the drowsiness or inattention of the driver and can generate some warning alarms to alert the driver and the other people in the vehicle. In the recent years many techniques and methods which can detect whether the driver is tired have been proposed by researchers and few of them have been implemented. But, due to a variety of factors, despite the success of existing systems and approaches for extracting characteristics of a driver using computer aided technologies, and other current efforts in this area, it is a challenging issue to develop a driver fatigue detection system. The one of the main factor is the variety of eye moving speed of driver, external illumination interference and realistic lighting conditions. In the realistic lighting condition the eye motion is highly nonlinear. So the use of driver fatigue detection method that is based on linear movement of driver eye is very difficult in real scenario. In references [3, 6], Qiang Ji et al. have made significant improvements of facial fatigue detection over existing techniques. However, their methods need infrared (IR) eye detector, or bright pupils and steady illumination. Their eyetracking method that used Kalman filtering is a linear system estimation algorithm. In fatigue detection system, the eye motion has the high nonlinearity of the likelihood model that the standard Kalman filter is no longer optimal in realistic driving environments. To tackle some of those problems, in reference [1], ZHANGs have also proposed a new real-time eye tracking based on a nonlinear unscented Kalman filter for diver fatigue detection. But these proposed systems/detectors works on IR image which is a problem. To tackle this problem we have proposed a system that can be used without IR illuminator that illuminates a person’s face and use an IR-sensitive camera to acquire an image. Further sections are organized as: description of Eye tracking with Kalman filtering, Mean shift eye tracking, Kalman filteringbased fatigue detection system, proposed driver fatigue detection system in section II, III, IV and V respectively. Finally the future work and a conclusion of the discussion are provided in last section. II. INTRODUCTION In references [3, 6] Qiang Ji et al., says that the motion of a pupil at each instance can be described using its position and velocity. Let (s t, r t ) parameters be the horizontal and vertical positions of the pupil measured in pixels and (u t , v t ) be the horizontal and vertical components of the velocity of pupil measured in deg/s. thus, the state vector at time t can be represented as X t = (s t r t u t v t ) t . The system can therefore be modeled as X (t+1) = $ X t + w t , (1) Where, w t represents system perturbation. They further assumed that a fast feature extractor estimates Y t = (^s t, ^r t ) as the pupil position at time t. Therefore, the measurement model in the form needed by the Kalman filter is www.ijsrp.org
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