Elsevier

Knowledge-Based Systems

Volume 38, January 2013, Pages 37-47
Knowledge-Based Systems

Linear fuzzy space based road lane model and detection

https://doi.org/10.1016/j.knosys.2012.01.002Get rights and content

Abstract

In this paper, we propose a new road lane model based on linear fuzzy space mathematics, coupled with a robust road lane detection method using fuzzy c-means clustering. The fuzzy line based road lane model presented here describes a lane as a set of fuzzy collinear fuzzy points. The proposed algorithm for road line detection is able to deal with imprecise data and enables reduced computational complexity (proportional to the number of fuzzy points multiplied by the number of fuzzy lines) versus a standard Hough transformation. Experimental results show that the proposed method is fast, and robust enough for use in real-time applications. The proposed method has been implemented as an Android-based mobile phone application.

Introduction

Demand for traffic safety systems designed to minimize the risk of accidents is increasing. Lane detection plays a significant role in driver assistance systems, and can help to estimate the geometry of the road ahead. According to the International Data Corporation, nearly 300 million smart phones were shipped in 2010; and the smart phone market is expected to grow to 450 million units in 2011. Smart phones are often equipped with a digital camera, GPS and WiFi capability, and represent promising devices for driver assistance systems. Thus, the development and implementation of efficient imprecise space representation models capable of feature extraction and detection in smart phones is increasingly relevant.

A typical complete model-based lane detection system consists of four parts: (1) lane modeling, (2) feature extraction, (3) detection, and (4) tracking. Lane modeling involves the development of mathematical descriptions to represent road lanes; while feature extraction involves identification of particular lane features, such as color, texture or edge, etc. During the detection stage, the lane model is then fit with the set of extracted features. Finally, lane tracking is applied to follow lane changes using reduced system complexity, which is achieved by reducing the search region.

Although the Hough transform [1] remains one of the most commonly applied lane detection techniques [2], [3], [4]; other techniques have also been applied to this problem. For example, Pomerleau [5] used neural networks in their ALVINN system; while Kang and Jung [6] used connected-component analysis and dynamic programming. In addition, probabilistic methods, such as Maximum a posteriori estimation evaluated using the Metropolis algorithm, have been reported for use in lane detection systems [7], [8]. More recently, Wang et al. [9] proposed the use of fuzzy methods during the feature extraction stage for automatic brightness compensation. With respect to the line model, several different approaches have been reported in the literature, including representing road lane models as: a straight line [10]; B-spline [11]; parabola [4]; or hyperbola [12]. A more detailed survey of lane detection strategies has been published [4]. A common component of nearly all lane detection systems is the use of specialized hardware or a PC, coupled with a vehicle mounted video camera.

Common problems in lane detection arise from the fact that discrete space (digital raster image) is used for real-world element representation, while the spatial relations used apply the rules of continual space. For example, lines are represented as a set of discrete points that typically do not have to be collinear, in contradiction with the definition of a line. In addition, because real-world objects are mapped to a digital raster image via a variety of sensors, the resulting image is only an approximation of the real-world object. Thus, imperfections in either the image data or the edge detector may result in missing points or pixels on lines, as well as spatial deviations between an ideal line and the set of imprecise points obtained from the edge detector. The overall effect is an image containing varying levels of geometric distortion.

This present study focuses on modeling basic planar imprecise geometry objects and the relationships between them. The application of these models to spatial data management systems is then described, and results are briefly presented.

An overview of studies in the literature dealing with imprecise point object modeling has been published [13].

In general, three basic approaches to spatial data uncertainty/imprecision are recognized: (1) Exact Models [14], [15], [16], [17], [18], [11], (2) Probabilistic Models [7], [8], [19], [20], [21], [22], [23], and (3) Fuzzy Models [13], [24], [25], [26], [27], [28], [29], [30], [31].

One of the earliest and still most commonly used techniques for feature extraction is known as the Generalized Hough transformation, proposed by Duda and Hart [1] in 1972. The Generalized Hough transformation is based on a voting procedure carried out in parameter space. Line candidates are obtained as local maxima of the Hough transformation, which highly depend on spatial relation co-linearity.

Based on our previous results [13], we introduce here a novel mathematical model of fuzzy lines, as well as models of basic spatial relations, including: coincidence, between and collinear. Practical applications of the results obtained in this paper are based on simple, yet effective, modeling of imprecise data using fuzzy sets, which enables the gradual estimation of object spatial relations. Instead of using a set of discrete 2D points, we propose the use of a set of fuzzy points, which makes road lane detection more robust then the crisp approach, due to the incorporation of a gradual estimation of feature spatial relations.

This work consists of six sections (Sections 1 Introduction, 2 The road lane model, 3 Road feature extraction, 4 Road lane detection, 5 Experiments, 6 Conclusion). Following this introduction (Section 1), a novel road lane mathematical model is presented, along with definitions of basic spatial fuzzy relations (Section 2). After that, a new algorithm for road feature extraction is described (Section 3), followed by a novel road lane detection algorithm based on fuzzy relations defined in linear fuzzy space (Section 4), and experimental results (Section 5). Finally, concluding remarks and future research directions are discussed (Section 6).

Section snippets

The road lane model

The conceptual scheme proposed in this paper, consisting of a driver assistance system integrated into a smart phone, is illustrated in Fig. 2.1. The software components are divided in four functional groups: (1) image capture, (2) road feature extraction, (3) road lane detection, and (4) a decision module. The focus of the present work is on road feature extraction and road lane detection.

Capturing images on Android based smart phones is a part of the Android operating system. The common

Road feature extraction

In this work, we propose a modified edge extraction method for road feature extraction. The best way to describe a road is to identify lane marks, which define lanes in almost any well-painted road. Usually, this is done by applying some well-known edge extraction method, such as the Canny and Sobel edge detector. Results from these methods usually contain relatively large sets of discrete points. Instead of using precise discrete points, we propose the use of fuzzy points. Also, we apply edge

Road lane detection

In this section, we describe a novel algorithm for fuzzy line detection from digital raster images (FLDetector). The algorithm is implemented as a modified fuzzy c-means algorithm for clustering sets of fuzzy points. Each fuzzy point belongs to a fuzzy line (cluster centroid) according to a fuzzy relation fuzzy collinear. This method allows one fuzzy point to belong to two or more fuzzy lines.

Experiments

The proposed approach has been implemented as a Java class library and tested in two environments: (1) a Java application running on a PC using a data set; and (2) a Java application running on an Android 2.1 platform. The same set of 50 images taken by a smart phone camera was applied. In addition, our new approach was compared with the classical Hough transform using the same feature extraction algorithm. The aim of these experiments was to check the correctness of our proposed approach

Conclusion

In this work, we present a model of imprecise road lanes, based on our previously published model of fuzzy imprecise points [13], as the union of a linear combination of two fuzzy points. Using this model, a fuzzy line can be represented with only two fuzzy points, providing a simple, yet descriptive extension of the precise ideal line. Imprecise spatial relations applied in this paper are based on fuzzy relations between fuzzy points and fuzzy lines, while the proposed algorithm for line

Acknowledgments

Results presented in this paper are a part of research conducted within the Project “Technology Enhanced Learning Infrastructure in Serbia”, Grant No. II 47003 of the Ministry of Education and Science of the Republic of Serbia and Provincial Secretariat for Science and Technological Development of Vojvodina. The third author was supported by Project Number: MPNRS 174009.

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