Vision-based on-road vehicle detection is one of the key techniques in automotive driver assistance systems.However, due to the huge within-class variability in vehicle appearance and environmental changes, it remains a challenging task to develop an accurate and reliable detection system. In general, a vehicle detection system consists of two steps. The candidate locations of vehicles are found in the Hypothesis Generation (HG) step, and the detected locations in the HG step are verified in the Hypothesis Verification (HV) step. Since the final decision is made in the HV step, the HV step is crucial for accurate detection. In this paper, we propose using a reduced multivariate polynomial pattern classifier (RM) for the HV step. Our experimental results show that the RM classifier outperforms the well-known Support Vector Machine (SVM) classifier, particularly in terms of the fast decision speed, which is suitable for real-time implementation. 640 research area aiming to prevent car accidents and reduce the severity of injuries [1] . Generally, a vehicle detection system can be classified into either an active system or a passive system based on the type of sensors used. An active system makes use of active sensors such as laser and radar [19] for imaging. Although the active system can obtain vehicle information directly, it has drawbacks such as low resolution, interference with other active systems, and high cost. On the other hand, a passive system which uses an optical camera is more cost effective than an active system. Moreover, it can be applied to wider applications such as lane detection, traffic sign recognition and object identification than that of an active system. In the passive vehicle detection research, existing vehicle detection systems adopt methods from fields such as pattern classification [7][8] , optical flow [6] , background subtraction [9] and stereo vision [5] . Even though many researchers tried to make robust vehicle detection system through a variety of methods, a credible detection system is yet to be available due to the huge within-class variability in vehicle appearance and environmental variations. There are many kinds of vehicles in terms of appearance such as shape, size and color. Also, complex outdoor environments such as illumination conditions, weather conditions and cluttered backgrounds can be critical for accurate vehicle detection [1] . . The purpose of the HG step is to find out candidate locations of vehicles. After the HG step, the HV step is performed to verify the detected candidate vehicles from the HG step.The HG step can be classified into three categories. First, knowledge-based methods use information which we already known such as symmetry [10] , color [11] , shadow [12] and corners [13] information. Second, stereo-based methods take advantage of 3D information such as Inverse Perspective Mapping (IPM) [14] and Disparity Map [15] but it has the shortcoming of high computational cost. Third, motion-based methods use the information of moving object s...