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In this paper, we propose a vision-based vehicle detection system. We use a method composed of a hypothesis generation (HG) step and a hypothesis verification (HV) step, following the general approach to vision-based vehicle detection systems. In the HG step, the system extracts hypotheses using shadow regions that appear under vehicles. In the HV step, the system classifies feature vectors extracted from hypotheses to determine whether those hypotheses are vehicles. Along with the histogram of oriented gradients (HOG), we propose and implement a new type of feature vector, i.e., HOG symmetry vectors, in this paper. We also propose a new classification method that uses data importance in the HV step. The data importance value is based on the locations of hypotheses to prioritize hypotheses that have greater risks of accident. Experimental results show the strong performance of our proposed system.