This paper presents a general algorithm for pedestrian detection by on-board monocular camera which can be applied to cameras of various view ranges. Under the assumption that motion of background can be nearly approximated as a linear function, the Spatio-Temporal MRF (S-T MRF) model segments foreground objects. The foreground objects contain both pedestrian and non-pedestrian urban objects, verification was conducted by a cascaded classifier. However, the segmentation results based on motion were not exactly fit into pedestrian on the image so that shrunk or inflated pedestrian were generated. This causes errors on extracting pedestrian trajectory. For precise positioning, we implemented two types of feedback algorithm for ROI correction using the Kalman filter and the voting result of Motion-classifier and HOG-classifier. We confirmed that those ROI Corrections successfully extract precise area of pedestrian and decrease the false negative rate. Elaborately extracted pedestrian trajectory could be used as a useful source for predicting collision to pedestrian.