Supervised binarization is a method that learn pre-classified data in order to classify a particular pixel whether it is belong to a foreground or a background. The performance of supervised approach is usually better than that of unsupervised ones since it is designed to use classification criteria determined by ground truth data. By using this approach, orientations of local neighbourhood grey level information that are based on eight orientations have been developed to characterize a particular pixel. These orientations are combined together since it may reduce the risk of making a particular poor selection of these orientations. In order to ensemble all orientations, heuristic method have been used to determine weights for each orientation. However, determination of weights using heuristic method is not efficient and not enough as it provides incomplete information. Furthermore, these orientations might be influenced by other different factors. This will lead to wrongly assigning weights to a particular orientation. Hence, determination of weights to combine eight orientations to characterize a particular pixel by using QR decomposition method is proposed. By using QR decomposition method, computational complexity is low and weights obtained for each orientation are optimal. In order to test the proposed approach, 21 document images from DIBCO2009 and DIBCO2011 databases and 55 retinal images from DRIVE and STARE databases have been used. The results of the proposed method clearly show significant improvement where higher average accuracy is obtained compared to by using heuristic method.