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Multiresolution segmentation (MRS) is one of the most commonly used image segmentation algorithms in the remote-sensing community. This algorithm has three user-defined parameters: scale, shape, and compactness. The scale parameter (SP) is the most crucial one in determining the average size of the image segments generated. Since setting this parameter typically requires a trial-and-error process, automatically estimating it can expedite the segmentation process. However, most of automatic approaches are still iterative and can lead to a time-consuming process. In this article, we propose a new, non-iterative framework for estimating the SP with an emphasis on extracting individual urban buildings. The basis of the proposed method is to investigate the feasibility of associating the size of urban buildings with a corresponding ‘optimal’ (or at least reasonable) SP using an explicit mathematical equation. Using the proposed method, these two variables are related to each other by constructing a mathematical (regression) model. In this framework, the independent variables were chosen to be the typical size of buildings in a given urban area and the spatial resolution of the image under consideration; and the dependent variable was chosen to be the corresponding optimal SP. To assess the potential of the proposed approach, two regression models that yielded explicit equations (i.e. degree-2 polynomial (DP), and regression tree (RT)) were employed. In addition, as a sophisticated and versatile nonlinear model, support vector regression (SVR) was utilized to further measure the performances of DP and RT models compared with it. According to the comparisons, the DP model was selected as a representative of the proposed approach. In the end, to evaluate the proposed methodology, we also compared the results derived from the DP model with those derived from the Estimation of Scale Parameter (ESP) tool. Based on our experiments, not only did the DP model produce acceptable results, but also it outperformed ESP tool in this study for extracting individual urban buildings.