Baselines estimation is a critical preprocessing step for many tasks of document image processing and analysis. The problem is very challenging due to arbitrarily complicated page layouts and various types of image quality degradations. This paper proposes a method based on slope fields recovery for curved baseline extraction from a distorted document image captured by a hand-held camera. Our method treats the curved baselines as the solution curves of an ordinary differential equation defined on a slope field. By assuming the page shape is a smooth and developable surface, we investigate a type of intrinsic geometric constraints of baselines to estimate the latent slope field. The curved baselines are finally obtained by solving an ordinary differential equation through the Euler method. Unlike the traditional text-lines based methods, our method is free from text-lines detection and segmentation. It can exploit multiple visual cues other than horizontal text-lines available in images for baselines extraction and is quite robust to document scripts, various types of image quality degradation (e.g., image distortion, blur and non-uniform illumination), large areas of non-textual objects and complex page layouts. Extensive experiments on synthetic and real-captured document images are implemented to evaluate the performance of the proposed method.