This paper describes a new framework, called repulsive attractive (RA) network for baseline extraction on document images. The RA network is an energy minimizing dynamical system, which interacts with the document text image through the attractive and repulsive forces defined over the network components and the document image. Experimental results indicate that the network can successfully extract the baselines under heavy noise and overlaps between the ascending and descending portions of the characters of adjacent lines. The proposed framework is applicable to a wide range of image processing applications, such as curve fitting, segmentation and thinning.