Based on the greedy-point removal (GPR) scheme of Demaret and Iske, a simple yet highly effective framework for constructing triangle-mesh representations of images, called GPRFS, is proposed. By using this framework and ideas from the error diffusion (ED) scheme (for mesh-generation) of Yang et al., a highly effective mesh-generation method, called GPRFS-ED, is derived and presented. Since the ED scheme plays a crucial role in our work, factors affecting the performance of this scheme are also studied in detail. Through experimental results, our GPRFS-ED method is shown to be capable of generating meshes of quality comparable to, and in many cases better than, the state-of-the-art GPR scheme, while requiring substantially less computation and memory. Furthermore, with our GPRFS-ED method, one can easily trade off between mesh quality and computational/memory complexity. A reduced-complexity version of the GPRFS-ED method (called GPRFS-MED) is also introduced to further demonstrate the computational/memory-complexity scalability of our GPRFS-ED method.