Exemplar-based texture synthesis is defined as the process of generating, from an input texture sample, new texture images that are perceptually equivalent to the input. Efros and Freeman's method is a non-parametric patch-based method which computes an output texture image by quilting together patches taken from the input sample. The main innovation of their work relies in the stitching technique which significantly reduces the transition effect between patches. In this paper, we propose a detailed analysis and implementation of their work. We provide a complete mathematical description of the linear programing problem used for the quilting step as well as implementation details. Additionally we propose a partially parallel version of the quilting technique. https://doi.org/10.5201/ipol.2017.171