“…A great deal of existing works synthesize texture using either parametric [1,2], nonparametric [3][4][5], or patch-based [6][7][8][9] approaches. Among these methods, optimization-based methods [10,12,13], which belong to a kind of patch-based methods, have been proved very successful in terms of the quality of the synthesized results, and have been efficiently applied in image and video synthesis [10,12], solid texture synthesis [13], inverse texture synthesis [18], and geometry-surface texture synthesis [11]. However, the synthesis procedure of these optimization-based methods is done by minimizing a global texture energy function, which is a time and memory consuming process, and it limits the wider applications of optimization-based methods.…”