This article describes how attractive structures are always correspond to objects of interest in human perception, thus extracting attractive structures is a fundamental problem in many image analysis tasks, which is of great practical importance. In this article, the authors propose a novel nonuniform method to maintain the attractive structures of images while removing their meaningless details. Different from the existing norm based operators that are a uniform method proposed on regular image grids, our nonuniform method is not limited to special type of datum and grid structure, which has better performance for image analysis tasks. Besides, a strategy based on proximal algorithms is put forward to obtain fast convergence in practice due to the nonconvex and nonsmooth property of the corresponding optimization. Though the model with our proposed nonuniform operator can be used for various applications, the authors chose the tasks of image smoothing and saliency detection to demonstrate the good performances of our nonuniform method and show its superiority against other state-of-the-art alternatives.