An explainable, efficient and lightweight method for texture generation, called TGHop (an acronym of Texture Generation PixelHop), is proposed in this work. Although synthesis of visually pleasant texture can be achieved by deep neural networks, the associated models are large in size, difficult to explain in theory, and computationally expensive in training. In contrast, TGHop is small in its model size, mathematically transparent, efficient in training and inference, and able to generate high quality texture. Given an exemplary texture, TGHop first crops many sample patches out of it to form a collection of sample patches called the source. Then, it analyzes pixel statistics of samples from the source and obtains a sequence of fine-to-coarse subspaces for these patches by using the PixelHop++ framework. To generate texture patches with TGHop, we begin with the coarsest subspace, which is called the core, and attempt to generate samples in each subspace by following the distribution of real samples. Finally, texture patches are stitched to form texture images of a large size. It is demonstrated by experimental results that TGHop can generate texture images of superior quality with a small model size and at a fast speed.

A non-parametric interpretable texture synthesis method, called the NITES method, is proposed in this work. Although automatic synthesis of visually pleasant texture can be achieved by deep neural networks nowadays, the associated generation models are mathematically intractable and their training demands higher computational cost. NITES offers a new texture synthesis solution to address these shortcomings. NITES is mathematically transparent and efficient in training and inference. The input is a single exemplary texture image. The NITES method crops out patches from the input and analyzes the statistical properties of these texture patches to obtain their joint spatial-spectral representations. Then, the probabilistic distributions of samples in the joint spatial-spectral spaces are characterized. Finally, numerous texture images that are visually similar to the exemplary texture image can be generated automatically. Experimental results are provided to show the superior quality of generated texture images and efficiency of the proposed NITES method in terms of both training and inference time.