Automatic synthesis of visually pleasant texture that resembles exemplary texture finds applications in computer graphics. We have witnessed amazing quality improvement of synthesized texture in the last 5-6 years due to the resurgence of neural networks. Texture synthesis based on deep learning (DL), such as convolutional neural networks (CNNs) and generative adversarial networks (GANs), yield visually pleasant results. DL-based methods learn transform kernels from numerous training data through end-to-end optimization.  However, these methods have two main shortcomings: 1) lack of mathematical transparency and 2) higher training and inference complexity.

To address these shortcomings, we investigate a non-parametric and interpretable texture synthesis method, called NITES, in this work. NITES is mathematically transparent and efficient in training and inference.  NITES consists of three steps. First, it analyzes the texture patches (as training samples) which are cropped from the input exemplary texture image to obtain its joint spatial-spectral representations. Second, the probabilistic distributions of training samples in the joint spatial-spectral spaces are characterized. The sample distribution in the core subspace was carefully studied, which allows us to build a core subspace generation model. Furthermore, a successive subspace generation model was developed to build a higher-dimensional subspace based on a lower-dimensional subspace. Finally, new texture images are generated by mimicking probabilities and/or conditional probabilities of the source texture patches. In particular, we adopt a data-driven transform, known as the channel-wise (c/w) Saab trans-form, which provides a powerful representation in the joint spatial-spectral space. The c/w Saab transform is derived from the successive subspace learning (SSL) theory.

Experimental results show the superior quality of generated texture images and efficiency of the proposed NITES method in terms of both training and inference time. It can generate visually pleasant texture images effectively, including some unseen patterns. And the time to generate a new texture image is much faster than existing CNN-based methods.

[1] Lei, X., Zhao, G., & Kuo, C. C. J. (2020). NITES: A Non-Parametric Interpretable Texture Synthesis Method. arXiv preprint arXiv:2009.01376.