Accelerating ADMM for efficient simulation and optimization

The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications, including physical simulation, geometry processing, and image processing. However, ADMM can take a long time to converge to a solution of high accuracy. Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization. In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations. We show that in the general case, ADMM is a fixed-point iteration of the second primal variable and the dual variable, and Anderson acceleration can be directly applied. Additionally, when the problem has a separable target function and satisfies certain conditions, ADMM becomes a fixed-point iteration of only one variable, which further reduces the computational overhead of Anderson acceleration. Moreover, we analyze a particular non-convex problem structure that is common in computer graphics, and prove the convergence of ADMM on such problems under mild assumptions. We apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed

Distinguishing Computer-generated Graphics from Natural Images Based on Sensor Pattern Noise and Deep Learning

Computer-generated graphics (CGs) are images generated by computer software. The~rapid development of computer graphics technologies has made it easier to generate photorealistic computer graphics, and these graphics are quite difficult to distinguish from natural images (NIs) with the naked eye. In this paper, we propose a method based on sensor pattern noise (SPN) and deep learning to distinguish CGs from NIs. Before being fed into our convolutional neural network (CNN)-based model, these images---CGs and NIs---are clipped into image patches. Furthermore, three high-pass filters (HPFs) are used to remove low-frequency signals, which represent the image content. These filters are also used to reveal the residual signal as well as SPN introduced by the digital camera device. Different from the traditional methods of distinguishing CGs from NIs, the proposed method utilizes a five-layer CNN to classify the input image patches. Based on the classification results of the image patches, we deploy a majority vote scheme to obtain the classification results for the full-size images. The~experiments have demonstrated that (1) the proposed method with three HPFs can achieve better results than that with only one HPF or no HPF and that (2) the proposed method with three HPFs achieves 100\% accuracy, although the NIs undergo a JPEG compression with a quality factor of 75.Comment: This paper has been published by Sensors. doi:10.3390/s18041296; Sensors 2018, 18(4), 129