GAUSSIAN MIXTURE NOISED RANDOM FRACTALS WITH ADVERSARIAL LEARNING FOR AUTOMATED CREATION OF VISUAL OBJECTS

Abstract

Because of the self-similarity properties of nature, fractals are widely adopted as generators of natural object multimedia contents. Unfortunately, fractals are difficult to control due to their iterated function systems, and traditional researches on fractal generating visual objects focus on mathematical manipulations. In Generative Adversarial Nets (GANs), visual object generators can be automatically guided by a single image. In this work, we explore the problem of guiding fractal generators with GAN. We assume that the same category of fractal patterns is produced by a group of parameters of initial patterns, affine transformations and random noises. Connections between these fractal parameters and visual objects are modeled by a Gaussian mixture model (GMM). Generator trainings are performed as gradients on GMM instead of fractals, so that evaluation numbers of iterated function systems are minimized. The proposed model requires no mathematical expertise from the user because parameters are trained by automatic procedures of GMM and GAN. Experiments include one 2D demonstration and three 3D real-world applications, where high-resolution visual objects are generated, and a user study shows the effectiveness of artificial intelligence guidances on fractals.