A Geometrical Perspective on Image Style Transfer With Adversarial Learning

Xudong Pan, Mi Zhang, Daizong Ding, Min Yang

Abstract: Recent years witness the booming trend of applying generative adversarial nets (GAN) and its variants to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">image style transfer</i> . Although many reported results strongly demonstrate the power of GAN on this task, there is still little known about neither the interpretations of several fundamental phenomenons of image style transfer by generative adversarial learning, nor its underlying mechanism. To bridge this gap, this paper presents a general framework for analyzing style transfer with adversarial learning through the lens of differential geometry. To demonstrate the utility of our proposed framework, we provide an in-depth analysis of Isola <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> ’s pioneering style transfer model <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pix2pix</i> <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> and reach a comprehensive interpretation on their major experimental phenomena. Furthermore, we extend the notion of generalization to conditional GAN and derive a condition to control the generalization capability of the pix2pix model. From a higher viewpoint, we further prove a learning-free condition to guarantee the existence of infinitely many perfect style transfer mappings. Besides, we also provide a number of practical suggestions on model design and dataset construction based on these derived theoretical results to facilitate further researches.