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Universal style transfer (UST) infuses styles from arbitrary reference imagesinto content images. Existing methods, while enjoying many practical successes,are unable of explaining experimental observations, including differentperformances of UST algorithms in preserving the spatial structure of contentimages. In addition, methods are limited to cumbersome global controls onstylization, so that they require additional spatial masks for desiredstylization. In this work, we provide a systematic Fourier analysis on ageneral framework for UST. We present an equivalent form of the framework inthe frequency domain. The form implies that existing algorithms treat allfrequency components and pixels of feature maps equally, except for thezero-frequency component. We connect Fourier amplitude and phase with Grammatrices and a content reconstruction loss in style transfer, respectively.Based on such equivalence and connections, we can thus interpret differentstructure preservation behaviors between algorithms with Fourier phase. Giventhe interpretations we have, we propose two manipulations in practice forstructure preservation and desired stylization. Both qualitative andquantitative experiments demonstrate the competitive performance of our methodagainst the state-of-the-art methods. We also conduct experiments todemonstrate (1) the abovementioned equivalence, (2) the interpretability basedon Fourier amplitude and phase and (3) the controllability associated withfrequency components.

Style Spectroscope: Improve Interpretability and Controllability through Fourier Analysis