  Semantic editing of images is the fundamental goal of computer vision.
Although deep learning methods, such as generative adversarial networks (GANs),
are capable of producing high-quality images, they often do not have an
inherent way of editing generated images semantically. Recent studies have
investigated a way of manipulating the latent variable to determine the images
to be generated. However, methods that assume linear semantic arithmetic have
certain limitations in terms of the quality of image editing, whereas methods
that discover nonlinear semantic pathways provide non-commutative editing,
which is inconsistent when applied in different orders. This study proposes a
novel method called deep curvilinear editing (DeCurvEd) to determine semantic
commuting vector fields on the latent space. We theoretically demonstrate that
owing to commutativity, the editing of multiple attributes depends only on the
quantities and not on the order. Furthermore, we experimentally demonstrate
that compared to previous methods, the nonlinear and commutative nature of
DeCurvEd facilitates the disentanglement of image attributes and provides
higher-quality editing.
