  This paper addresses the automatic colorization problem, which converts a
gray-scale image to a colorized one. Recent deep-learning approaches can
colorize automatically grayscale images. However, when it comes to different
scenes which contain distinct color styles, it is difficult to accurately
capture the color characteristics. In this work, we propose a fully automatic
colorization approach based on Symmetric Positive Definite (SPD) Manifold
Learning with a generative adversarial network (SPDGAN) that improves the
quality of the colorization results. Our SPDGAN model establishes an
adversarial game between two discriminators and a generator. The latter is
based on ResNet architecture with few alterations. Its goal is to generate fake
colorized images without losing color information across layers through
residual connections. Then, we employ two discriminators from different
domains. The first one is devoted to the image pixel domain, while the second
one is to the Riemann manifold domain which helps to avoid color misalignment.
Extensive experiments are conducted on the Places365 and COCO-stuff databases
to test the effect of each component of our SPDGAN. In addition, quantitative
and qualitative comparisons with state-of-the-art methods demonstrate the
effectiveness of our model by achieving more realistic colorized images with
less artifacts visually, and good results of PSNR, SSIM, and FID values.
