  Although equirectangular projection (ERP) is a convenient form to store
omnidirectional images (also known as 360-degree images), it is neither
equal-area nor conformal, thus not friendly to subsequent visual communication.
In the context of image compression, ERP will over-sample and deform things and
stuff near the poles, making it difficult for perceptually optimal bit
allocation. In conventional 360-degree image compression, techniques such as
region-wise packing and tiled representation are introduced to alleviate the
over-sampling problem, achieving limited success. In this paper, we make one of
the first attempts to learn deep neural networks for omnidirectional image
compression. We first describe parametric pseudocylindrical representation as a
generalization of common pseudocylindrical map projections. A computationally
tractable greedy method is presented to determine the (sub)-optimal
configuration of the pseudocylindrical representation in terms of a novel proxy
objective for rate-distortion performance. We then propose pseudocylindrical
convolutions for 360-degree image compression. Under reasonable constraints on
the parametric representation, the pseudocylindrical convolution can be
efficiently implemented by standard convolution with the so-called
pseudocylindrical padding. To demonstrate the feasibility of our idea, we
implement an end-to-end 360-degree image compression system, consisting of the
learned pseudocylindrical representation, an analysis transform, a non-uniform
quantizer, a synthesis transform, and an entropy model. Experimental results on
$19,790$ omnidirectional images show that our method achieves consistently
better rate-distortion performance than the competing methods. Moreover, the
visual quality by our method is significantly improved for all images at all
bitrates.
