  State-of-the-art 2D image compression schemes rely on the power of
convolutional neural networks (CNNs). Although CNNs offer promising
perspectives for 2D image compression, extending such models to omnidirectional
images is not straightforward. First, omnidirectional images have specific
spatial and statistical properties that can not be fully captured by current
CNN models. Second, basic mathematical operations composing a CNN architecture,
e.g., translation and sampling, are not well-defined on the sphere. In this
paper, we study the learning of representation models for omnidirectional
images and propose to use the properties of HEALPix uniform sampling of the
sphere to redefine the mathematical tools used in deep learning models for
omnidirectional images. In particular, we: i) propose the definition of a new
convolution operation on the sphere that keeps the high expressiveness and the
low complexity of a classical 2D convolution; ii) adapt standard CNN techniques
such as stride, iterative aggregation, and pixel shuffling to the spherical
domain; and then iii) apply our new framework to the task of omnidirectional
image compression. Our experiments show that our proposed on-the-sphere
solution leads to a better compression gain that can save 13.7% of the bit rate
compared to similar learned models applied to equirectangular images. Also,
compared to learning models based on graph convolutional networks, our solution
supports more expressive filters that can preserve high frequencies and provide
a better perceptual quality of the compressed images. Such results demonstrate
the efficiency of the proposed framework, which opens new research venues for
other omnidirectional vision tasks to be effectively implemented on the sphere
manifold.
