  Omnidirectional vision is becoming increasingly relevant as more efficient
$360^o$ image acquisition is now possible. However, the lack of annotated
$360^o$ datasets has hindered the application of deep learning techniques on
spherical content. This is further exaggerated on tasks where ground truth
acquisition is difficult, such as monocular surface estimation. While recent
research approaches on the 2D domain overcome this challenge by relying on
generating normals from depth cues using RGB-D sensors, this is very difficult
to apply on the spherical domain. In this work, we address the unavailability
of sufficient $360^o$ ground truth normal data, by leveraging existing 3D
datasets and remodelling them via rendering. We present a dataset of $360^o$
images of indoor spaces with their corresponding ground truth surface normal,
and train a deep convolutional neural network (CNN) on the task of monocular
360 surface estimation. We achieve this by minimizing a novel angular loss
function defined on the hyper-sphere using simple quaternion algebra. We put an
effort to appropriately compare with other state of the art methods trained on
planar datasets and finally, present the practical applicability of our trained
model on a spherical image re-lighting task using completely unseen data by
qualitatively showing the promising generalization ability of our dataset and
model. The dataset is available at:
vcl3d.github.io/HyperSphereSurfaceRegression.
