  This paper analyzes the robustness of recent 3D shape descriptors to SO(3)
rotations, something that is fundamental to shape modeling. Specifically, we
formulate the task of rotated 3D object instance detection. To do so, we
consider a database of 3D indoor scenes, where objects occur in different
orientations. We benchmark different methods for feature extraction and
classification in the context of this task. We systematically contrast
different choices in a variety of experimental settings investigating the
impact on the performance of different rotation distributions, different
degrees of partial observations on the object, and the different levels of
difficulty of negative pairs. Our study, on a synthetic dataset of 3D scenes
where objects instances occur in different orientations, reveals that deep
learning-based rotation invariant methods are effective for relatively easy
settings with easy-to-distinguish pairs. However, their performance decreases
significantly when the difference in rotations on the input pair is large, or
when the degree of observation of input objects is reduced, or the difficulty
level of input pair is increased. Finally, we connect feature encodings
designed for rotation-invariant methods to 3D geometry that enable them to
acquire the property of rotation invariance.
