Transformation Properties of Learned Visual Representations
This work addresses the challenge of building interpretable and efficient visual representations for computer vision, though it appears incremental as it builds on existing group representation theory.
The paper tackles the problem of designing visual representations that transform linearly under scene motions, showing that such representations are equivalent to combinations of irreducible group representations and linking irreducibility to statistical decorrelation under certain conditions. It demonstrates this with a model using a latent representation of the 3D rotation group SO(3) on rotating NORB objects.
When a three-dimensional object moves relative to an observer, a change occurs on the observer's image plane and in the visual representation computed by a learned model. Starting with the idea that a good visual representation is one that transforms linearly under scene motions, we show, using the theory of group representations, that any such representation is equivalent to a combination of the elementary irreducible representations. We derive a striking relationship between irreducibility and the statistical dependency structure of the representation, by showing that under restricted conditions, irreducible representations are decorrelated. Under partial observability, as induced by the perspective projection of a scene onto the image plane, the motion group does not have a linear action on the space of images, so that it becomes necessary to perform inference over a latent representation that does transform linearly. This idea is demonstrated in a model of rotating NORB objects that employs a latent representation of the non-commutative 3D rotation group SO(3).