  Learning discriminative and invariant feature representation is the key to
visual image categorization. In this article, we propose a novel invariant deep
compressible covariance pooling (IDCCP) to solve nuisance variations in aerial
scene categorization. We consider transforming the input image according to a
finite transformation group that consists of multiple confounding orthogonal
matrices, such as the D4 group. Then, we adopt a Siamese-style network to
transfer the group structure to the representation space, where we can derive a
trivial representation that is invariant under the group action. The linear
classifier trained with trivial representation will also be possessed with
invariance. To further improve the discriminative power of representation, we
extend the representation to the tensor space while imposing orthogonal
constraints on the transformation matrix to effectively reduce feature
dimensions. We conduct extensive experiments on the publicly released aerial
scene image data sets and demonstrate the superiority of this method compared
with state-of-the-art methods. In particular, with using ResNet architecture,
our IDCCP model can reduce the dimension of the tensor representation by about
98% without sacrificing accuracy (i.e., <0.5%).
