  Learning transformation invariant representations of visual data is an
important problem in computer vision. Deep convolutional networks have
demonstrated remarkable results for image and video classification tasks.
However, they have achieved only limited success in the classification of
images that undergo geometric transformations. In this work we present a novel
Transformation Invariant Graph-based Network (TIGraNet), which learns
graph-based features that are inherently invariant to isometric transformations
such as rotation and translation of input images. In particular, images are
represented as signals on graphs, which permits to replace classical
convolution and pooling layers in deep networks with graph spectral convolution
and dynamic graph pooling layers that together contribute to invariance to
isometric transformations. Our experiments show high performance on rotated and
translated images from the test set compared to classical architectures that
are very sensitive to transformations in the data. The inherent invariance
properties of our framework provide key advantages, such as increased
resiliency to data variability and sustained performance with limited training
sets.
