Invariant representation for blur and down-sampling transformations

Invariant representations of images can significantly reduce the sample complexity of a classifier performing object identification or categorization as shown in a recent analysis of invariant representations for object recognition. In the case of geometric transformations of images the theory [1] shows how invariant signatures can be learned in a biologically plausible way from unsupervised observations of the transformations of a set of randomly chosen template images. Here we extend the theory to non-geometric transformations such as blur and down-sampling. The proposed algorithm achieve an invariant representation via two simple biologically-plausible steps: 1. compute normalized dot products of the input with the stored transformations of each template, and 2. for each template compute the statistics of the resulting set of values such as the histogram or moments. The performance of our system on challenging blurred and low resolution face matching tasks exceeds the previous state-of-the-art by a large margin which grows with increasing image corruption.