In this talk, we will study the PhD-work of Risi Kondor in which he demonstrates how bispectrum invariants can be used to classify translated and rotated images. The basic idea is to map the image in some 2-dimensional space to a unit sphere. Then a translation or a rotation of the input image is given by an element of the group $SO(3)$ acting on the (image wrapped about the) sphere. Kondor shows that the bispectrum of the image yields a translation and rotation invariant feature vector, which can be used to classify digits (this work was done at CMI under the guidance of K. V. Subrahmanyam).
