Learning pattern transformation manifolds with parametric atom selection

We address the problem of building a manifold in order to represent a set of geometrically transformed images by selecting a good common sparse approximation of them with parametric atoms. We propose a greedy method to construct a representative pattern such that the total distance between the transformation manifold of the representative pattern and the input images is minimized. In the progressive construction of the pattern we select atoms from a continuous dictionary by optimizing the atom parameters. Experimental results suggest that the representative pattern built with the proposed method provides an accurate representation of data, where the invariance to geometric transformations is achieved due to the transformation manifold model.