Optimal translational-rotational invariant dictionaries for images
This work addresses the need for efficient image representation in computer vision, though it appears incremental as it builds on existing invariant dictionary methods.
The paper tackled the problem of constructing optimal dictionaries for image approximation that are invariant under translations and rotations, achieving this through abstract harmonic analysis and providing numerical results on natural image datasets.
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques. Optimality is considered with respect to the quadratic error of approximation of the images in the dataset with their projection onto a linear subspace that is invariant under translations and rotations. In addition, we provide an elementary and fully self-contained proof of optimality, and the numerical results from datasets of natural images.