Image registration with sparse approximations in parametric dictionaries
This work addresses image registration for computer vision applications, offering a novel approach with theoretical guarantees, though it appears incremental as it builds on sparse approximation methods.
The paper tackles image registration by representing images as sparse approximations in parametric dictionaries of geometric functions, and proposes an algorithm that estimates global transformations by analyzing relative geometric transformations between features, showing improved performance in transformation-invariant distance computation and classification on simple visual objects and handwritten digits.
We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an estimate of the global transformation between sparse images by examining the set of relative geometrical transformations between the respective features. We propose a theoretical analysis of our registration algorithm and we derive performance guarantees based on two novel important properties of redundant dictionaries, namely the robust linear independence and the transformation inconsistency. We propose several illustrations and insights about the importance of these dictionary properties and show that common properties such as coherence or restricted isometry property fail to provide sufficient information in registration problems. We finally show with illustrative experiments on simple visual objects and handwritten digits images that our algorithm outperforms baseline competitor methods in terms of transformation-invariant distance computation and classification.