Image registration with sparse approximations in parametric dictionaries

TL;DR

This paper introduces a new image registration method using sparse approximations in parametric dictionaries, providing theoretical guarantees and outperforming existing methods in experiments with simple objects and handwritten digits.

Contribution

The paper presents a novel registration algorithm based on sparse representations and introduces new dictionary properties, with theoretical analysis and practical validation.

Findings

The proposed algorithm outperforms baseline methods in transformation-invariant distance computation.

Performance guarantees are derived based on robust linear independence and transformation inconsistency.

Common dictionary properties like coherence are insufficient for registration tasks.

Abstract

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.