Matching visual objects computationally has many practical applications. Observational instruments placed in various positions related to the same physical object usually produce very different images; thus, accurately matching these images computationally can be challenge. Therefore, image matching has been an active research topic in the field of machine intelligence.

To improve accuracy, researchers have developed higher-order computational approaches to study the relationship of featured edges (second-order) and beyond. While higher-order matching methods increase accuracy as expected, significantly increased computational costs often negatively impact their practicality.

By approximating the affinity tensor between feature points with the linear combination of the Kronecker product between bases and index tensors, the authors of this paper present efficient algorithms that require much less memory than previous methods, and they effectively find the principal eigenvector of the approximated affinity tensor. In their extensive experiments on synthetic points and real images, they demonstrate remarkable improvements on both accuracy and efficiency. Datasets used in the experiments include the Carnegie Mellon University house dataset, natural images from the Oxford visual geometry group database, and others reported in reputable publications.

People working on graph matching will definitely benefit from reading this paper. However, it may also be worthwhile to others: for example, those working in data mining, knowledge processing, and machine learning. I enjoyed reading it and was inspired by the authors’ ideas, even though matching images is not my research specialty. Efficient and scalable data representation and processing are among the fundamentals in computing.