Focusing the Normalised Information Distance on the Relevant Information Content for Image Similarity

This paper investigates the normalised information distance (NID) proposed by Bennet et~al~(1998) as an approach to measure the visual similarity (or dissimilarity) of images. Earlier studies suggest that compression-based approximations to the NID can yield dissimilarity measures that correlate well with visual comparisons. However, results also indicate that conventional feature-based dissimilarity measures often outperform those that are based on the NID. This paper proposes that a theoretical decomposition of the NID can help explain why the NID-based dissimilarity measures might not perform well compared to feature-based approaches. The theoretical decomposition considers the perceptually relevant and irrelevant information content for image similarity. We illustrate how the NID-based dissimilarity measures could be improved by discarding the irrelevant information, and applying the NID on only the relevant information.