Log-Euclidean Metric for Robust Multi-Modal Deformable Registration

Registration of images from different modalities in the presence of intra-image fluctuation and noise contamination is a challenging task. The accuracy and robustness of the deformable registration largely depend on the definition of appropriate objective function, measuring the similarity between the images. Among them the multi-dimensional modality independent neighbourhood descriptor (MIND) is a promising method, yet its ability is limited by non-uniform bias fields and image noise, etc. Motivated by the fact that Log-Euclidean metric has promising invariance properties such as inversion invariant and similarity invariant, this paper introduces an objective function that embeds Log-Euclidean similarity metric between patches to form a multi-dimensional descriptor. The Gaussian-like penalty function consisting of the log-Euclidean metric between images to be registered is incorporated to better reflect the degree of preserving feature discriminability and structure ordering. Experimental results show the advantages of the proposed method over state-of-the-art techniques both quantitatively and qualitatively.