A method on calculating high-dimensional mutual information and its application to registration of multiple ultrasound images

Using mutual information as a criterion for medical image registration, which requires no prior segmentation or preprocessing, has been both theoretically and practically proved to be an effective method in these years. However, this technique is confined in registering two images and hard to apply to multiple ones. The reason is that unlike mutual information between two variables, high-dimensional mutual information is ill defined. In textbooks and theoretical essays, three-dimensional mutual information is proposed based on Venn diagram. Unfortunately, mutual information defined in this way is not necessarily nonnegative. In order to overcome the problem, in this paper, we introduce the mutual information matrix. By calculating its eigenvalues, high-dimensional mutual information is defined. This definition is nonnegative, bounded, and could be extended to higher dimensions, thus enables us to register more than three images. In the end, this definition is tested and proved to be effective on registration of multiple US images through simulation.