Overlap invariance of cumulative residual entropy measures for multimodal image alignment

Cumulative residual entropy (CRE)1,2 has recently been advocated as an alternative to differential entropy for describing the complexity of an image. CRE has been used to construct an alternate form of mutual information (MI),3,4 called symmetric cumulative mutual information (SCMI)5 or cross-CRE (CCRE).6 This alternate form of MI has exhibited superior performance to traditional MI in a variety of ways.6 However, like traditional MI, SCMI suffers from sensitivity to the changing size of the overlap between images over the course of registration. Alternative similarity measures based on differential entropy, such as normalized mutual information (NMI),7 entropy correlation coefficient (ECC)8,9 and modified mutual information (M-MI),10 have been shown to exhibit superior performance to MI with respect to the overlap sensitivity problem. In this paper, we show how CRE can be used to compute versions of NMI, ECC, and M-MI that we call the normalized cumulative mutual information (NCMI), cumulative residual entropy correlation coefficient (CRECC), and modified symmetric cumulative mutual information (M-SCMI). We use publicly available CT, PET, and MR brain images* with known ground truth transformations to evaluate the performance of these CRE-based similarity measures for rigid multimodal registration. Results show that the proposed similarity measures provide a statistically significant improvement in target registration error (TRE) over SCMI.