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.