Similarity metrics based on nonadditive entropies for 2D-3D multimodal biomedical image registration

Abstract

Information theoretic similarity metrics, including mutual information, have been widely and successfully employed in multimodal biomedical image registration. These metrics are generally based on the Shannon-Boltzmann-Gibbs definition of entropy. However, other entropy definitions exist, including generalized entropies, which are parameterized by a real number. New similarity metrics can be derived by exploiting the additivity and pseudoadditivity properties of these entropies. In many cases, use of these measures results in an increased percentage of correct registrations. Results suggest that generalized information theoretic similarity metrics, used in conjunction with other measures, including Shannon entropy metrics, can improve registration performance.

The Superiority of Tsallis Entropy over Traditional Cost Functions for Brain MRI and SPECT Registration

“…Likewise, Wachowiak et al [30] found that Tsallis Entropy in the Normalized Mutual Information (NMI) presented the best MRI intra-modality alignment, with the difference that the lower errors were obtained with a higher q value (q = 1.1). In their study, the authors used the Euclidean Distance and Root Mean Square (RMS) error to determine the Correctness Ratio (Cr), and results showed that Tsallis Entropy generally had better performance (in terms of producing fewer misregistration) than Shannon NMI for q value very close to 1 (q = 0.9, 1.1) [31]. They argue that the poor performance of low q values in their study might be due to the use of the Powell optimization method for registration.…”

Multiresolution Biomedical Image Registration Using Generalized Information Measures

“…Parameters much different than unity have rough similarity metric functions, and are difficult to optimize [6,7]. The I R α and I S α metrics, with α slightly greater than 1 (α ∈ [1.1, 2]), were the overall best performers, with about the same efficiency as I. Misregistrations often result from entrapment in local extrema of the registration function, to which local optimization methods are susceptible.…”

“…The I R α and I S α metrics, with α slightly greater than 1 (α ∈ [1.1, 2]), were the overall best performers, with about the same efficiency as I. Misregistrations often result from entrapment in local extrema of the registration function, to which local optimization methods are susceptible. Many of the generalized metrics have smoother registration surfaces than MI [7], and are more sensitive to changes in dependence (Fig. 1).…”

“…They are parameterized by a real number, and typically specialize to Shannon metrics in a limit of their parameter. Some such metrics have already been used for registration [6,7]. The current work applies additional measures to single slice/3D registration for MRI and CT brain and cardiac images, and shows that improvements can be obtained when the generalized and Shannon measures differ only slightly.…”

“…Metrics based on the Rényi and Havrda-Charvat entropy definitions are compared with Shannon mutual information (MI), normalized mutual information (NMI), the entropy correlation coefficient (ECC), and the correlation ratio (CR), as well as with other generalized metrics that have appeared in the literature [6,7].…”