By pointing out an important analogy between the well known mutual information (MI) and MTM, we introduce the term normalized unexplained variance (nUV) for MTM to emphasize its relevance and applicability beyond image processing. MTM operates by binning the template, but the ideal binning for a particular problem is an open question. The recently introduced Matching by Tone Mapping (MTM) dissimilarity measure enables template matching under smooth non-linear distortions and also has a well-established mathematical background.
L 3 CIVILIZATION V IMAGE REGISTRATION
Tsallis entropy can improve brain MRI MI affine registration with long-range translation registration, lower-cost interpolation, and faster registrations through a better gradient space. Tsallis entropy obtained 99.75% success in the Monte Carlo simulation of 2,000 translation registrations with 1,113 double randomized subjects T1 and T2 brain MRI against 56.5% success for the Shannon entropy. Results show significantly prolonged registration ranges, without local minima in the metric space, with a registration capability of 100% for translations, 88.2% for rotations, 100% for scaling and 100% for skewness. The improvements detected were then tested through Monte Carlo simulation of actual registrations with brain T1 and T2 MRI from the HCP dataset.
A simulated gradient descent algorithm was also used to calculate the registration capability. The data were evaluated using 3D visualization of gradient and contour curves. The range used was 150 mm for translations, 360° for rotations, for scaling, and for skewness. We assessed the GMI metric output space using separable affine transforms to seek a better gradient space. This paper proposes and evaluates Generalized MI (GMI), using Tsallis entropy, to improve affine registration. Although MI provides a robust registration, it usually fails when the transform needed to register an image is too large due to MI local minima traps. Mutual information (MI) is consolidated as a robust similarity metric often used for medical image registration.
L 3 CIVILIZATION V IMAGE TRIAL
It demonstrates advantages of H-C entropy-based surrogacy measures in the evaluation of scheduling longitudinal biomarker visits for a phase 2 randomized controlled clinical trial for treatment of multiple sclerosis. The new model is illustrated through the analysis of data from a completed clinical trial. Furthermore, we extend our approach to a new model based on the information-theoretic measure of association for a longitudinally collected continuous surrogate endpoint for a binary clinical endpoint of a clinical trial using H-C entropy. In this paper, a new family of surrogacy measures under Havrda and Charvat (H-C) entropy is derived which contains Alonso’s definition as a particular case. (2007) proposed a unified framework based on Shannon entropy, a new definition of surrogacy that departed from the hypothesis testing framework. Surrogate endpoints have been used to assess the efficacy of a treatment and can potentially reduce the duration and/or number of required patients for clinical trials.
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