Mattes Mutual Info basic doubts on 3D image registration
Similarity metrics in ITK usually give the cost, so the optimizers try to minimize them. Mutual information is an exception to this rule (higher MI is better), so in order to fit into the existing framework it has negative values -  bigger negative number is better than small negative number, while still following the logic that it should be minimized.
Modified time is used to check whether a certain filter should be updated or not.
Generally lower metric means better registration. But it is not comparable between different metrics, or even between different types of images using the same metric.
Random sampling will take 10-20% of samples in your RoI. I am not sure whether it picks randomly within RoI, or picks randomly within image and then checks whether it is in RoI.
1. Mattes Mutual Info Doubts
In SimpleITK Mattes Mutual information is a similarity metric measure, is this a maximizing function or minimizing function?
I have tried a 3D registration(image size : 480*480*60) with
Metric Mattes Mutual Info metric and Gradient Descent Optimizer
Output

numofbins = 30
Optimizer stop condition: RegularStepGradientDescentOptimizerv4: Step too small after 24 iterations. Current step (7.62939e-06) is less than minimum step (1e-05).
Iteration: 25
Metric value: -0.871268982129

numofbins = 4096
Optimizer stop condition: RegularStepGradientDescentOptimizerv4: Step too small after 34 iterations. Current step (7.62939e-06) is less than minimum step (1e-05).
Iteration: 23
Metric value: -1.7890

If it is a minimization function then the lower one is better, which I suspect.
2. Transformation matrix final Output
TranslationTransform (0x44fbd20)
RTTI typeinfo: itk::TranslationTransform
Reference Count: 2
Modified Time: 5528423
What is Modified Time?
3. Final Metric is a registration accuracy measurement?
Is metric a sign of registration accuracy? Is a higher metric value mean better registration? Or it is just a value at optimum point after optimization?
4. Random sampling for registration
10-20% of random sample points suffice for a registration. But the doubt arises whether the samples are taken from the main ROI or outside the ROI? Masking is an option, is there any other option in SimpleITK?
Thanks