Local optima one of the optimization problems. while I am reading a MIND: Modality independent neighbourhood descriptor for multi-modal deformable registration paper I found the authors say:
"The main disadvantage is that MI is intrinsically a global measure and therefore its local estimation is difficult, which can lead to many false local optima in non-rigid registration.The main disadvantage is that MI is intrinsically a global measure and therefore its local estimation is difficult, which can lead to many false local optima in non-rigid registration."
http://www.sciencedirect.com/science/article/pii/S1361841512000643
Hi,
For measuring self-similarities locally (within a surrounding image region), and not globally see the following link
http://www.wisdom.weizmann.ac.il/~vision/VideoAnalysis/Demos/SelfSimilarities/SelfSimilarities_ShechtmanIrani07.pdf
They use sum of square differences (SSD) between patch colors.
Hope this helps.
I would say: yes. There is one and only one local optimum, that is also a global optimum (i.e. the best of all local optima), and that can be considered 'correct'. By 'correct' is meant: best performing according to the cost-function.
Of course it might be that the cost-function is totally wrong, but in your case (multi-modality registration), mutual information still seems the best we got.
From mathematical perspective, uniqueness of a local optimum is not guaranteed for a local registration problem. Lambert Zijp above states correctly that you can define 'correct' optimum in multiple numerical ways, and each of them will be 'correct' according to your definition.
Finally, you should check what is considered good registration fit in your application area. I.e. in clinical imaging, a trained radiologist would be in position to judge whether alignment is satisfactory - and thus you build your cost function to approximate that judgement as good as you can.
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