"Egalitarian Gradient Descent": A General Preconditioning Scheme for Deformable Image Registration

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• Darko Zikic, TU Munich
• Tuesday 09 August 2011, 10:00-11:00
• Small lecture theatre, Microsoft Research Ltd, 7 J J Thomson Avenue (Off Madingley Road), Cambridge.

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In this talk, I will discuss a simple, yet theoretically justified approach for improving the efficiency of optimization in deformable registration problems, for arbitrary difference measures.

Given the registration problem as optimization of an energy containing a difference measure, the key step of our approach is extremely simple: We modify the vector field corresponding to the gradient of the difference measure, by normalizing the single point-wise vectors of the field to approximately unit length. We show that this simple scheme improves the convergence speed of optimization, while being 1) theoretically justified, 2) computationally efficient, and 3) applicable to arbitrary difference measures. Since the above scheme incorporates our idea to give roughly the same influence to all relevant points in the image domain, we dub the resulting approach “egalitarian”.

1) The above scheme is theoretically justified, as we demonstrate that it corresponds to a preconditioning of the difference measure. Actually, the scheme approximates the optimal preconditioning with respect to the analyzed model.

2) Due to the simplicity of the gradient modification and the resulting computational efficiency, the improvement in convergence speed is directly translated to shorter effective runtimes.

3) Finally, a very important aspect of our approach is that it is applicable to arbitrary difference measures. This is of high practical value for problems in which the range of applicable optimization methods is limited, such as deformable registration tasks in multi-modal settings, which utilize statistical difference measures such as Mutual Information.

Besides discussing the actual method, the talk will focus on providing an intuitive motivation for the approach, highlighting its relations to other optimization schemes, and demonstrating its application in popular registration frameworks. Also, the talk will contain a brief overview of some of my other image registration projects, including deformable 2D-3D registration, and linear registration by MRFs and discrete optimization.

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