NDLI: Analysis of Descent-Based Image Registration

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vural, Elif Frossard, Pascal
Copyright Year	2013
Abstract	We present a performance analysis for image registration with gradient descent. We consider a typical multiscale registration setting where the global two-dimensional translation between a pair of images is estimated by smoothing the images and minimizing the distance between them with gradient descent. Our study particularly concentrates on the effect of noise and low-pass filtering on the alignment accuracy. We analyze the well-behavedness of the image distance function by estimating the neighborhood of translations for which it is free of undesired local minima. This is the neighborhood of translations that are correctly computable with a simple gradient descent minimization. We show that the area of this neighborhood increases at least quadratically with the smoothing filter size. We then examine the effect of noise on the alignment accuracy and derive an upper bound for the alignment error in terms of the noise properties and filter size. Our main finding is that the error increases at a rate that is at least linear with respect to the filter size. Therefore, smoothing improves the well-behavedness of the distance function; however, this comes at the cost of amplifying the alignment error in noisy settings. Our results provide a mathematical insight into why hierarchical techniques are effective in image registration, suggesting that the multiscale alignment strategy of these techniques is very suitable from the perspective of the tradeoff between the well-behavedness of the objective function and the registration accuracy. To the best of our knowledge, this is the first such study for descent-based image registration.
Starting Page	2310
Ending Page	2349
Page Count	40
File Format	PDF
DOI	10.1137/130909858
e-ISSN	19364954
Journal	SIAM Journal on Imaging Sciences (SJISBI)
Issue Number	4
Volume Number	6
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-11-21
Access Restriction	Subscribed
Subject Keyword	Explicit machine computation and programs hierarchical registration methods Sensitivity analysis Applications image registration Convexity, generalizations image smoothing gradient descent performance analysis
Content Type	Text
Resource Type	Article

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