Models of Noise and Robust Estimates

Given n noisy observations g; of the same quantity f, it is common use to give an estimate of f by minimizing the function Eni=1(gi-f)2. From a statistical point of view this corresponds to computing the Maximum likelihood estimate, under the assumption of Gaussian noise. However, it is well known that this choice leads to results that are very sensitive to the presence of outliers in the data. For this reason it has been proposed to minimize the functions of the form Eni=1V(gi-f), where V is a function that increases less rapidly than the square. Several choices for V have been proposed and successfully used to obtain "robust" estimates. In this paper we show that, for a class of functions V, using these robust estimators corresponds to assuming that data are corrupted by Gaussian noise whose variance fluctuates according to some given probability distribution, that uniquely determines the shape of V.

2D-3D Rigid-Body Registration of X-Ray Fluoroscopy and CT Images

The registration of pre-operative volumetric datasets to intra- operative two-dimensional images provides an improved way of verifying patient position and medical instrument loca- tion. In applications from orthopedics to neurosurgery, it has a great value in maintaining up-to-date information about changes due to intervention. We propose a mutual information- based registration algorithm to establish the proper align- ment. For optimization purposes, we compare the perfor- mance of the non-gradient Powell method and two slightly di erent versions of a stochastic gradient ascent strategy: one using a sparsely sampled histogramming approach and the other Parzen windowing to carry out probability density approximation. Our main contribution lies in adopting the stochastic ap- proximation scheme successfully applied in 3D-3D registra- tion problems to the 2D-3D scenario, which obviates the need for the generation of full DRRs at each iteration of pose op- timization. This facilitates a considerable savings in compu- tation expense. We also introduce a new probability density estimator for image intensities via sparse histogramming, de- rive gradient estimates for the density measures required by the maximization procedure and introduce the framework for a multiresolution strategy to the problem. Registration results are presented on uoroscopy and CT datasets of a plastic pelvis and a real skull, and on a high-resolution CT- derived simulated dataset of a real skull, a plastic skull, a plastic pelvis and a plastic lumbar spine segment.