Abstract:
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This paper introduces a new approach for the joint alignment of a large collection of
segmented images into the same system of coordinates while estimating at the same time an optimal
common coordinate system. The atlas resulting from our group-wise alignment algorithm is
obtained as the hidden variable of an Expectation-Maximization (EM) estimation. This is achieved
by identifying the most consistent label across the collection of images at each voxel in the common
frame of coordinates.
In an iterative process, each subject is iteratively aligned with the current probabilistic atlas
until convergence of the estimated atlas is reached. Two different transformation models are successively
applied in the alignment process: an affine transformation model and a dense non-rigid
deformation field. The metric for both transformation models is the mutual information that is
computed between the probabilistic atlas and each subject. This metric is optimized in the affine
alignment step using a gradient based stochastic optimization (SPSA) and with a variational approach
to estimate the non-rigid atlas to subject transformations.
A first advantage of our method is that the computational cost increases linearly with the number
of subjects in the database. This method is therefore particularly suited for a large number of
subjects. Another advantage is that, when computing the common coordinate system, the estimation
algorithm identifies weights for each subject on the basis of the typicality of the segmentation.
This makes the common coordinate system robust to outliers in the population.
Several experiments are presented in this paper to validate our atlas construction method on
a population of 80 brain images segmented into 4 labels (background, white and gray matters and ventricles). First, the 80 subjects were aligned using affine and dense non-rigid deformation
models. The results are visually assessed by examining how the population converges closer to
a central tendency when the deformation model allows more degrees of freedom (from affine to
dense non-rigid field). Second, the stability of the atlas construction procedure for various sizes of
population was investigated by starting from a subset of the total population which was incrementally
augmented until the total population of 80 subjects was reached. Third, the consistency of our
group-wise reference (hidden variable of the EM algorithm) was also compared to the choice of an
arbitrary subject for a subset of 10 subjects. According to William’s index, our reference choice
performed favorably. Finally, the performance of our algorithm was quantified on a synthetic population
of 10 subjects (generated using random B-Spline transformations) using a global overlap
measure for each label. We also measured the robustness of this measure to the introduction of
noisy subjects in the population. |