Bee brains, B-splines and computational democracy: Generating an average shape atlas

We describe a method to generate an average atlas from segmented 3-D images of a population of subjects. Using repeated application of an intensity-based non-rigid registration algorithm based on third-order 3-D B-splines, a sequence of average label images is created. Averaging of the non-numerical label data employs a generalization of the mode of sets of corresponding voxels, parameterized by a threshold value specifying the required level of classification confidence. The number of voxels that cannot be assigned a unique average value provides a criterion for the convergence of the iteration. For improved accuracy, efficiency, and robustness of the non-rigid registration, deformations computed during one iteration are propagated to the next iteration as initial transformation estimates. The usefulness of our method is demonstrated by applying it to generate an average atlas from segmented 3-D confocal microscopy images of 20 bee brains. We validate that the deformations found by our algorithm are meaningful by deforming the original gray-level images according to the transformations computed for the label fields.