Statistical Analysis of Brain Maps: Some Lessons from Morphometrics

Current methodologies for functional brain images, which inhabit data sets of ridiculously high dimension, can likely be enhanced by techniques borrowed from morphometrics, a companion methodology suiting the lower-dimensional modality of structural images. Over the last decade, modern morphometries has converged on an important algebraic/statistical core that incorporates an explicitly theorem-driven representation of “shapes” (our principal subject of study) distinct from merely normalized images, realistic models for noise distributions in these derived spaces, permutation tests for practical issues of scientific inference, and least-squares methods for extracting predictions and patterns wherever scientific theory is weak. Variants of these tactics should apply as well in the more complicated arena of functional image analysis. This essay touches on three areas of common concern in regard to which morphometric tactics may ease comparable perplexities in the sister domain: issues of symmetry, the meanings of “localization” for image phenomena, and correlations of shape with other aspects of shape or with behavior. For some aspects of these topics, such as the description of focal phenomena, analyses of functional images already exploit stereotyped methods for which morphometries provides interesting alternatives. For others, such as the modeling of noise after image normalization, morphometric methodology seems well ahead of functional methodology in prototyping sharp new tools.