C H A P T E R Anatomically Driven Strategies for High-Dimensional Brain Image Warping and Pathology Detection PAUL THOMPSON and ARTHUR W. TOGA Laboratory ofNeuro Imaging, Department of Neurology, Division of Brain Mapping, UCLA School of Medicine, Los Angeles, California Challenges in Three-Dimensional Human Brain Mapping Digital Brain Atlases Deformable and Probabilistic Brain Atlases Brain-to-Atlas Transformations Measuring Brain Changes Classification of Warping Algorithms Model-Driven and Intensity-Driven Algorithms Cortical Surface Matching Summary of Method Algorithm Details Colorized RGB Maps of the Cortical Parameter Space Cortical Curvature Covariant Formalism Summary of Covariant Approach to Cortical Matching Advantages Pathology Detection Probabilistic Atlasing Approaches Random Vector Fields Pathology Detection Random Field Maxima Departures from Normal Brain Asymmetry Shape Theory Approaches Pattern-Theoretic Approaches Applications Aging and Alzheimer's Disease Mapping Brain Development in Four Dimensions Conclusion References CHALLENGES IN THREE-DIMENSIONAL HUAAAN BRAIN MAPPING The rapid growth in brain imaging technologies has been matched by an extraordinary increase in the number of investigations focusing on the structural and functional organization of the brain. Human brain structure is so com- plex and variable across subjects that engineering ap- proaches drawn from computer vision, image analysis, computer graphics, and artificial intelligence research fields are required to manipulate, analyze, and communicate brain data. Extreme variations in brain structure, especially in the gyral patterns of the human cortex, present two major types of challenges in brain mapping studies. First, anatomic variations make it especially difficult to design computer- ized strategies for detecting abnormal brain structure. Analysis of regional neuroanatomy and cortical morphol- ogy are key factors in the radiologic assessment of a wide range of neurological disorders, including Alzheimer's dis- ease. Pick's disease, and other dementias (Friedland & Lux- enberg, 1988), schizophrenia (Kikinis et al., 1994), epilepsy (Cook et al., 1994), cortical dysplasias (Sobire et al., 1995), and other developmental disorders. To distinguish abnor- malities from normal variants, a realistically complex math- ematical framework is needed to encode information on anatomic variability in homogeneous populations (Grenan- der & Miller, 1994). Second, integrating and comparing data from multiple subjects and groups is hampered by the extreme complexity of anatomic variations (Meltzer & Frost, 1994; Woods, 1996). Ideally, when analyzing func- tional imaging data, we would like to remove all morpho- logical differences between individual brains before consid- ering the distribution of functional information on the anatomic substrate. As a result, both the detection of struc- tural abnormalities in disease and the pooling of multisub- ject brain data present considerable challenges, both neuro- biological and mathematical in nature. These difficulties have prompted us to explore hybrid approaches for brain image registration and pathology de- tection. In these approaches, computer vision algorithms Brain Warping 311 Copyright © 1999 by Academic Press. All rights of reproduction in any form reserved.