“Vertical” and “horizontal”: complementary biometric spaces for medical image analysis

Landmark points, when they can be located reliably over a sample of medical images, serve both to generate a statistical space of biometric shape variables and to specify an unwarping by which variation of pixel values associated with displacements of the landmarks can be corrected with respect to all landmarks simultaneously. There thus arise two separate spaces of descriptors of the same images: “horizontal” descriptions of the landmark configurations, and “vertical” descriptors, like image averaging or subtraction, applied only after pictures have been unwarped to adjust out this horizontal variation. A large class of image features may be generated by combining these two channels of analysis. In this paper, a series of figure captions, demonstrates their interplay in a little study of brain form in schizophrenia