Edge information at landmarks in medical images

In many current medical applications of image analysis, objects are detected and delimited by boundary curves or surfaces. Yet the most effective multivariate statistics available pertain to labelled points (`landmarks') only. In the finite-dimensional feature space that landmarks support, each case of a data set is equivalent to a deformation map deriving it from the average form. This paper reviews a recent extension of a spline-based approach so as to incorporate edge information, and extends it further to apply to images that incorporate landmarks. In this implementation, edgels are restricted to landmark loci: they are interpreted as pairs of landmarks at infinitesimal separation in a specific direction. To shears of these infinitesimal edgels correspond well-defined incremental deformations of the entire image. There results a very flexible new strategy for normalizing the geometry of a specimen scene before representing its grey levels as functions of position. Applications of this strategy will include more powerful approaches to picture averaging and more precise visualizations of biological processes that affect the shapes of medical images, their content, or both.