Feature space for edgels in images with landmarks

Fred L. Bookstein; William D. K. Green

doi:10.1117/12.130906

9 December 1992 Feature space for edgels in images with landmarks

Fred L. Bookstein, William D. K. Green

Proceedings Volume 1768, Mathematical Methods in Medical Imaging; (1992) https://doi.org/10.1117/12.130906
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

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 introduces a new extension of the finite-dimensional spline-based approach to incorporate edge information. In this implementation, edgels are restricted to landmark loci: they are interpreted as pairs of landmarks at infinitesimal separation in a specific direction. The effect of changing edge direction is a singular perturbation of the thin- plate spline for the landmarks alone. An appropriate normalization yields a basis for image deformations corresponding to changes of edge direction without landmark movement; this basis complements the basis of landmark deformations ignoring edge information. We derive explicit formulas for these edge warps, evaluate the quadratic form expressing bending energies of their formal combinations, and show the resulting spectrum of edge features in typical scenes. These expressions will aid all investigations into medical images that entail comparisons of anatomical scene analyses to a normative or typical form.

Citation Download Citation

Fred L. Bookstein and William D. K. Green "Feature space for edgels in images with landmarks", Proc. SPIE 1768, Mathematical Methods in Medical Imaging, (9 December 1992); https://doi.org/10.1117/12.130906

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