Macro- and mesomorphology of frontal sinuses in humans: noisiness models relating to their ontogeny.

The debate about the role of the frontal sinuses remains unresolved. In this paper, I explore several statistical and fractal features of the frontal sinus outlines in order to better assess the spatial models of supraorbital torus formation. Although the analyses are restricted to a suite of techniques dealing with two-dimensional projections of the frontal sinuses, here I report many features that explain why it is so difficult to describe the spatial models. I show how the outline circumference scales with enclosed area, how the fractal dimensions of the outlines are distributed, how the method of singular value decomposition is used to define surrogate landmarks, and how a principal component analysis of vectors between these landmarks indicates directions of high variability in some of the inferior-distal directions. All these analysis techniques reveal regularities underlying the statistical noise. I believe that uncovering them necessitates a fresh look at the biology of noisy ontogeny phenomena.