There have been a number of papers in recent years that demonstrate that global aspects of faces can be extremely important in face perception and memory. We contend in this chapter that a quite natural theory immediately yields the quintessence of holism. This theory is constituted by our Riemannian Face Space. It is eminently holistic because each face in the theory is the entire function that is a perfect description of the perceptual object. Each is more than the sum of the parts, in that in the space, each face is a unique point, in an analogous sense to a finite feature description that leads to a unique finite vector space representation. The space is infinite dimensional and yet we show that the space bears potential for a number of standard and useful geometric properties. For instance, we devote considerable effort to showing that such notions as angle and distance may attend these seemingly esoteric spaces. There are various metrics that appear to be appropriate for different perceptual and cognitive tasks which we discuss. Other global and local aspects of such spaces, for instance morphing, and low-dimensional subspaces, are considered. The final discussion relates our work to the important notions of templates, prototypes and similar concepts in categorization and identification models and experiments.
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