The Perfect Gestalt: Infinite Dimensional Riemannian Face Spaces and Other Aspects of Face Perception
A number of papers in recent years have demonstrated that global aspects of faces can be extremely important in face perception and memory (e.g., Baenninger, 1994; Biederman & Kalocsai, 1998; Cottrell, Dailey, Padgett, & Adolphs, chap. 9, this volume; Farah, Wilson, Drain, & Tanaka, 1998; Tanaka & Sengco, 1997). Recently, Farah et al. (1998) adduced evidence that there are holistic properties of face cognition that go beyond conﬁgural (i.e., relational) properties of features and other landmarks of faces. A longtime student of perception and philosophy of science in psychology, William Uttal, has repeatedly called for mathematics and related psychological theories that are suitable for capturing holistic aspects of perception (Uttal, 1988, chap. 12, this volume; see also Cottrell et al., chap. 9, this volume; Wenger & Townsend, chap. 7, this volume). It is becoming increasingly clear that no one approach could ever sufﬁce for all aspects of face perception (e.g., Uttal, chap. 12, this volume; Wenger & Townsend, 2000). Nevertheless, 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.