In mathematics, an inflection point is the point on a curve at which the gradient of the tangent, i.e., the curvature, changes sign. Under this definition, the stimuli in
Figure 1 easily divide into contours that contain inflections and those that do not. Inflections are important descriptors in mathematics (Ewing,
1938; Irwin & Wright,
1917), linguistics (Faroqi-Shah & Thompson,
2007,
2010), and architecture/engineering (Chatila & Tabbara,
2004; Jahnkassim,
2002) in which contour inflections are known as “Ogee” curves. The importance of inflections for human vision is evidenced by the fact that contour inflections are not only ubiquitous features of natural scenes (Elder & Goldberg,
2002; Geisler, Perry, Super, & Gallogly,
2001), but they provide unique information about the shapes of objects (Bell, Hancock, Kingdom, & Peirce,
2010; Bertamini & Farrant,
2005; De Winter & Wagemans,
2008; Ivanov & Mullen,
2012; Mullen, Beaudot, & Ivanov,
2011) and the relations among edges (Singh & Hoffman,
1999). In addition, contour inflections along the 2-D silhouette of an object provide important cues to 3-D structure (Koenderink,
1984; Richards, Koenderink, & Hoffman,
1987). Despite their apparent importance, inflections have received little attention in models of shape and object coding, which have tended to focus on the role of oriented lines and curves (Barenholtz & Tarr,
2008; Carlson, Rasquinha, Zhang, & Connor,
2011; Connor,
2004; Hoffman & Richards,
1984; Pasupathy & Connor,
2002; Poirier & Wilson,
2006,
2010; Yamane, Carlson, Bowman, Wang, & Connor,
2008). Models based on these features are popular because of the large body of evidence for specialized detectors in the cortex for oriented lines (Hubel & Wiesel,
1962,
1968; Kapadia, Westheimer, & Gilbert,
1999,
2000) and curves (Muller, Wilke, & Leopold,
2009; Pasupathy & Connor,
1999,
2001). Is there evidence for inflection coding mechanisms in the cortex? Neurophysiological studies of macaque monkeys have revealed subpopulations of neurons in visual area V4 (Pasupathy & Connor,
1999,
2001) and posterior inferotemporal cortex (PIT) (Brincat & Connor,
2004,
2006; Yau, Pasupathy, Brincat, & Connor,
2010) that respond best to contour fragments containing inflections. In light of these findings, we ask whether the human visual system has mechanisms
specific to coding contour inflections.