An important step in understanding how objects are recognized is to identify the local features that are salient for recognition and furthermore to determine how they are encoded. It has been suggested that local curvature is important for recognizing objects from their outline shapes (Attneave,
1954; Biederman,
1987) and for detecting deviations from circularity in radial frequency (RF) contours (Bell & Badcock,
2008; Bell, Badcock, Wilson, & Wilkinson,
2007; Bell, Dickinson, & Badcock,
2008; Habak, Wilkinson, & Wilson,
2006; Habak, Wilkinson, Zakher, & Wilson,
2004; Loffler, Wilson, & Wilkinson,
2003; Poirier & Wilson,
2007). Recent models of global shape perception propose that local curvature is an important intermediate step in object shape representation (Cadieu et al.,
2007; Pasupathy & Connor,
2002; Poirier & Wilson,
2006). The current study contributes toward our understanding of curvature encoding mechanisms by investigating whether those mechanisms are tuned for the orientation of a curve.
Evidence for curvature detectors comes from both neurophysiology and psychophysics. A subset of neurons in macaque area V4 is selective for curvature (Connor,
2004; Pasupathy & Connor,
1999,
2001), and some of these neurons are tuned for the orientation, position, and curvature of a curve. Pasupathy and Connor (
2002) and Cadieu et al. (
2007) have utilized these curvature tuning characteristics to develop models of shape coding, in which the positions and curvatures of the parts of an outline shape are projected onto a two-dimensional (2D) plane and encoded in an object-centric space.
Psychophysical studies of curvature (Arguin & Saumier,
2000; Gheorghiu & Kingdom,
2007b,
2008,
2009; Hancock & Peirce,
2008; Treisman & Gormican,
1988; Watt,
1984; Watt & Andrews,
1982; Wilson & Richards,
1989) are consistent with the idea of specialized detectors for curvature, but the most direct evidence comes from the finding that curvature is an adaptable stimulus feature (Gheorghiu & Kingdom,
2007b,
2008,
2009; Hancock & Peirce,
2008). For example a sinusoidal-shaped contour can appear distorted in either shape amplitude or shape frequency following adaptation (Gheorghiu & Kingdom,
2006,
2007a,
2007b,
2008), and the evidence points to both effects being mediated by mechanisms sensitive to local curvature, rather than to local orientation, average curvature, periodicity, or shape frequency (Gheorghiu & Kingdom,
2007b,
2009). Hancock and Peirce (
2008) showed that the induced angle between a pair of collinear elements following adaptation to an opposite-angled pair is not solely a manifestation of the tilt after-effect but involves a genuine after-effect of curvature.
The aforementioned studies by Gheorghiu and Kingdom have revealed several properties of curvature encoding mechanisms, such as selectivity for luminance-contrast polarity, luminance spatial frequency, color direction, curvature polarity, and the two dimensions of a curve—sag and cord. What has not been revealed by these, or any other appearance-based study of curvature processing, is whether human curvature detectors are tuned for the orientation of the curve, as has been shown to be the case for curvature-sensitive neurons in macaque V4 (Pasupathy & Connor,
1999,
2001).
To test whether curvature encoding mechanisms are tuned for the orientation of a curve, we used an analogue of the shape amplitude after-affect, or SAAE, found with sinusoidal-shaped contours (Gheorghiu & Kingdom,
2006,
2007b,
2008). The adapting and test stimuli each comprised a single curve, specifically a half-cycle rather than a full sine-wave contour, and we term the associated after-effect the curvature after-effect, or CAE. We measured the CAE as a function of the orientation difference between the adapting pattern and test pattern. Subsequently, we fitted a Gaussian function to the data to provide an estimate of orientation tuning bandwidth. We also measured the size and direction of the CAE for opposite polarity (180° orientation difference) adaptor and test curves to determine if there are populations of neurons in the visual system that are not selective for the sign of curvature.