3.1 INTRODUCTION.
W ork on the integration of shape cues has covered a wide range of cue combinations. M ost studies on cue integration have used combinations o f either motion and other monocular cues (Andersen & Braunstein, 1983; Braunstein, et al., 1982; Landy, et al., 1990; Maloney & Landy, 1989; Ono, et al., 1988; Rogers & Rogers, 1992), or stereopsis and monocular cues (Blake, Zisserman & Knowles, 1985; Bradshaw, Rogers & Frisby, 1991; Buckley, et al., 1989; Bulthoff & Mallot, 1988; Dosher, et al., 1986; Johnston, et al., 1994; Johnston, et al., 1993; Rogers & Cagenello, 1989; Rogers, 1986; Stevens & Brookes, 1988). Only a few studies have addressed the question o f pictorial cue integration. For example, Ramachandran (1988) investigated the disambiguating role of occluding contours when combined with shading information. Similarly, B u lth o ff s (1991) work focused on the integration of two monocular cues, texture and shading; although it should be noted that subjects’ depth judgements were made by comparing stimuli against a stereo-defined standard.
The experiments in this chapter are designed to address two issues. Recent developments suggest that shape cues may not be integrated at the level of a depth representation (He & Nakayama, 1994; Todd & Reichel, 1989) but at some other representational level, such
as curvature (Johnston & Passmore, 1994a; Stevens, 1992; Stevens, et al., 1991). Experiments one and two attempt to identify the locus of integration for two monocular shape cues, shading and texture. Experiment one investigates whether subjects performing a curvature-matching task base their responses on information about depth or distance, or curvature. The results of this experiment, while not unequivocal, suggest that the information extracted from shading and texture is more likely to be integrated at the level of a curvature representation than a depth representation. Support for this conclusion is found in the results of experiment two. When the data from this experiment were expressed in curvature units they provided a better fit to a number o f models tested than the same data expressed in depth-range units. Experiment two also provides the opportunity to test whether a linear model best describes the integration of these two cues. The results of this experiment suggest that this is not the case; instead, a non-linear model, which provides a better fit to the data, is proposed.
3.2 EXPERIMENT ONE: INVESTIGATING DEPTH RANGE AS
A CUE TO CURVATURE.
Chapter two identified those parameters that co-vary with curvature and, consequently, are potential cues for subjects performing a curvature-matching task. These are the depth parameter, caused by a difference in the proximity of the surfaces to the viewer; the size cue; and the depth-range cue. It is possible to ensure that the first two cues are not available to subjects making a curvature matching judgement (see chapter two). However, it is not possible to eliminate the depth range cue while controlling for the size and depth cues. Consequently, in a curvature-matching task using these controls, one cannot rule out the possibility that subjects’ decisions are based on the depth-range cue. The present
F ig u re 3.1. An exam ple pair o f spherical patch stim uli used in exeperim ent one. Both patches are identical in their curvature (0.66 cm '), and differ only with respect to the size o f their occluding
boundaries. The spherical patch on the left is bounded by a 1.25 cm radius aperture, and the spherical
patch on the right is bounded by a 1 cm aperture.
experim ent was designed to investigate that possibility.In this experiment subjects were presented with pairs of spherical surface patches which differed in the spatial extent of their bounding contours (see Figure 3.1). Thus the diameter of the aperture bounding each stimulus was fixed at 70 pixels (2cms) for one of the stimuli, and at 88 pixels (2.5cms) for the other stimulus. The curvature o f the stimulus bounded by the larger o f the two windows was fixed at .66 c m '\ Subjects were given a ^5% curvature discrimination task, in which they had to decide whether the test surface appeared more curved than the standard. The standard stimulus was the one with the larger bounding aperture, and the test stimulus was the one with the smaller bounding aperture. Subjects were given two blocks o f trials, with each block consisting o f 64 trials.
Using the above paradigm provides the opportunity to observe directly whether subjects are using the depth-range cue when carrying out curvature-discrimination tasks. For each stimulus curvature value there is a corresponding depth-range value
L D -z -\J - a ^
where r is the radius of the spherical surface, and a is the aperture radius in the image plane (see Figure 3.2). Thus, in the case o f a spherical surface with a radius of 1.5cm (curvature = .66 cm'^) and bounded by a 1.25cms radius aperture, the depth range is 0.67cms. If we set the aperture radius to 1cm, the depth range for the same surface will now be 0.38cms. If subjects’ judgements in this experiment were based on the depth range parameter, the surface surrounded by the smaller of the two apertures would require a curvature
Occluding aperture
/
AD
Figure 3.2. A normal cross-section of a spherical patch and occluding aperture. The patch’s curvature can be expressed in depth-range units as