Downhill slope perception may depend on combining optical information with proprioception regarding head and gaze orientation. When looking down a hill or sloped surface (see figure), the angle formed between the hill surface and the line of gaze (optical slant) is the difference between the declination of gaze below the horizontal (or pitch) and the declination of the surface from the horizontal (geographical slant). Thus if one steps back from the edge of a hill so that one’s incident gaze is nearly parallel with the hill surface, the angle of gaze itself provides an excellent estimate of the slope of the hill. Interestingly, perceived downhill slopes viewed in this way appear much steeper than they are. Importantly, the head itself feels like it is also steeply inclined. One might imagine that the misperception of head orientation (pitch) during hillside viewing was itself somehow due to the misperception of the hill surface. However, blindfolded experimental participants in the laboratory also misperceive their head pitch. When asked to produce elevations or declinations of the head by 10 to 60 degrees, the produced head orientations are about half what they should be: perceived head orientation seems to increase twice as fast as actual head orientation. Downhill slope misperception may be related to proprioceptive errors concerning the pitch of the head and of gaze.
We designed an experiment to compare perceived downhill slope from different vantage points atop a simulated hill. Using an optically-correct immersive virtual reality depicting a virtual environment with rich 3D textures of rocks to specify surface orientations, we simulated realistic downhill slopes from 5 to 34 degrees. Twenty-four observers made verbal slope judgments of these slopes while viewing them from the edge of the slope or from a meter back from the edge.
Perceived optic slant can be inferred from slope judgments under different models of the perception of gaze orientation according to the geometry outlined above. The assumption that perceived optical slant was a continuous function of actual optical slant (using a logarithmic function) was sufficient to constrain our simple geometric model: The model only fit the judgment data when perceived head/gaze pitch was assumed to be exaggerated by a factor of about 2, consistent with our direct measurements of the gain of head pitch proprioception. Whereas hills appear quite steep when viewed back from the edge, we found that they appeared much shallower – both in virtual reality and in the real world – when viewed from near the edge of the hill. In our model this reflects a logarithmic coding of optical slant in combination with a linear exaggeration of gaze declination. When optical slant is small, the hill appears parallel to misperceived gaze, as shown at the left side of the figure. When optical slant is larger however, the hill surface will appear more frontal to gaze than it is, resulting in the situation depicted on the right side of the figure. This frontal tendency more than makes up for the exaggerated sense of head pitch when looking down on the hill from near the edge. We conclude that perceived downhill slope combines both proprioceptive and visual information.