Task-dependent geometry of a perceptual space

There is increasing interest in analyzing the geometry of perceptual spaces. One approach directly uses explicit judgments of perceptual similarity to infer a distance model; other approaches first assign coordinates to each stimulus and then compute distances from these coordinates. Here we combine and compare the two approaches in a stimulus domain of synthetic black and white textures. Previous threshold psychophysics established coordinates for these textures that quantitatively accounted for discrimination data. We selected stimuli that lay along four orthogonal axes in this space for a similarity-judgment experiment. Stimuli had positive and negative coordinates on each axis, and were symmetrically located around the origin (a random texture). Opposing rays from the origin corresponded to textures with increasing positive or negative values of the same kind of correlation structure. We then compared this a priori coordinate structure with the geometry inferred from similarity judgments. In each of 1000 unique trials, 8 different stimuli appeared around a central reference. The subject's task was to click these 8 stimuli in order of their similarity to the central reference. Based on the coordinate structure, we expected the similarity judgments to arrange the stimuli along four orthogonal axes through the origin. In preliminary results (n=2), the arrangement of stimuli in the inferred space, although four-dimensional, differed from expectations based on the coordinate structure. While rays of increasing positive or negative correlation strength in the coordinate structure mapped, approximately, to rays in the inferred space, angles were not preserved. Specifically, rays in opposite directions in the coordinate structure were often at acute angles in the inferred space, and orthogonal rays in the coordinate space did not correspond to orthogonal rays in the inferred space. These differences show that a single perceptual space is accessed in a task-dependent manner.