There's more behind it: Perceived depth order biases perceived numerosity/density

Humans have a clear sense of the numerosity of elements in a surface. However, recent studies showed that the binding of features to the single elements is severely limited. By studying the relationship of depth order and perceived numerosity of overlapping, pseudotransparent surfaces, we show that the binding of elements to the surfaces is also limited. In transparent motion, anisotropies for perceived depth order and perceived numerosity were highly correlated: directions that were more likely to be perceived in the back were also more likely to be perceived as more numerous. The magnitude of anisotropies, however, was larger for depth order than for numerosity, and the correlation with eye movement anisotropies also developed earlier for depth order than for numerosity judgments. Presenting the surfaces at different disparities removed the anisotropies but lead to a consistent bias to overestimate the numerosity of the surface in the back and to underestimate the surface in the front. The magnitude of this bias did not depend on dot density or lifetime. However when the speed of motion was reduced or when the two surfaces were presented at different luminance polarities, the magnitude of anisotropies and the numerosity bias were greatly reduced. These results show that the numerosity of pseudotransparent surfaces is not processed independent of the depth structure in the scene. Instead there is a strong prior for higher numerosity in the back surface.