Underestimation of numerosity with occlusion is density dependent

Estimating the number of objects in a crowd can be complicated by the fact that some of the objects might be hidden behind occluders. It has been shown that numerosity is underestimated in partially-occluded displays when the visible objects are sparsely distributed (Men et al., 2023). Since there is a transition from a numerosity to a texture-density mechanism at larger numbers and higher densities (Anobile et al., 2014), it might be that the underestimation of numerosity in partially-occluded displays decreases at larger numbers and densities. Here, we investigated how the number and density of visible objects affects the estimation of numerosity in a partially occluded scene. Two gray boards with different numbers of randomly arranged pieces were displayed simultaneously. Participants had to first discriminate which board contained more pieces, and subsequently report their confidence in discriminating the numerosity. Both of the boards could be fully visible or partially occluded, or one of the boards fully visible and the other partially occluded. We manipulated the size of the board and the number of visible pieces to achieve three combinations of numerosity and density: Large numerosity and high density, small numerosity and low density and small numerosity and high density. Results showed that the underestimation of numerosity was smaller for displays of high densities than for displays of low density. Since these effects were present in numerosity and confidence judgments, they represent genuine perceptual effects rather than response biases. Despite this underestimation, participants were equally confident in their judgments with or without occlusion. Weber fractions were smaller in displays with high density, indicating that participants indeed might have relied on a texture-density mechanism at high densities. Our results show that numerosity is underestimated in partially-occluded scenes, and that the strength of such underestimation depends on the number and density of visible objects.