Density discrimination with occlusions in 3D clutter

We examined how well human observers can discriminate the density of surfaces in two halves of a rotating three-dimensional cluttered sphere. The observer's task was to compare the density of the front versus back half or the left versus right half. We measured how the bias and sensitivity in judging the denser half depended on the level of occlusion and on the area and density of the surfaces in the clutter. When occlusion level was low, observers in the front-back task were biased to judge the back as denser, and when occlusion level was high they were biased to judge the front as denser. Weber fractions decreased as density increased for both the front-back and left-right tasks, consistent with previous findings for two-dimensional density discrimination. Weber fractions did not vary significantly with area for the front-back task, but increased with area for the left-right task, and we attribute this difference to occlusions that have different effects in the two tasks. We also ran model observers that compared the image occupancies of the two halves against a known expected difference. As the occlusion level increased, this expected difference followed a similar trend as the biases of the human observers, with a roughly constant offset between them. Weber fractions for human and model observers followed some similar trends, but there were discrepancies as well that can be partly explained by the information available to human versus model observers in carrying out their respective tasks.