Visual perception of extent and the geometry of visual space

The question of how perceived extents are related to the corresponding physical extents is a very old question that has not been satisfactorily answered. The common model is that perceived extent is proportional to the product of image size and perceived distance. We describe an experiment that shows that perceived extents are substantially larger than this model predicts. We propose a model that accounts for our results and a large set of other results. The principal assumption of the model is that, in the computation of perceived extent, the visual angle signal undergoes a magnifying transform. Extent is often perceived more accurately than the common model predicts, so the computation is adaptive. The model implies that, although the perception of location and the perception of extent are related, they not related by Euclidean geometry, nor by any metric geometry. Nevertheless, it is possible to describe the perception of location and extent using a simple model.