For animals with advanced nervous systems, survival and reproduction can depend upon accurate perception of the environment. To understand how a perceptual system should solve a perception task, it is important to consider designs for an ideal observer, a theoretical system that solves a perception task in an optimal way given specific constraints. I studied three specific classification tasks related to the problem of identifying and segmenting leaves in foliage-rich images. In order to derive the ideal observers for these tasks, I created a database of hand-segmented leaves which served to define the ground-truth for these tasks. I also created a new method that uses the ground-truth as a basis for performing statistical inference (classification) in a nearly optimal way. This made it possible for me to approximate ideal observers by approximating an optimal classifier for each task. I also conducted psychophysical experiments to measure human performance in these tasks. The results provide information about how the human visual system should and does interpret foliage-rich images. / text