The optical structure sampled by the human observer is insufficient to determine the structure of a scene. The equivalence class of scenes that lead to the same optical structure can be worked out precisely for specific 'cues' (shading, texture, ...). If the 'observed scene' is a member of the correct class, the observation must be considered 'veridical,' even if the observed scene differs from the actual one. In many cases it is impossible to indicate the equivalence classes, and it therefore must remain undecided whether observations that deviate from physical reality should be denoted 'veridical' or not. For observations on the basis of images, such as straight photographs of physical scenes, the equivalence classes are unknown, but are certainly large. This case is especially important in the design of computer interfaces where a scene is being presented to the user as an image. We find that observations differ appreciably according to the precise task. The observer uses the freedom resulting from the iconic underdetermination to choose some idiosyncratic perspective by directing the 'mind's eye.' This can be demonstrated with simple means. Stretchings of depth by a few hundred percent and changes in viewing direction (not rotations, but shears) of tens of degrees are quite common.