THE PERCEPTUAL ANALYSIS OF STRUCTURE FROM MOTION FOR ROTATING OBJECTSUNDERGOING AFFINE STRETCHING TRANSFORMATIONS

In two experiments, we evaluated the ability of human observers to mak e use of second-order temporal relations across three or more views of an apparent motion sequence for the perceptual analysis of three-dime nsional form. Ratings of perceived rigidity were obtained in Experimen t 1 for objects rotating in depth that were simultaneously subjected t o sinusoidal affine stretching transformations along the line of sight or in a direction parallel to the image plane. Such transformations a re theoretically interesting because they cannot be detected by analys es that are restricted to first-order temporal relations (i.e., two vi ews), but they can be detected by more conventional analyses of struct ure from motion in which second-order temporal relations over three or more views are used. The current results show that human observers ca n perceive stretching transformations of a rotating 3-D object in a di rection parallel to the image plane but that they fail to perceive str etching transformations along the line of sight. This result suggests that human observers can make use of some limited second-order tempora l information. This finding was confirmed in Experiment 2, in which we investigated the effects of several specific optical consequences of sinusoidal stretching transformations applied in different directions. The results indicate that observers may be sensitive to the sign of a cceleration, but that they cannot make use of the precise magnitude of second-order relations necessary to recover euclidean metric structur e.