Movie-1 This movie shows that we can reliably recover the shape of dynamically occluded objects (people in this case) whose projection to the eyes is occluded by intervening shrubs. At a given instance the leaves admit only small portions of the human figure. It can be seen by stopping the movie at any instance that the information available in a single frame is insufficient to identify the human. However, our visual system processes the available information over space and time in a way such that we perceive connected object.

Palmer, Kellman and Shipley (2006) proposed a model of spatiotemporal relatability (STR) to explain how the visual system processes dynamically occluded objects. The model specifies relations in space and time that lead to object formation. Tests of the model indicated that object completion, as shown by objective performance advantages in shape discrimination, was predicted by STR. The following movies illustrate conditions that support and do not support dynamic object formation, for occluded and illusory displays. 

The objects and occluder were designed so that objects cannot be perceptually completed from information in any static frame of the animation sequence. Movie-2 and Movie-4 demonstrate spatiotemporal relatable cases for real and illusory contours. Movie-3 and Movie-5 show that object formation breaks down when contours are no longer relatable. The visible areas in Movie-3 and Movie-5 were exactly the same image fragments as in the relatable condition (Movie-2 and Movie-4 respectively) except that the top and bottom ones were reversed. 

Movie-2: Real Relatable Contour

Movie-3: Real Permuted Contour (Non-Relatable)

Movie-4: Illusory Relatable Contour

Movie-5: Illusory Permuted Contour (Non-Relatable)

Movie-6: Perception of dynamically occluded shapes is robust under normal, ecological circumstances. Research suggests that this is accomplished by preservation of contour information over time along with position updating of previously visible parts. In some circumstances, however, a powerful illusion can occur. If one piece of an object becomes occluded and is not seen again, its position at a later time is incorrectly represented. A simple way to express this idea is that “occlusion velocity” is often slower than would be expected from previously given velocity signals. That this can lead to robust illusions of misalignment indicate that the visual system combines previously visible and currently visible information to determine perceptual experience. This is demonstrated in the movie below in the condition where the rod moves behind the occluder. 
The viewer can change the perception of the display by either maintaining steady fixation on the rod or occluder or by sweeping their eyes back and forth with the rod or occluder. If the occluder is moving, fixating the rod leads to pretty accurate perception that the rod is aligned but tracking the moving occluder causes the rod to look misaligned.

Reference 
Palmer, E. M., Kellman, P. J., & Shipley, T. F. (2006). A theory of dynamic occluded and illusory object perception. Journal of Experimental Psychology: General, 135, 513–541. 
(Note: Evan Palmer received the 2006 American Psychological Association Young Investigator Award for best paper published in JEP: General in 2006 by a young investigator.)