We examine the spatiotemporal power spectra of image sequences that depict dense motion parallax, namely the
parallax seen by an observer moving laterally in a cluttered 3D scene. Previous models of the spatiotemporal
power have accounted for effects such as a static 1/f spectrum in each image frame, a spreading of power at high
spatial frequencies in the direction of motion, and a bias toward either lower or higher image speeds depending
on the 3D density of objects the scene. Here we use computer graphics to generate a parameterized set of image
sequences and qualitatively verify the main features of these models. The novel contribution is to discuss how
failures of 1/f scaling can occur in cluttered scenes. Such failures have been described for the spatial case, but
not for the spatiotemporal case. We find that when objects in the cluttered scene are visible over a wide range
of depths, and when the image size of objects is smaller than the image width, failures of 1/f scaling tend to
occur at certain critical frequencies, defined by a correspondence between object size and object speed.
Typical studies of the visual motion of specularities have been concerned with how to discriminate the motion of
specularities from the motion of surface markings, and how to estimate the underlying surface shape. Here we
take a different approach and ask whether a field of specularities gives rise to motion parallax that is similar to
that of the underlying surface. The idea is that the caustics that are defined by specularities exist both in front of
and behind the underlying surface and hence define a range of depths relative to the observer. We asked whether
this range of depths leads to motion parallax. Our experiments are based on image sequences generated using
computer graphics and Phong shading. Using low relief undulating surfaces and assuming a laterally moving
observer, we compare the specular and diffuse components of the resulting image sequences. In particular, we
compare the image power spectra. We find that as long as the undulations are sufficiently large, the range of
speeds that are indicated in the power spectra of the diffuse and specular components will be similar to each
other. This suggests that specularities could provide reliable motion parallax information to a moving observer.
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