1
Motion of specularities on smooth random
surfaces Michael Langer Yousef Farasat School
of Computer Science, McGill University,
Montreal, Canada
light source (sun) at infinity
not visible
V
New observation specular reflections and
visibility windows

• The set of rays in which any given specularity is
  visible must begin at the surface region that
  defines that specularity, and must pass through
  that specularity. Thus, at any instant of
  time, the local surface region defines a window
  in which that specularity may be visible. This
  window is defined by the region over which the
  surface is a parabola
• where fx and fy are the focal lengths which
  are roughly constant in the window. In the
  figure, the window is the surface region bounded
  by the red lines. (Previous studies of
  specularity motion expressed this windowing
  effect in terms of caustics.)
• The observer moves relative to the specularity
  and relative to the surface window defining the
  specularity. The surface window and its
  specularity are at different depths, and thus
  there is motion parallax between them. This
  parallax gives rise to second order motion,
  namely the resulting image is the product of the
  image of the moving specularity and the moving
  window.
• A surface having many concave and convex parts
  has many specularities and these lie in front of
  and behind the surface. One might expect that
  when an observer moves laterally, the motion of
  the specularities yields rich motion parallax.
  Unfortunately, the windowing severely restricts
  the visibility of the specularities.
• CONCLUSION The relative motion of specularities
  is primarily parallel to the observer motion.
  However, each specularity is visible over a
  limited distance of observer motion (or baseline,
  in case of stereo). From a computational
  perspective, these local windows make it
  difficult to track/match specularities.

V
visible
Background specularities and motion parallax

• (e.g. Koenderink van Doorn 1976, Zisserman et
  al. 1989, Blake Buelthoff 1990)
• Curved surfaces that have a mirror-like
  reflectance produce images of light sources
  (specularities). A convex region produces a
  specularity behind the surface. A concave region
  produces a specularity in front of the surface.
• The distance from the surface to the specularity
  depends on surface curvature. If the curvature
  is high (low) then the distance is small (large).
• When an observer moves laterally relative to the
  surface, motion parallax results. If the
  surface is convex (concave), then the
  specularity moves slower (faster) than the
  surface.