Motion and Surface Recovery using Curvature and Motion Consistency
Authors: G. Soucy and F.P. Ferrie
File name: soucy-motion-recovery.ps.gz
Abstract:
A key problem in the recovery of scene descriptions from multiple views is the
fusion of information from different vantage points. The contribution of this
paper is a set of algorithms for reconstructing surfaces obtained from
overlapping range images in a common frame of reference. Surfaces are assumed
to be piecewise-smooth but not necessarily rigid. Motion parameters,
rotations and translations that describe correspondence between views, are
recovered locally under the assumption that the curvature structure at a point
on a surface varies slowly under transformation. The recovery problem can
thus be posed as finding the set of motion parameters that preserves curvature
across two views. We show that an appropriate similarity functional can be
devised that is convex in the vicinity of the true motion parameters. This
leads to an efficient local algorithm that recovers motion parameters in
gradient descent fashion.
Fusion of information from different viewpoints is accomplished by applying
local motion estimates to map data points between frames. However, because
these estimates are determined locally, they are subject to the usual effects
of noise and quantization error. To increase the robustness of this
reconstruction procedure the additional constraint of motion consistency is
introduced, that variations in the velocities of adjacent regions are also
piecewise-smooth. This is cast as a second local minimization problem which
seeks to find the set of motion parameters that minimizes differences in the
relative positions and orientations at adjacent points. The resulting
algorithm serves to smooth out local perturbations and blend adjacent surface
patches. In contrast to global rigid body motion approaches, our procedure
for reconstructing surfaces from different viewpoints is tolerant of local
errors in correspondence and can accommodate objects that are articulated.