VASC Seminar Announcement
            =========================

Date: Monday, 9/13/99
Time: 3:30-4:30
Place: Smith Hall 2nd Floor Common Area

Speaker:  Daniel Morris
          CMU Robotics Institute
          http://www.cs.cmu.edu/~ddmorris


Title: Uncertainty Modeling for Optimal Structure from Motion

Abstract:

The parameters estimated by Structure from Motion contain inherent
indeterminacies.  In particular, shape and motion parameters are only
recovered up to a similarity transformation.  Past work on uncertainty
modeling has imposed gauge constraints on the coordinates and the scale to
reduce the number of parameters and eliminate these indeterminacies.  In
this paper our approach is instead to maintain these indeterminacies, or
gauge freedoms, in our covariance-based uncertainty representation.  The
solution is not unique so we define the normal form for a covariance matrix
which captures the essential geometric uncertainty in the parameters along
with the indeterminacies, and derive an equivalence relationship between
covariances that capture the same geometric uncertainty.  We then propose
an efficient method for estimating the shape and motion covariances.  The
indeterminacies imply that Structure from Motion over-parametrizes the
problem and that the parameters do not have direct physical meaning.  We
show how to obtain physically meaningful quantities and how to obtain their
covariances by transforming our singular covariances.