Candidate:  Hsing-Kuo Kenneth Pao
            Advisor:  Davi Geiger

                 A Continuous Model for
        Salient Shape Selection and Representation

             4:00 p.m., Friday, April 6, 2001
            7th floor conference room, 715 Broadway


We propose a new framework for shape representation
and salient shape selection.
The framework is considered as a low- to middle-level
vision process.
The framework can be applied to various topics, including
figure/ground separation, searching of the shape axis,
junction detection and illusory figure finding.
The model construction is inspired by the Gestalt studies.
They suggest that proximity, convexity, similarity, good continuation,
closure, symmetry, etc, are useful for
figure/ground separation and visual organization construction.
First, we quantify those attributes for (completed or partial) shapes
by our distributed systems.
The shape will be evaluated and represented
by those results.
In particular, the shape convexity, rather than other shape
attributes like the symmetry axis or size
which were well-studied before, will be emphasized
in our discussion.

Our problem is proposed in a continuous manner.
For the shape convexity, unlike the conventional mathematical definition,
we are aimed at deriving
a definition to describe a shape ``more convex'' or ``less convex''
than the other.
To search the shape axis, more than a binary information
telling a point on or off any axis,
a continuous information will be obtained.
We distinguish axes with ``stronger'' or ``weaker'' declarations.
An Easy and natural scheme of pruning can be applied by such representation.
For the junction detection,
we do not assume any artificial threshold.
Instead, the transition from low-curvature to high-curvature
curves or curves with discontinuities
will be shown by our representation.
The model is based on a variational approach, provided
by the minimization of the data fitting error
as well as the neighborhood discrepancy.
Two models will be proposed, the decay diffusion process
and the orientation diffusion process.