Digital Signal Processing Reference
In-Depth Information
R
(
x,y
) is the additive term for using a subproblem
x
to solve the sub-
problem
y
, and
c
(
x, y
) are the weighted connectivities of positive value
between subproblems. We find the optimal solution of
E
dynamic
effi-
ciently via the algorithm in Figure 4.13. Translation of our energy func-
tion
→ →
→
→
→ →
E
(
S,I,M
)
into
the
compatible
form
of
E
dynamic
may
affect
the
search for our optimal solution of our desired energy function.
In our application, we choose a DP solution. DP can produce not only
an optimized surface but also its parameterization [Amini et al., 1990].
The optimal solution from DP returns the set of optimal solutions of
subproblems that were used in the calculation of the optimal solution
and we can use this set to parameterize our surface. While we can
dynamically change the surface parameterization in a gradient-based
optimization by adding and removing parameters between the iterations,
the DP algorithm gives us a more straightforward and elegant solution.
For our system, the translation of surface energy function to a form
acceptable to DP is not problematic.
In the future, we believe that a hybrid of dynamic programming and
gradient methods would provide the best solution. DP can converge
quickly on both a good parameterization of the surface and an good
initial surface estimate. When surface parameterization becomes fixed,
gradient methods integrate 2-D structure better and can use the orig-
inal energy function. A hybrid method of surface optimization that
alternates between the two methods of optimization is in our future re-
search.
CONTOUR OPTIMIZATION BY DP: VITERBI
RINGS
As a stepping stone in analysis of our surface optimization, we analyze
a contour optimization algorithm that finds the Viterbi Rings with a
circularly ordered space. The contour optimization, a variation of the
Viterbi path-finding algorithm, is used within our surface optimization
algorithm, but is applied over a Voronoi Ordered Space. DP requires
three steps: 1) the formulation of energy function, 2) translation of the
energy function into a recurrence relation that is compatible with DP,
and 3) the application of DP to find the optimal contour. From this
optimization, we then extract our Viterbi Rings.
We encode the heuristics of the Viterbi Rings as a contour optimiza-
tion problem. The Viterbi Rings are a set of edges to be classified by
probable relevance (to be defined shortly) to a given object center X.
Edges are assumed to be more relevant when
Search WWH ::
Custom Search