A new approach for reconstruction of
3D surfaces from 2D cross-sectional contours is presented.
By using the so-called ``Equal Importance Criterion,''
we reconstruct the
surface based on the assumption that every point in the region
contributes equally to the
surface reconstruction process.
In this context, the problem is formulated in terms of
a partial differential equation (PDE), and we show
that the solution for dense contours
(contours in close proximity)
efficiently derived from distance transform. In the
case of sparse contours, we add a regularization
term to ensure smoothness in surface recovery.
The approach is also generalized to other types of cross-sectional
contours where the spine may not be a straight line.
The proposed technique allows for surface recovery
at any desired resolution.
The main advantages of our method is that
inherent problems due to correspondence, tiling, and branching
are avoided. In contrast to existing implicit methods,
we find an optimal
field function and develop an
interpolation method that does not generate any artificial surfaces.
We will demonstrate that the computed high-resolution
surface is well represented
for subsequent geometric analysis.
We present results on both synthetic and real data.
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Publication number: LBNL-43265