In this paper, we propose a new approach for interpolating curves
in time, which is a process of gradually changing a source
through intermediate curves (unknown) into a target curve (known).
The novelty of our approach is in the deployment of
a new regularization term and the corresponding Euler equation.
Our method is applicable to implicit curve
representation and it establishes
a relationship between curve interpolation and a two dimensional
This is achieved by minimizing the supremum of the gradient, which
leads to the Infinite Laplacian Equation (ILE).
ILE is optimal in the sense that interpolated curves are
equally distributed along their normal direction.
We point out that the existing Distance Field
Manipulation (DFM) methods are
only an approximation to the proposed optimal solution and
that the relationship between ILE and
DFM is not local as it has been asserted before.
The proposed interpolation can also be
used to construct multiscale curve representation.
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Publication number: LBNL-45325