Topologically Faithful Implicit Curve Approximation by Constrained Least Squares

I have presented my research about implicit curve approximation in Meeting of the Minds 2019 (Undergraduate Research Symposium at CMU).

• My poster presented at Meeting of the Minds 2019
• Implementation of present implicit curve approximation methods

Our method is based on the topologically faithful implicit curve approximation method proposed by Keren (2004). One shortcomming of the method is that it requires high-degree non-linear optimization. We propose a method to transform the problem into contrained least squares, which can be solved by quadratic programming.

Shortcommings of our method are

• It requires an ordering of the data points.
• It requires control points.
• The representation power is not sufficient.

References

1. Keren, D. (2004). Topologically Faithful Fitting of Simple Closed Curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(1), 118–123. https://doi.org/10.1109/TPAMI.2004.1261095