Fitting IP curves to data

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Problem: Given a discrete set of data points sampled on a curve, find a coefficient vector of degree d such that the IP curve "best" represents the data.

Intuitive solution: Minimize the sum of euclidean distances from data points to the IP curve. No closed form expression for distance for general degrees.

Simple alternative (classical LS): Minimize sum of squared values of f at the data points. Gives poor representation of the data. Not robust under noise or shape perturbations.

Other approaches:

• Linear approximations to euclidean distance. [Taubin] Improves the quality of the representation in some cases.
• Non-linear methods: constraints on the topology of the IP curve, boundedness [Keren etal.]

Our approach: Develop a robust fitting method while staying within a linear solution framework.

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