  We formulate as an inverse problem the construction of sparse parametric
continuous curve models that fit a sequence of contour points. Our prior is
incorporated as a regularization term that encourages rotation invariance and
sparsity. We prove that an optimal solution to the inverse problem is a closed
curve with spline components. We then show how to efficiently solve the task
using B-splines as basis functions. We extend our problem formulation to curves
made of two distinct components with complementary smoothness properties and
solve it using hybrid splines. We illustrate the performance of our model on
contours of different smoothness. Our experimental results show that we can
faithfully reconstruct any general contour using few parameters, even in the
presence of imprecisions in the measurements.
