Coupled Splines for Sparse Curve Fitting

TL;DR

This paper introduces a method for constructing sparse, continuous curve models from contour points using coupled splines, effectively balancing sparsity, rotation invariance, and smoothness.

Contribution

It formulates a novel inverse problem for sparse curve fitting with regularization, proving solutions are spline-based and extending to hybrid splines for mixed smoothness contours.

Findings

Faithful contour reconstruction with few parameters

Effective handling of measurement imprecisions

Extension to hybrid spline models for diverse contours

Abstract

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.