Average-distance problem with curvature penalization for data parameterization: regularity of minimizers
Average-distance problem with curvature penalization for data parameterization: regularity of minimizers
We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functional to measure the quality of the approximation and penalizes the curvature, similarly to the elastica functional. Introducing the curvature penalization overcomes some of the …