Robust curve reconstruction with k-order α-shapes

We combine classical concepts from different disciplines - those of robust curve reconstruction with k-order alpha-shapes-hull and robust curve reconstruction with k-order alpha-shapes-shape from computational geometry, splitting data into training and test sets from artificial intelligence, density-based spatial clustering from data mining, and moving average from time series analysis - to develop a robust algorithm for reconstructing the shape of a curve from noisy samples. The novelty of our approach is two-fold. First, we introduce the notion of k-order alpha-hull and alpha-shape - generalizations of alpha-hull and alpha-shape. Second, we use white noise to "train" our k-order alpha-shaper, i.e., to choose the right values of alpha and k. The difference of the k-order alpha-hull and alpha-shape from the alpha-hull and alpha-shape is also two-fold. First, k-order alpha-hull and alpha-shape provide a robust estimate of the shape by ignoring outliers. Second, it reconstructs the "inner" shape, with the amount of "digging" into the data controlled by k.