Robust curve reconstruction with k-order alpha-shapes

We combine classical concepts from different disciplines — those of α-hull and α-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 α-hull and α-shape — generalizations of α-hull and α-shape. Second, we use white noise to “train” our k-order α-shaper, i.e., to choose the right values of α and k. The difference of the k-order α-hull and α-shape from the αhull and α-shape is also two-fold. First, k-order α-hull and α-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.