Sequential mean shift algorithms for space–time point data

Principal component mean shift (PCMS) algorithms are well-established methods for denoising and smoothing manifold data. Main fields of application are feature detection and recognition in point data produced by laser scanning, seismic catalogs and remote sensing. Till now, they have been applied to pure spatial processes in 2D or 3D forms, obtaining good estimates of principal curves and surfaces. However, in space–time processes a specific treatment must be devoted to their temporal component. Earthquakes data, in particular, are characterized by the occurrence time which requires a dynamic approach to their smoothing for tectonic fault identification. In this paper, we treat this aspect by developing sequential PCMS algorithms, both in normal and in blurring form, and by dealing with the selection of their smoothing coefficients. Using both real and simulated data, we show that the sequential approach does improve the detection performance of classical PCMS in the presence of complex point clouds. In particular, it turns out to be effective in tracking multiple overlapping curves and nonsmooth corners.