Step detection

Examples of signals that may contain steps corrupted by noise. (a) DNA copy-number ratios from microarray data, (b) cosmic ray intensity from a neutron monitor, (c) rotation speed against time of R. Sphaeroides flagellar motor, and (d) red pixel intensity from a single scan line of a digital image.

In statistics and signal processing, step detection (also known as step smoothing, step filtering, shift detection, jump detection or edge detection) is the process of finding abrupt changes (steps, jumps, shifts) in the mean level of a time series or signal. It is usually considered as a special case of the statistical method known as change detection or change point detection. Often, the step is small and the time series is corrupted by some kind of noise, and this makes the problem challenging because the step may be hidden by the noise. Therefore, statistical and/or signal processing algorithms are often required.

The step detection problem occurs in multiple scientific and engineering contexts, for example in statistical process control[1] (the control chart being the most directly related method), in exploration geophysics (where the problem is to segment a well-log recording into stratigraphic zones[2]), in genetics (the problem of separating microarray data into similar copy-number regimes[3]), and in biophysics (detecting state transitions in a molecular machine as recorded in time-position traces[4]). For 2D signals, the related problem of edge detection has been studied intensively for image processing.[5]

  1. ^ E.S. Page (1955). "A test for a change in a parameter occurring at an unknown point". Biometrika. 42 (3–4): 523–527. doi:10.1093/biomet/42.3-4.523. hdl:10338.dmlcz/103435.
  2. ^ Cite error: The named reference Gill1970 was invoked but never defined (see the help page).
  3. ^ Snijders, A.M.; et al. (2001). "Assembly of microarrays for genome-wide measurement of DNA copy number". Nature Genetics. 29 (3): 263–264. doi:10.1038/ng754. PMID 11687795. S2CID 19460203.
  4. ^ Sowa, Y.; Rowe, A. D.; Leake, M. C.; Yakushi, T.; Homma, M.; Ishijima, A.; Berry, R. M. (2005). "Direct observation of steps in rotation of the bacterial flagellar motor". Nature. 437 (7060): 916–919. Bibcode:2005Natur.437..916S. doi:10.1038/nature04003. PMID 16208378. S2CID 262329024.
  5. ^ Serra, J.P. (1982). Image analysis and mathematical morphology. London; New York: Academic Press.