Persistence Mapping and the Time Convolution Mapping Method

Barbara J. Thompson and C. Alex Young

Persistence Mapping is a simple image processing technique that is useful for the visualization and depiction of gradually evolving or intermittent structures. Persistence Mapping allows the user to isolate extreme values in a data set, and is particularly useful for the problem of capturing phenomena that are evolving in both space and time.

While integration or “time lapse” imaging uses the full sample (of size N), Persistence Mapping rejects (N-1)/N of the data set and identifies the most relevant 1/N values using the following rule: if a pixel reaches an extreme value, it retains that value until that value is exceeded. The simplest examples isolate minima and maxima, and the technique has been used to extract the dynamics in long-term evolution of comet tails, erupting material, CMEs, and EUV dimming regions.

Our paper in preparation describes the technique and gives clearer examples:
link to paper draft

The associated “Time Convolution Mapping Method” allows the user to identify the time history of the phenomenon. The Time Convolution Mapping Method (TCMM) highlights distinct “rainbow profiles” in the data, allowing users to separate features with different propagation characteristics. For example, one of the well-known obstacles (particularly for fast and wide CMEs) is separating “true” CME mass from CME-associated brightenings. Our CME identification algorithm, the “Time Convolution Mapping Method,” convolves the brightness of the persistence maps with a color scale that indicates the time at which the CME reached the persistence brightness. and separate the “true” CME from CME-associated brightenings.

This method was introduced at the 2014 Meeting of the American Astronomical Society:

(link to poster, download from http://sdo.gsfc.nasa.gov/assets/mov/depot/Misc/Poster_AAS_2014.ppt)

Stay tuned for more examples and movies, and feel free to contact either author to discuss how these techniques can be implemented further.

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