What is it about?
A response surface is conceptually a continuous surface of intensity (grey) values. A fault line is the locus of an edge; for example, the outline of an object before its background. A paper in 2008 with P. Hall and P.H. Qiu discusses the case of intersecting fault lines.
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This page is a summary of: Tracking a smooth fault line in a response surface, The Annals of Statistics, May 2000, Institute of Mathematical Statistics,
DOI: 10.1214/aos/1015951995.
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