Editing Piecewise function (section)

== Applications ==

In applied mathematical analysis, "piecewise-regular" functions have been found to be consistent with many [[Visual perception#Cognitive and computational approaches|models of the human visual system]], where images are perceived at a first stage as consisting of smooth regions separated by edges (as in a [[cartoon]]);<ref>{{cite journal |title = Introduction to shearlets |first1 = Gitta |last1 = Kutyniok|author1-link=Gitta Kutyniok |first2 = Demetrio |last2 = Labate |journal = Shearlets |pages = 1–38 |year = 2012 |publisher = [[Birkhäuser]] |url = https://www.math.uh.edu/~dlabate/SHBookIntro.pdf }} Here: p.8</ref>
a '''cartoon-like function''' is a [[Smoothness#Example:_finitely-times_differentiable_(Ck)|C<sup>2</sup>]] function, smooth except for the existence of discontinuity curves.<ref name="s150">{{cite journal | last1=Kutyniok | first1=Gitta | last2=Lim | first2=Wang-Q | title=Compactly supported shearlets are optimally sparse | journal=Journal of Approximation Theory | volume=163 | issue=11 | date=2011 | doi=10.1016/j.jat.2011.06.005 | pages=1564–1589| arxiv=1002.2661 }}</ref>
In particular, [[shearlet]]s have been used as a representation system to provide sparse approximations of this model class in 2D and 3D.

Piecewise defined functions are also commonly used for interpolation, such as in [[nearest-neighbor interpolation]].