May 2015
Intermediate to advanced
246 pages
6h 33m
English
book
A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing
by Daniel Cohen-Or, Chen Greif, Tao Ju, Niloy J. Mitra, Ariel Shamir, Olga Sorkine-Hornung, Hao Zhang
Content preview from A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing
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36 Least-Squares Solutions
indeed a good estimate of the underlying model if the points are
samples arising from a line segment. What if the points come from
a parabola, or some other higher-order function (see Figure 3.5)?
As we will shortly see, this approach is not all that different from
what we have learned for the linear case.
x
y y = f(x)
Figure 3.5: LS polynomial fit to a given set of points. The LS solution
gives the best curve fit to a set of given points by optimizing over all
curves from a family specified by a polynomial of the form y = f(x).
Given a point set P := {p
i
}, say we want to find the best-
fitting m-th order polynomial function represen ...
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