Theoretical understanding of the properties of smoothing depends upon the eigenstructure of the smoothing matrix. Hastie, Tibshirani, and Freidman (2001; The Elements of Statistical …

In other words, we have moved from estimating linear transformations of the features to ones, which we fit using a smoother (traditional packages use kernel smoothing, or spline …

Gaussian Smoothing Filter Smoothing filter that does weighted averaging. The coefficients are a 2D Gaussian. Gives more weight at the central pixels and less weight to the neighbors. The …

If nearby pixels have similar ”true”intensities, then we can use smoothing to reduce the noise. We can also think of smoothing as a simple example of how information can be passed between …

An issue with kernel smoothing (including running means) is that these methods have bad behavior at the edges of the plot. Observe what kernel smoothing does with perfectly regular, …

From this point of view the equations (6.1) are just a transparent reformulation of Fubini’s theorem, because by definition of T œ f (x + y)dμ(x)d∫(y) = Z f ±T d(μ£∫).

After the first pass the residuals are computed (called reroughing); the same smoothing sequence is applied to the residuals in a second pass, adding the result to the smooth of the first pass.