gaussianSmoothingSlope: gaussianSmoothingSlope

In tbgitoo/textureAnalyzerGels: Reading and analyzing texture analyzer data

gaussianSmoothingSlope

Description

Slope of a curve smoothed by a gaussian filter; this is a classical difference of gaussian filter (Gonzalez and Woods 2008) with the possibility to indicate specific output points.

Usage

gaussianSmoothingSlope(x,y,sd=1,xout=x,...)

Arguments

x	The x values formatted as a vector
y	The y values, formatted as a vector of length identical to the length of x
sd	Standard deviation for the smoothing, in terms of x-coordinates
xout	The x values where an output is desired
...	Supplementary arguments to be passed to gaussianSmoothing, used internally

Value

A numerical vector of the same length as xout, giving the estimated slope at each point given in xout

Author(s)

Thomas+Marina Braschler

References

Digital Image Processing, 3rd edition, Gonzalez R.C. and Woods R.E., Pearson, 2008, ISBN 9780133002324

Examples

# First, without boundary extension. In theory, the smoothened curve should rise linearly, and the slope be constant at 1/100 (=10 when multiplied with 1000)

x=seq(from=0,to=1500,by=0.25)
xout=x
y=runif(length(x))+x/100
sd=50
smoothed=gaussianSmoothing(x=x,y=y,sd=sd,xout=xout)
slope=gaussianSmoothingSlope(x=x,y=y,sd=sd,xout=xout)
plot(x=x,y=y,type="p")
plot.xy(xy.coords(x=xout,y=smoothed),type="l",col="red")
plot.xy(xy.coords(x=xout,y=slope*1000),type="l",col="green")

# In particular the slope in the above example nicely shows the edge problem. This can be first-order corrected with linear boundary extension:


x=seq(from=0,to=1500,by=0.25)
xout=x
y=runif(length(x))+x/100
sd=50
boundary_extension=500
smoothed=gaussianSmoothing(x=x,y=y,sd=sd,xout=xout,boundary_extension=boundary_extension)
slope=gaussianSmoothingSlope(x=x,y=y,sd=sd,xout=xout,boundary_extension=boundary_extension)
plot(x=x,y=y,type="p")
plot.xy(xy.coords(x=xout,y=smoothed),type="l",col="red")
plot.xy(xy.coords(x=xout,y=slope*1000),type="l",col="green")

tbgitoo/textureAnalyzerGels documentation built on March 30, 2022, 4:53 a.m.