kza (version 4.2.1)

rlv: Rolling Variance Function

Description

Rolling variance function, (rlv) will detect data variations of 1-dimensional vector, 2-dimensional matrix and/or 3-dimensional array, which in turn display their local discontinuities (boundaries).

Usage

rlv(inpt, krnl, pad = c("clamp", "zero"))

Arguments

inpt

input data.

krnl

length of the rolling window for detecting. Must be an odd number for the centered mode; krnl = 1 selects the legacy one-sided mode (the maximum over the corner windows that include the center cell).

pad

boundary policy. "clamp" (the default) clamps windows at the data edge and computes each variance from the cells actually present. "zero" reproduces the pre-4.2.0 behavior exactly: the data is conceptually zero-padded by the window radius, so windows near the border mix zeros into the variance, biasing it upward wherever the data is far from zero.

Details

The rlv is calculated based on a dynamic rolling window. Within a given window, directly estimating its variance allows to capture the local variations of the signal underlying analysis. Since this window is moving, when its size is optimal, the significant local variance atlas will be captured. It is neither necessary to make any assumption, nor to model anything, so it is a nonparametric statistic. However, direct application of rlv to data embedded in heavy background noises could fail to identify the significant local variations. In situations when the estimated data are embedded in background noise, necessary smoothness may be expected.

References

Igor G Zurbenko, Mingzeng Sun. Estimation of spatial boundaries with rolling variance and 2D KZA algorithm. Biometrics & Biostatistics International Journal. 7(4):263.270, 2018

Examples

## A. Signal/objects
# to create a cylinder
circleFun <- function(center = c(0,0),diameter = 1, npoints = 200){
  r = diameter / 2
  tt <- seq(0,2*pi,length.out = npoints) 
  xx <- center[1] + r * cos(tt)
  yy <- center[2] + r * sin(tt)
  return(data.frame(x = xx, y = yy))
}
rxo1 <- circleFun(center = c(38, 38), diameter = 38, npoints = 200)
rxi1 <- circleFun(center = c(38, 38), diameter = 18, npoints = 200)
rxo2 <- circleFun(center = c(58, 58), diameter = 38, npoints = 200)
rxi2 <- circleFun(center = c(58, 58), diameter = 18, npoints = 200)
rxo3 <- circleFun(center = c(28, 78), diameter = 18, npoints = 200)
rxi3 <- circleFun(center = c(28, 78), diameter = 8, npoints = 200)

set.seed(3)
s2 <- matrix(rep(0,100*100),nrow=100) 
for(i in 1:nrow(rxo1)) {
s2[rxo1[i,2],38:rxo1[i,1]]=0.5
}
for(i in 1:nrow(rxi1)) {
s2[rxi1[i,2],38:rxi1[i,1]]=1
}
# second cylinder
for(i in 1:nrow(rxo2)) {
s2[rxo2[i,2],58:rxo2[i,1]]=0.5
}
for(i in 1:nrow(rxi2)) {
s2[rxi2[i,2],58:rxi2[i,1]]=1
}
#third separated cylinder
for(i in 1:nrow(rxo3)) {
s2[rxo3[i,2],28:rxo3[i,1]]=0.3
}
for(i in 1:nrow(rxi3)) {
s2[rxi3[i,2],28:rxi3[i,1]]=0.6
}
signal=s2
## Graphing Library plotly
if (FALSE) {
plot_ly(z=signal, type="surface")
}

## B. Rolling variance atlas

rolv=rlv(s2,3)
if (FALSE) {
plot_ly(z=rolv, type="surface")
}