localCurvature: Local Curvature

Description

Computes signed curvature along a line.

Usage

localCurvature(x, h, maxk)

Arguments

A data frame or matrix of dimensions N x 2 containing the coordinates of the line, where N is the number of points. The points should be ordered according to their position on the line. The columns should contain the x and y coordinates. The curvature calculation is unaffected by any permutation of the columns. Directly accepts a list element from ocontour.

Specifies the length of the smoothing window. See locfit::lp for more details.

maxk

See locfit::locfit.raw for details.

Value

Returns a list containing the contour coordinates x, the signed curvature at each point curvature and the arc length of the contour length.

Details

localCurvature fits a local non-parametric smoothing line (polynomial of degree 2) at each point along the line segment, and computes the curvature locally using numerical derivatives.

Examples

Run this code

  ## curvature goes as the inverse of the radius of a circle
  range=seq(3.5,33.5,by=2)
  plotRange=seq(0.5,33.5,length=100)
  circleRes=array(dim=length(range))
  names(circleRes)=range
  for (i in  seq_along(1:length(range))) {
   y=as.Image(makeBrush('disc', size=2*range[i]))
   y=ocontour(y)[[1]]
   circleRes[i]=abs(mean(localCurvature(x=y,h=range[i])$curvature, na.rm=TRUE))
  }
  plot(range, circleRes, ylim=c(0,max(circleRes, na.rm=TRUE)), xlab='Circle Radius', ylab='Curvature', type='p', xlim=range(plotRange))
  points(plotRange, 1/plotRange, type='l')

  ## Calculate curvature
  x = readImage(system.file("images", "shapes.png", package="EBImage"))[25:74, 60:109]
  x = resize(x, 200)
  y = gblur(x, 3) > .3
  display(y)
  
  contours = ocontour(bwlabel(y))
  c = localCurvature(x=contours[[1]], h=11)
  i = c$curvature >= 0
  pos = neg = array(0, dim(x))
  pos[c$contour[i,]+1]  = c$curvature[i]
  neg[c$contour[!i,]+1] = -c$curvature[!i]
  display(10*(rgbImage(pos, , neg)), title = "Image curvature")