Voronoi-based segmentation on image manifolds

Description

R implementation of the Voronoi-based image segmentation on image manifolds [2].

Usage

    # S4 Method for Image-class

    propagate(x, seeds, mask=NULL, lambda=0.005, ext=1)

Arguments

x

An object of Image-class to be segmented, in the Grayscale mode.

seeds

An object of Image-class of the same size as x in all three dimensions; in the Grayscale mode with integer-based object encoding, as returned by watershed. This image provides seed points for object detection.

mask

An object of Image-class of the same size as x in all three dimensions; in the Grayscale mode. All zero regions will be excluded from object detection.

lambda

A numeric value. The regularisation parameter for the distance calculations, determines the trade-off between the Euclidian distance in the image plane and the contribution of the gradient of the values in x. See details.

ext

Extension of the neighborhood to estimate image gradient, in pixels in every direction from the central point, i.e. ext=1 means a 3x3 neighborhood.

Value

An image of Image-class, with the same object indexing as seeds. No new objects are created, only those specified by seeds are propagated. Use getObjects to assign the feature matrix.

Details

The method operates by computing a discretized approximation of the Voronoi regions for given seed points on a manifold with a metric controlled by local image features.

The metric is a Riemannian metric defined in terms of the image I and a regularization parameter lambda. With this metric the distance between pixels used to let the given seeds grow outwards (propagate) is

$d^2 = (grad(I)^2 + lambda * (dx^2 + dy^2)) / (lambda + 1)$

The gradient is calculated on a neighborhood of pixels (the width of which is controlled by the argument ext) to avoid relying on single (noisy) pixels. Lambda controls the weight of the Euclidian distance term. In case of large lambda, d turns into Euclidian distance in the (x,y)-plane. For small lambda, the distance will be dominated by the intensity gradient.

Author

Original CellProfiler code: Anne Carpenter <carpenter@wi.mit.edu>, Thouis Jones <thouis@csail.mit.edu>, In Han Kang <inthek@mit.edu>.

Port for this package: Oleg Sklyar <osklyar@ebi.ac.uk> and Wolfgang Huber <huber@ebi.ac.uk>.

License

The underlying C++ code is based on code from CellProfiler [1,3]. An LGPL license was granted by Thouis Jones to use this part of CellProfiler's code for the propagate function.

References

[1] A. Carpenter, T.R. Jones, M.R. Lamprecht, C. Clarke, I.H. Kang, O. Friman, D. Guertin, J.H. Chang, R.A. Lindquist, J. Moffat, P. Golland and D.M. Sabatini, "CellProfiler: image analysis software for identifying and quantifying cell phenotypes", Genome Biology 2006, 7:R100

[2] T. Jones, A. Carpenter and P. Golland, "Voronoi-Based Segmentation of Cells on Image Manifolds", CVBIA05 (535-543), 2005

[3] CellProfiler: http://www.cellprofiler.org

See Also

Image-class, watershed, getObjects

Examples

    if ( interactive() ) {
      ddir <- paste( system.file(package="EBImage"), "images", sep="/" )
      a <- read.image( paste(ddir, c("A04w0.jpg", "A04w1.jpg"), sep="/") )
      rgb <- channel(a[,,1],"asred") + channel(a[,,2],"asgreen")

      ## Not run: detecting nuclei by watershed
      t <- thresh( blur(a[,,2], 4, 2), 15, 15)
      t <- opening( closing(t, morphKern(9)) )
      w <- watershed( distmap(t) )

      ## Not run: generating mask for propagate
      mask <- thresh( a[,,1], 50, 50, -0.01)
      mask <- closing( mask, morphKern(13) )
      mask <- opening( mask, morphKern(11) )
      mask <- erode(mask)

      ## Not run: propagate with the mask and gradient-driven metric
      wx <- propagate( a[,,1], w, mask, 0.0001, 2)
      prev <- paintObjects(wx, paintObjects(w, rgb))
      display(prev)

      ## Not run: pure Voronoi: no mask and almost no gradient term in metric
      wx1 <- propagate( a[,,1], w, NULL, 1e8, 2)
      prev1 <- paintObjects(wx1, rgb)
      display(prev1)
    }