HMRF: Image Segmentation using Hidden Markov Random Field with EM...

In rwang14/implant: A High-throughput Phenotyping Pipeline for Image Processing and Functional Growth Curve Analysis

Description

This function can be used to obtain the segmented image using HMRF-EM Algorithm.

Usage

HMRF(X, Y, Z, em_iter, map_iter, beta = 2,
        epsilon_em = 0.00001, epsilon_map = 0.00001)

Arguments

X	an m by n binary matrix of the inital labels for an image, which can be obtained using initital segmentation methods, such as K-means or thresholding methods. Note that X could be any binary matrix, for example, its element could be 0 & 1, or 1 & 2, or 2 & 3, ..., etc.
Y	an m by n matrix of pixel intensity. For plant segmentation, we recommend to use relative green.
Z	an m by n binary matrix, giving an estimate for the object edges in Y. We can obtain Z using the Canny edge detector: Z = t(cannEdges (Y) [ , , 1, 1]) from the package: imager. See the example for details.
em_iter	a positive integer, which is the number of iteration steps of the EM Algorithm.
map_iter	a positive integer, which is the number of iteration steps of calculating MAP (the maximum a posterior estimation).
beta	The clique potential parameter for neighbourhood dependence. In default, beta = 2. See details in the supplementary file on the HMRF Model. This beta is equivalent to the Psi in the supplentary file (see page 20, 21).
epsilon_em	a small positive number, which is the convergence criterion of the EM Algorithm.
epsilon_map	a small positive number, which is the convergence criterion of MAP (maximum a posterior estimation).

Details

1. More detailed explanation about this method can be found in the supplymentary file:

https://github.com/rwang14/implant/blob/master/vignettes/HMRF_EM.pdf

2. The arguement Z can be obatined by CannyEdge detector using function cannEdges( ) from the package: imager. However, since this package needs to involve Rcpp and other dependent packages which may increase installation complexity of our package, we recommend the users to install the package “imager" by themselves if needed.

Value

image_matrix

A matrix giving labels for the segmented image.

Note

This function is modified based on the matlab code written by Quan Wang (see reference).

References

Wang, Quan (2012), “Hmrf-em-image: implementation of the hidden markov random field model and its expectation-maximization algorithm.”arXivpreprintarXiv:1207.3510

See Also

image_kmeans

Examples

library(implant)
library(png)
orig = readPNG(system.file("extdata", "reduced.png", package = "implant", mustWork = TRUE))
#Define the response as relative green.
Y = orig[ , , 2]/(orig[ , , 1] + orig[ , , 2] + orig[ , , 3])
#Z is a matrix obtained by CannyEdge detector
Z = readPNG(system.file("extdata", "Z.png",
                         package = "implant", mustWork = TRUE))
##Note: Users can obtain Z using the package "imager" and the function
#CannyEdges( ) for different images
#Z = t(cannyEdges(orig)[ , , 1, 1])
#Take the initial label of EM algorithm using K-means
X = image_kmeans(Y, k = 2)$X
#Obtain the image produced by kmeans clustering
output = matrix(as.numeric(X), nrow = nrow(X), ncol = ncol(X)) - 1
writePNG(output,"~/kmeans.png")
#Run the HMRF Model. Note that it may take a lot of time ...
img = HMRF(X, Y, Z, em_iter = 20, map_iter = 20, beta = 2,
              epsilon_em = 0.00001, epsilon_map = 0.00001)
#Obtain the matrix of the segmented image
image = img$image_matrix
#Morphological Operations
imageD = dilation(image)
imageDE = erosion(imageD)
imageDEE = erosion(imageDE)
imageDEED = dilation(imageDEE)
writePNG("~/HMRF.png")

rwang14/implant documentation built on Sept. 6, 2020, 3:21 a.m.