ANTsR Algorithms

Here, we provide an overview of the methods available within ANTsR.

• core image processing and I/O: ITK (B. B. Avants, Tustison, et al. 2014);

• registration and utilities for image processing: ANTs mappings (Tustison, Cook, et al. 2014) and feature extraction (Tustison, Shrinidhi, et al. 2014);

• dimensionality reduction: Eigenanatomy (Dhillon et al. 2014) and SCCAN (B. B. Avants, Libon, et al. 2014);

• methods for ASL-based cerebral blood flow quantification (Kandel et al. 2015);

• neighborhood representations of images that enable rich statistical models (Kandel et al. 2015)

• core statistics and temporal filtering via R packages that is amenable to BOLD image processing

In combination, these tools enable one to go from near-raw medical imaging data to a fully reproducible scientific publication (Avants 2015).

Data organization and access in ANTsR

This package uses an antsImage S4 class to hold pointers to ITK images. We convert antsImage objects to R objects before passing them to R statistical methods. E.g. we convert a scalar image to a vector, a collection of scalar images to a matrix or a time series image to a matrix. Currently, ANTsR does not explicitly represent images with vector valued voxels (e.g. tensor or warp images) although these may be supported in the future in a way that is similar to our current support for time series images. The large majority of images employed within ANTsR are of 2, 3 or 4 dimensions with float pixel types. This information is stored within the antsImage class.
A few example images are built into ANTsR, but more can be downloaded. See ?getANTsRData.

img<-antsImageRead( getANTsRData("r16"), 2 ) # built in image
img

## antsImage
##   Pixel Type          : float 
##   Components Per Pixel: 1 
##   Dimensions          : 256x256 
##   Voxel Spacing       : 1x1 
##   Origin              : 0 0 
##   Direction           : 1 0 0 1 
##   Filename           : /Users/travis/R/Library/ANTsRCore/extdata/r16slice.jpg

Take a quick look at the image.

Contributions of the package

ANTsR includes:

• An organizational system such that relatively small scripts may implement full studies

• Implementation of foundational methods
  • Smoothing, temporal filtering, etc
  • functional image denoising via compcor and *DenoiseR
  • flexible: easy to estimate voxel-wise statistical models

• Reference simulation data and examples distributed with the package

• Interpretation of results
  • sparse low-dimensional predictors
  • anatomical labeling of predictors based on AAL and other coordinate systems

• Openness and reproducibility

In total, ANTsR is a rigorous framework upon which one may build customized statistical implementations appropriate for large-scale functional, structural or combined functional and structural image analyses. Because much of the core is implemented with C++, the framework also remains efficient. Finally, note that Rscript allows one to send ANTsR scripts to clusters and take advantage of distributed computing resources.

Basic ANTsR functionality

Here, we quickly summarize ANTsR functionality and useful tools.

The travis build system

We test ANTsR regularly. The status of the build (and an expected build result) can be seen here: . Take a look at the detailed log to see what one might expect if building ANTsR from source.

Image input and output

If nothing else, ANTsR makes it easy to read and write (medical) images and to map them into a format compatible with R. Formats we frequently use include jpg, tiff, mha, nii.gz and nrrd. However, only the last three have a proper physical space representation necessary for mapping. Below is an example of how we access this type of image and see its geometry. Check antsImageWrite for the primary supported I/O.

mnifilename<-getANTsRData("r27")
img<-antsImageRead(mnifilename, pixeltype="unsigned char")
img

## antsImage
##   Pixel Type          : unsigned char 
##   Components Per Pixel: 1 
##   Dimensions          : 256x256 
##   Voxel Spacing       : 1x1 
##   Origin              : 0 0 
##   Direction           : 1 0 0 1 
##   Filename           : /Users/travis/R/Library/ANTsRCore/extdata/r27slice.jpg

# retval<-antsImageWrite(img,mnifilename)
antsGetSpacing(img)

## [1] 1 1

antsGetDirection(img)

##      [,1] [,2]
## [1,]    1    0
## [2,]    0    1

antsGetOrigin(img)

## [1] 0 0

print(img[120,122]) # same type of thing in 3 or 4D

##      [,1]
## [1,]  182

print(max(img))

## [1] 255

Index an image with a label

Often, you would like to summarize or extract information from within a known region of an image with arbitrary shape but within a given intensity “zone”. We simulate this below and show a few accessors and type conversions.

gaussimg<-array( data=rnorm(125), dim=c(5,5,5) )
arrayimg<-array( data=(1:125), dim=c(5,5,5) )
img<-as.antsImage( arrayimg )
print( max(img) )

## [1] 125

print( mean(img[ img > 50  ]))

## [1] 88

print( max(img[ img >= 50 & img <= 99  ]))

## [1] 99

# if using SUBSET using an antsImage, you must be explicit
sub = as.array(img >= 50 & img <= 99) > 0
print( mean( gaussimg[ sub  ]) )

## [1] 0.09836209

Convert a 4D image to a matrix

Four dimensional images are generated and used in the same way. One can easily transform from 4D image to matrix and back.

gaussimg<-makeImage(c(5,5,5,10), voxval = rnorm(125*10)  )
print(dim(gaussimg))

## [1]  5  5  5 10

avg3d<-ANTsR::getAverageOfTimeSeries( gaussimg )
mask <- avg3d < 0.25
gmat<-timeseries2matrix( gaussimg, mask )
print(dim(gmat))

## [1]  10 101

If one has a mask, then one can use makeImage to generate a new image from a scalar or vector.

newimg<-makeImage( mask, mean(avg3d) )    # from scalar
newimg<-makeImage( mask, colMeans(gmat) ) # from vector

Convert a list of images to a matrix

Often, one has several scalar images that need to be accumulated for statistical processing. Here, we generate a simulated set of these images and then proceed to smooth them, store them in a list and convert them to a matrix after extracting the information of each image within a data-driven mask.

nimages<-100
ilist<-list()
for ( i in 1:nimages )
  {
  simimg<-makeImage( c(50,50) , rnorm(2500) )
  simimg<-smoothImage(simimg,1.5)
  ilist[[ i  ]] = simimg
  }
# get a mask from the first image
mask<-getMask( ilist[[1]],
  lowThresh=mean(ilist[[1]]), cleanup=TRUE )
mat<-imageListToMatrix( ilist, mask )
print(dim(mat))

## [1] 100 192

Once we have a matrix representation of our population, we might run a quick voxel-wise regression within the mask. Then we look at some summary statistics.

mat<-imageListToMatrix( ilist, mask )
age<-rnorm( nrow(mat) ) # simulated age
gender<-rep( c("F","M"), nrow(mat)/2 ) # simulated gender
# this creates "real" but noisy effects to detect
mat<-mat*(age^2+rnorm(nrow(mat)))
mdl<-lm( mat ~ age + gender )
mdli<-bigLMStats( mdl, 1.e-4 )
print(names(mdli))

## [1] "fstat"      "pval.model" "beta"       "beta.std"   "beta.t"    
## [6] "beta.pval"

print(rownames(mdli$beta.t))

## [1] "age"     "genderM"

print(paste("age",min(p.adjust(mdli$beta.pval[1,]))))

## [1] "age 0.000605232845703203"

print(paste("gen",min(p.adjust(mdli$beta.pval[2,]))))

## [1] "gen 1"

Write out a statistical map

We might also write out the images so that we can save them for later or look at them with other software.

agebetas<-makeImage( mask , mdli$beta.t[1,] )
returnval<-antsImageWrite( agebetas, tempfile(fileext ='.nii.gz') )

More ANTsR functionality

We achieve quantification in biological or medical imaging by using prior knowledge about the image content.

Segmentation

In segmentation, we assume the image has a known set of tissues, organs etc. Here, we assume 3 tissues exist and use a classic k-means model with MRF penalty (Avants et al. 2011). Note that we also bias correct the image to help it match our model (Tustison et al. 2010).

fi<-antsImageRead( getANTsRData("r16") ,2)
fi<-n3BiasFieldCorrection(fi,2)
seg<-kmeansSegmentation( fi, 3 )
invisible(plot(seg$segmentation))

If you like segmentation, also look at rfSegmentation and atropos.

Registration

In registration, we assume the image can be mapped to some canonical shape or example, i.e. an atlas. Or to another individual. ANTsR provides a simple wrapper for SyN image registration (Tustison and Avants 2013),

mi<-antsImageRead( getANTsRData("r64") ,2)
mytx<-antsRegistration(fixed=fi , moving=mi ,
    typeofTransform = c('SyN'))
regresult<-iMath(mytx$warpedmovout,"Normalize")
fiedge<-iMath(fi,"Canny",1,5,12)
invisible(plot(regresult, list(fiedge), window.overlay=c(0.5,1)) )

while invariantImageSimilarity provides powerful multi-start search for lower dimensional affine registrations.

Deformable image registration results in a voxel-wise map of the contraction and expansion of the moving image (after affine transformation) that is needed to map to the fixed image. This deformation gradient is colloquially known as “the jacobian”.

jac<-createJacobianDeterminantImage(fi,mytx$fwdtransforms[[1]],1)
invisible(plot(jac))

Above, we compute and plot the image of the log-jacobian. This mapping is a useful summary measurement for morphometry (Avants et al. 2012,@Kim2008).

Registration and segmentation

Registration and segmentation are often applied jointly or iteratively to maximize some criterion. See the example in jointIntensityFusion for one such case (Wang and Yushkevich 2013).

Neighborhood operations

Basic I/O and management of images as vectors is critical. However, there is additional information that can be gained by representing an image and its neighborhood information. ANTsR represents image neighborhoods, which capture shape and texture, as a matrix. Here, extract an image neighborhood matrix representation such that we may analyze it at a given scale.

mnit<-getANTsRData("r16")
mnit<-antsImageRead( mnit )
mnit <- resampleImage( mnit , rep(4, mnit@dimension) ) # downsample
mask2<-getMask(mnit,lowThresh=mean(mnit),cleanup=TRUE)
radius <- rep(2,mnit@dimension)
mat2<-getNeighborhoodInMask(mnit, mask2, radius,
  physical.coordinates = FALSE,
  boundary.condition = "mean" )
print(dim(mat2))

## [1]   25 1113

The variable mat2 has size determined by the neighborhood radius (here, 5) and the number of non-zero voxels in the mask. The boundary.condition says how to treat data that is outside of the mask or the image boundaries. This example replaces missing data with the mean in-mask value of the local neighborhood.

Other useful tools in ANTsR include iMath, thresholdImage, quantifyCBF, preprocessfMRI, aslPerfusion, computeDVARS, getROIValues, hemodynamicRF, makeGraph, matrixToImages, rfSegmentation, antsRegistration, plotPrettyGraph, plotBasicNetwork, getTemplateCoordinates, antsSet*.

Several image mathematics operations (like ImageMath in ANTs) are accessible too via iMath.

Example label sets and data

ANTsR also provides AAL label (Tzourio-Mazoyer et al. 2002) names via:

data(aal,package='ANTsR')
labs<-1:90

with cortical labs defined by labs. The DKT atlas labels are similarly summarized in DesikanKillianyTourville (Klein and Tourville 2012).
An example BOLD correlation matrix is available in bold_correlation_matrix. This can be used to try out makeGraph and related functions.

Visualization and plotting

The basic plot function is implemented for the antsImage class. It can show 2 or 3D data with color overlays, the latter of which can display multiple slices side by side. Several color choices are available for the overlays.

For 3D images, see renderSurfaceFunction and plotBasicNetwork for rgl and misc3d based interactive surface and network plots. Another such example is in visualizeBlob. These are too long-running to compile into the vignette but the help examples for these functions will allow you to see their results.

A good visualization alternative outside of ANTsR is antsSurf.

BOLD data processing with ANTsR

Good approaches exist in ANTsR for preprocessing BOLD data. These yield both motion matrices and relevant summary measurements such as FD and DVARS. See ?preprocessfMRI for a simplified utility function. This function could be used on each run of an experiment and the results stored in organized fashion for later use.

Motion correction

To motion correct your data, one might run:

# get an average image
averageImage <- getAverageOfTimeSeries( boldImage )
motionCorrectionResults <- antsMotionCalculation( boldImage,
   fixed = averageImage )

A moreaccurate flag should be set to 1 or 2 for usable (not test) results. FD and DVARS are returned which may be used to summarize motion. One might also get this data from preprocessfMRI which also provides denoising options based on data-driven methods including frequency filtering.

For more fMRI focused tools, see RKRNS and its github site github RKRNS.

Dimensionality reduction

Images often have many voxels (\(p\)-voxels) and, in medical applications, this means that \(p>n\) or even \(p>>n\), where \(n\) is the number of subjects. Therefore, we often want to “intelligently” reduce the dimensionality of the data. We favor methods related to PCA and CCA but have a few ICA related tools too.

Eigenanatomy & SCCAN

Our sparse and geometrically constrained dimensionality reduction methods seek to both explain variance and also yield interpretable, spatially localized pseudo-eigenvectors (Kandel et al. 2014,@Cook2014). This is the point of “eigenanatomy” which is a variation of sparse PCA that uses (optionally) biologically-motivated smoothness, locality or sparsity constraints.

# assume you ran the population example above
eanat<-sparseDecom( mat, mask, 0.2, 5, cthresh=2, its=2 )
eanatimages = matrixToImages( eanat$eig, mask )
eseg<-eigSeg(mask, eanatimages ,F)
jeanat<-joinEigenanatomy(mat, mask, eanatimages, c(0.1))
eseg2<-eigSeg(mask,jeanat$fusedlist,F)

The parameters for the example above are set for fast processing. You can see our paper for some theory on these methods (Kandel et al. 2014). A more realistic study setup would be

eanat<-sparseDecom( inmatrix=mat, inmask=famask, nvecs=50,
  sparseness=0.005, cthresh=500, its=5, mycoption=0 )
jeanat<-joinEigenanatomy( mat , famask, eanat$eig,
  c(1:20)/100.0 , joinMethod='multilevel' )
useeig<-eanat$eig
useeig<-jeanat$fusedlist
avgmat<-abs(imageListToMatrix( useeig , famask ))
avgmat<-avgmat/rowSums(abs(avgmat))
imgmat<-(  mat %*% t(avgmat)  )

The imgmat variable would be your summary predictors entered into lm or randomForest.

More information is available within the examples that can be seen within the help for sparseDecom, sparseDecom2 and the helper function initializeEigenanatomy.

Sparse canonical correlation analysis

CCA maximizes \(PearsonCorrelation( XW^T, ZY^T )\) where \(X, W\) are as above and \(Z\) and \(Y\) are similarly defined. CCA optimizes the matrices \(W, Y\) operating on \(X, Z\) to find a low-dimensional representation of the data pair \(( X , Z )\) in which correlation is maximal. Following ideas outlined in Dhillon et al. (2014) and B. B. Avants, Libon, et al. (2014), this method can be extended with sparsity constraints that yield rows of \(W, Y\) with a controllable number of non-zero entries. See the sccan tutorial and sparseDecom2 for more information.

Conclusions

With the current ANTsR, one may:

• Exploit ANTs and ITK functionality within R

• Leverage R functionality to help understand and interpret imaging data

• Use feature selection based on various filtering strategies in iMath and elsewhere (e.g segmentShapeFromImage)

• Employ dimensionality reduction through eigenanatomy or SCCAN with a variety of incarnations, some of which are similar to ICA

• Use relatively few interpretable and low-dimensional predictors derived from high-dimensional data.

• Interpret multivariate results intuitively when used in combination with standard R visualization.

See ANTsR for all source code and documentation and RKRNS-talk for html slides that discuss extensions to BOLD decoding.

Enjoy and please refer issues to ANTsR issues.