The authors give an important correction to how to understand a thin-plate spline KernelTransform in image registration.  By re-adjusting homologous landmark estimates on the target ("fixed") image during image registration, Brooks and Arbel have cracked the problem of how to make the thin-plate spline a feasible high-dimensional warping method.

In my opinion, this coincides with the natural way we would want to fit a brain-imaging atlas with established landmarks onto fixed observation data that we do not wish to distort before measuring.

Completing the feasibility of a KernelTransform registration "code plan" is established by giving a tractable and correct definition of the Jacobian and showing that L-inverse need only be computed once.

In my opinion, this improved completion of the KernelTransform should work better in registration than a B-spline that scatters many more control points at regular intervals, whenever identifying a set of meaningful landmarks exactly expresses human expert knowledge of what to look for when identifying anatomy in 2D and 3D.

They implemented their idea in ITK.  A test was automated.

The code is provided along with a 2D test image and some transform points.  In the article these modifications are offered as similarly named replacements for 6 classes.

If I were going to take it upon myself to reproduce this work, I would be seeing if I could include KernelTransform2, as it is called, in one of our 3D brain imaging vehicles, BRAINSDemonWarp or BRAINSFit.  Since the IJ website reports that their test program performs as advertised, I choose not to postpone submiting a first version of my review until I can completely merge their work into an existing production-quality project meaningfully and satisfyingly.  Call it my opinion then, but I think this would be well worth making use of.

The code is fully N-dimensional, and I see no obstacle to trying this someday except getting permission to change BRAINSDemonWarp in this way and picking up an existing landmark data set and atlas, say for the cerebellum.  We do not believe, though, that thin-plate splines are a suitable representation of the anatomical variability in the folding of the cerebral cortex.

This is of interest to most prototype-based medical anatomy labeling, with the possible exception of the very troublesome case of the cerebral cortex, where the straightforward position in the head's 3D volume is just one of many factors in deciding what gyrus or sulcus is this.

Brooks and Arbel have fixed an important design flaw that was preventing medical image registration from adaptively fitting a 3D spline KernelTransform.  They have correctly identified that the atlas with its fixed landmarks gets mapped to the fixed specimen image with its adaptively placed landmarks, resulting in a new and feasible Lagrangian transform for atlas registration by some sort of gradient descent.

I suppose it would be nice if their lambda (see their definintion of L) were not a constant but a parameter....  The point of that is to let the algorithm avoid unwanted swirling of the inter-landmark texture field.

I suppose it would be nice if there were a compartmentally hierarchical version of thin-plate splines that uses nested enclosures marked out by landmark hulls....  The point of that is to limit the search for interior landmarks within the acceptable enclosing region of hierarchical focus.