In this paper we show how to use the approximate bilateral symmetry of the brain with respect to its interhemispheric fissure for intra-subject (rigid-body) mono- and multimodal 3D image registration. We propose to define
and compute an approximate symmetry plane in the two images to register and to use these two planes as constraints
in the registration problem. This 6-parameter problem is thus turned into three successive 3-parameter
problems. Our hope is that the lower dimension of the parameter space makes these three subproblems easier
and faster to solve than the initial one. We implement two algorithms to solve these three subproblems in the
exact same way, within a common intensity-based framework using mutual information as the similarity measure.
We compare this symmetry-based strategy with the standard approach (i.e. direct estimation of a 6-parameter
rigid-body transformation), also implemented within the same framework, using synthetic and real datasets.
We show our symmetry-based method to achieve subvoxel accuracy with better robustness and larger capture
range than the standard approach, while being slightly less accurate and slower. Our method also succeeds in
registering clinical MR and PET images with a much better accuracy than the standard approach. Finally, we
propose a third strategy to decrease the run time of the symmetry-based approach and we give some ideas, to
be tested in future works, on how to improve its accuracy.
The primary goal of this paper is to describe i) the pattern of pointwise distances between the human brain (pial surface)
and the inner surface of the skull (endocast) and ii) the pattern of pointwise bilateral asymmetries of these two structures.
We use a database of MR images to segment meshes representing the outer surface of the brain and the endocast. We
propose automated computational techniques to assess the endocast-to-brain distances and endocast-and-brain
asymmetries, based on a simplified yet accurate representation of the brain surface, that we call the brain hull. We
compute two meshes representing the mean endocast and the mean brain hull to assess the two patterns in a population
of normal controls. The results show i) a pattern of endocast-to-brain distances which are symmetrically distributed with
respect to the mid-sagittal plane and ii) a pattern of global endocast and brain hull asymmetries which are consistent with
the well-known Yakovlevian torque. Our study is a first step to validate the endocranial surface as a surrogate for the
brain in fossil studies, where a key question is to elucidate the evolutionary origins of the brain torque. It also offers
some insights into the normal configuration of the brain/skull interface, which could be useful in medical imaging
studies (e.g. understanding atrophy in neurodegenerative diseases or modeling the brain shift in neurosurgery).
The iterative closest point (ICP) algorithm is probably the most popular algorithm for fine registration of
surfaces. Among its key properties are: a simple minimization scheme, proofs of convergence as well as the
easiness to modify and improve it in many ways (e.g. use of fuzzy point correspondences, incorporation of a
priori knowledge, extensions to non-linear deformations, speed-up strategies, etc.) while keeping the desirable
properties of the original method. However, most ICP-like registration methods suffer from the fact that they
only consider the distance between the surfaces to register in the criterion to minimize, and thus are highly
dependent on how the surfaces are aligned in the first place. This explains why these methods are likely to be
trapped in local minima and to lead to erroneous solutions. A solution to partly alleviate this problem would
consist in adding higher-order information in the criterion to minimize (e.g. normals, curvatures, etc.), but
previous works along these research tracks have led to computationally intractable minimization schemes. In
this paper, we propose a new way to include the point unit normals in addition to the point coordinates to
derive an ICP-like scheme for non-linear registration of surfaces, and we show how to keep the properties of the
original ICP algorithm. Our algorithm rests on a simple formula showing how the unit normal changes when
a surface undergoes a small deformation. The use of this formula in an ICP-like algorithm is made possible by
adequate implementation choices, most notably the use of a local, differentiable, parametrization of the surfaces
and a locally affine deformation model using this local parametrization. Then we experimentally show the strong
added value of using the unit normals in a series of controlled experiments.
We propose a method for the automated computation of the mid-sagittal plane of the brain in diffusion tensor
MR images. We estimate this plane as the one that best superposes the two hemispheres of the brain by reflection
symmetry. This is done via the automated minimisation of a correlation-type global criterion over the tensor
image. The minimisation is performed using the NEWUOA algorithm in a multiresolution framework. We
validate our algorithm on synthetic diffusion tensor MR images. We quantitatively compare this computed plane
with similar planes obtained from scalar diffusion images (such as FA and ADC maps) and from the B0 image
(that is, without diffusion sensitisation). Finally, we show some results on real diffusion tensor MR images.
We propose to use a recently introduced optimisation method in the context of rigid registration of medical
images. This optimisation method, introduced by Powell and called NEWUOA, is compared with two other
widely used algorithms: Powell's direction set and Nelder-Mead's downhill simplex method. This paper performs
a comparative evaluation of the performances of these algorithms to optimise different image similarity measures
for different mono- and multi-modal registrations. Images from the BrainWeb project are used as a gold standard
for validation purposes. This paper exhibits that the proposed optimisation algorithm is more robust, more
accurate and faster than the two other methods.