Boklye Kim1,
Jennifer L. Boes1,
Kirk A. Frey 2,
Charles R. Meyer1
1Department of Radiology, University of Michigan Medical Center
2Department of Internal Medicine, Division of Nuclear Medicine,
University of Michigan Medical Center
Abstract
Objective
Automatic image registration tools based on the fundamental information theory metric of mutual information (MI) has been developed and implemented into multi-modality matching algorithms. The MI metric provides assessment of matching accuracy, which is effective for multimodal registrations involving 2D or 3D, and affine or warping transformations. Accurate registration capabilities employing MI as a global cost function have been demonstrated by automated 2D registration of autoradiographic (AR) images with video images of the block face as a reference using affine and TPS warping transformations.
Methods
Mutual information, based on classical theory of entropy [1,2], quantifies interdependency of two systems, i.e. image data. MI metric, defined by MI = -SUM[p(x,y)log(p(x,y)/p(x)p(y))], is calculated from the two-dimensional joint density function, p(x,y), of gray values of a geometrically mapped image pair, where p(x) and p(y) are marginal probability distributions. MI approaches its lower bound when two images are highly correlated and its upper bound when uncorrelated. The minimum MI for an image pair is achieved when the geometric mapping produces the most correlated, i.e. registered, data sets, independent of modality.
Registration of
deoxy-D-[14C]glucose (2DG)
autoradiograph (AR) and video image
of uncut specimen block face of the same slice (in 512x480 matrix), acquired as
described in literature [3], uses homologous feature points in each of the data
set. Selecting one point more than the spatial dimension constrains the
solution to the affine transformation and more points select a general TPS
warping solution. Registration of the two images is achieved by allowing the
control points in feature space to move to positions that minimize the MI index.
Results
Figure 1
displays (a) reference video image (uncut specimen block face) and
(b) 2DG AR deformed due to slice sectioning. Blue dots in both reference and AR
images indicate the location of control points used for initial vectors in TPS
registration and yellow dots in AR image indicate the final locations of TPS
warping solution achieved by cost function minimization of MI metric. Note that
some starting points in AR image were markedly displaced.
Figure 2
displays the result of MI registration of AR image with the reference, in
checker board pattern, using (a) affine and (b) TPS warping transformation
algorithms. While the affine transformation (2a) results in remarkably good
matches for most internal structures of the brain, some features around outer
edges denote local deformations that cannot be handled by the affine
transformation, e.g. in the mid section of the brain, top and bottom squares
show mismatches of outer edges and structures between hippocampus and cortex as
well as the lesion in frontal lobe. The final MI
values reflect contributions manifested by mismatches due to the non-linear
deformations not correctable by affine transformation. The final results are
evaluated by comparison of MI values; -0.575 (affine) versus -0.613 (TPS warp)
with starting MI = -0.462. The final solutions of (c) affine and (d) TPS warp are
graphically depicted in the bottom row.
Conclusions
Mapping of AR images with video references represents 2D image registration of
multimodality data using TPS warping algorithm to reconstitute 2DG volume data
for the purpose of 3D registration with MRI volume [4]. Implementation of MI
driven optimization loop that converges to the system global minimum to find the
accurate warping solution demonstrates robustness and feasibility of MI based
automatic registration. Further applications to the registrations of 3D data
sets such as volume MRI/PET or MRI/SPECT should be as feasible since MI is
calculated based on voxel gray value 2D histogram of the image pair.
References
1. Cover, TM., Thomas, JA., Elements of Information Theory, John Wiley & Sons,
Inc., New York, 1991.
Questions concerning this work may be addressed to
Boklye Kim.
Other links:
2. Collignon, A, Vandermeulen, D, Suetens, P, Marchal, G., IPMI 1995
3. Kim, B., Frey, KA., Mukhopadhyay, S., Ross, BD., Meyer, CR., Lecture Notes in
Computer Science, 1995, 905:262-266
4. Kim, B., Boes, J., Frey, KA., Ross, BD., Meyer, CR., Radiology, 1995