EMPOWERING ANATOMICAL SHAPE ANALYSIS

WITH MEDIAL CURVES AND 1-D GROUP-WISE REGISTRATION

1Boris Gutman, 2Yalin Wang, 1Priya Rajagopalan1Arthur W. Toga, 1Paul M. Thompson

1Laboratory of Neuro Imaging, Department of Neurology, UCLA School of Medicine, Los Angeles, CA, USA.2Department of Computer Science and Engineering, Arizona State University, Tempe, AZ.

Method1. Medial Curve

Assume that there is a single curve skeleton that approximately captures global geometry of the shape .

Use medial thickness for description:

,

Registration is based on features derived from medial skeleton, thickness and global orientation function (GOF):

Medial curve cost function:

2. Groupwise 1D Registration

Incorporating statistical analysis into the process means making registration descriptor – aware. We exploit reduced dimensionality of the skeleton to perform groupwise descriptor-aware registration quickly. Given a set of functions , we reduce the total group variance by diffeomorphic maps :

,

Scalar feature is the curve-based thickness:

GOF is adjusted by ,

B

Motivation: Shape Analysis as a Three Step Process

1. Description (an intuitive scalar feature)• Medial Thickness [1]• Surface Jacobian Tensor [2]• Gray Matter Density

2. Registration• Intrinsic (conformal, nearest-isometry, q-maps) vs. feature-based (LBO

eigenfunctions, Spherical Demons)• Direct vs. parametric

3. Local Statistical Analysis

Ideally, all three should be combined in one framework. How to do this in practice for large datasets?

3. Spherical RegistrationWe use existing spherical mapping framework [3], adding terms:

ResultsTwo Cohorts of left lateral ventricles:(1) ADNI baseline, 391 subjects with mild cognitive impairment (MCI),

and 229 age-matched controls. (2) 11 HIV subjects and 8 age-matched controls [2]

Caudate Nucleus(3) ADNI baseline, 199 AD subjects, 229 controls

Above: (a) Medial curve, (b) resulting GOF of a lateral ventricle

Left: 1D Thickness maps of 3 ADNI subjects before (top) and after (bottom) groupwise registration of all 620 subjects.

Comparison to SPHARM [4]

  Group No Group SPHARMHIV 0.00988 0.01039 0.0149ADNI vent. 0.00029 0.00046 0.0068ADNI caud. 0.00065 0.0014 0.027

Right: P-values for group difference after 100K perms

ConclusionWe developed a framework to register anatomical shapes that combines the description, registration, and statistical analysis aspects of shape comparison. By exploiting the reduced dimensionality and consistent topology of our medial skeleton, we reduce the problem of group-wise shape registration to one dimension. Our method leads to greater statistical sensitivity globally and more precise effect localization on the surface.

References

[1]. P.A. Yushkevich et al, “Parametric medial shape representation in 3-D via the Poisson partial differential equation with non-linear boundary conditions,” IPMI. 19. pp.162-73. 2005.

[2] Y.L. Wang et al., “Multivariate Tensor-Based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS,” NeuroImage, 49(3) pp. 2141-57, 2010.

[3] I. Freidel, P. Schroeder, M. Desburn, “Unconstrained Spherical Parameterization,” J. Graphics, GPU and Game Tools 12(1), pp. 17-26, 2007.

[4] Brechbuhler, Ch, Gerig G, Kubler, O, “Parametrization of closed surfaces for 3D shape description.” Computer Vision and Image Understanding 61(2), pp. 154–170, 1995.

Ventricle P-maps of HIV-NC (left column) and MCI-NC (right column) group difference after registering with (a) SPHARM, (b) proposed method without groupwise step, (c) groupwise method

Caudate P-maps of AD-NC group difference after registering with (a) SPHARM, (b) proposed method without groupwise step, (c) groupwise method