Statistical shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes and thus potentially discriminate between healthy and pathological structures. This paper describes a combined boundary and medial shape analysis based on two different shape descriptions applied to a study of the hippocampus shape abnormalities in schizophrenia. The first shape description is the sampled boundary implied by the spherical harmonic SPHARM description. The second one is the medial shape description called M-rep. Both descriptions are sampled descriptions with inherent point correspondence. Their shape analysis is based on computing differences from an average template structure analyzed using standard group mean difference tests. The results of the global and local shape analysis in the presented hippocampus study exhibit the same patterns for the boundary and the medial analysis. The results strongly suggest that the normalized hippocampal shape of the schizophrenic group is different from the control group, most significantly as a deformation difference in the tail region.

We present a new framework for 3D surface object classification that combines a powerful shape description method with suitable pattern classification techniques. Spherical harmonic parameterization and normalization techniques are used to describe a surface shape and derive a dual high dimensional landmark representation. A point distribution model is applied to reduce the dimensionality. Fisher’s linear discriminants and support vector machines are used for classification. Several feature selection schemes are proposed for learning better classifiers. After showing the effectiveness of this framework using simulated shape data, we apply it to real hippocampal data in schizophrenia and perform extensive experimental studies by examining different combinations of techniques. We achieve best leave-one-out cross-validation accuracies of 93 % (whole set, N = 56) and 90 % (right-handed males, N = 39), respectively, which are competitive with the best results in previous studies using different techniques on similar types of data. Furthermore, to help medical diagnosis in practice, we employ a threshold-free receiver operating characteristic (ROC) approach as an alternative evaluation of classification results as well as propose a new method for visualizing discriminative patterns.

Abstract — Shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes between healthy and pathological structures. This manuscript presents a comprehensive set of tools for the computation of 3D structural statistical shape analysis. It has been applied in several studies on brain morphometry, but can potentially be employed in other 3D shape problems. Its main limitations is the necessity of spherical topology. The input of the proposed shape analysis is a set of binary segmentation of a single brain structure, such as the hippocampus or caudate. These segmentations are converted into a corresponding spherical harmonic description (SPHARM), which is then sampled into a triangulated surfaces (SPHARM-PDM). After alignment, differences between groups of surfaces are computed using the Hotelling T 2 two sample metric. Statistical p-values, both raw and corrected for multiple comparisons, result in significance maps. Additional visualization of the group tests are provided via mean difference magnitude and vector maps, as well as maps of the group covariance information. The correction for multiple comparisons is performed via two separate methods that each have a distinct view of the problem. The first one aims to control the family-wise error rate (FWER) or false-positives via the extrema histogram of non-parametric permutations. The second method controls the false discovery rate and results in a less conservative estimate of the false-negatives. I.

Abstract—This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling’s 2 test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry. Index Terms—Brain, image analysis, Lie groups, magnetic resonance imaging (MRI), statistics. I.

An important goal of statistical shape analysis is the discrimination between populations of objects, exploring group differences in morphology not explained by standard volumetric analysis. Certain applications additionally require analysis of objects in their embedding context by joint statistical analysis of sets of interrelated objects. In this paper, we present a framework for discriminant analysis of populations of 3-D multi-object sets. In view of the driving medical applications, a skeletal object parametrization of shape is chosen since it naturally encodes thickening, bending and twisting. In a multi-object setting, we not only consider a joint analysis of sets of shapes but also must take into account differences in pose. Statistics on features of medial descriptions and pose parameters, which include rotational frames and distances, uses a Riemannian symmetric space instead of the standard Euclidean metric. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Joint analysis of 10 subcortical brain structures in a pediatric autism study demonstrates that multi-object analysis of shape results in a better group discrimination than pose, and that the combination of pose and shape performs better than shape alone. Finally, given a discriminating axis of shape and pose, we can visualize the differences between the populations. 1.

We present a novel method of statistical surface-based morphometry based on the use of non-parametric permutation tests. In order to evaluate morphological differences of brain structures, we compare anatomical structures acquired at different times and/or from different subjects. Registration to a common coordinate system establishes corresponding locations and the differences between such locations are modeled as a displacement vector field (DVF). The analysis of DVFs involves testing thousands of hypothesis for signs of statistically significant effects. We randomly permute the surface data among two groups to determine thresholds that control the familywise (type 1) error rate. These thresholds are based on the maximum distribution of the amplitude of the vector fields, which implicitly accounts for spatial correlation of the fields. We propose two normalization schemes for achieving uniform spatial sensitivity. We demonstrate their application in a shape similarity study of the lateral ventricles of monozygotic twins and non-related subjects.

Most of the approaches dedicated to automatic morphometry rely on a point-by-point strategy based on warping each brain towards a reference coordinate system. In this paper, we describe an alternative object-based strategy dedicated to the cortex. This strategy relies on an artificial neuroanatomist performing automatic recognition of the main cortical sulci and parcellation of the cortical surface into gyral patches. A set of shape descriptors, which can be compared across subjects, is then attached to the sulcus and gyrus related objects segmented by this process. The framework is used to perform a study of 142 brains of the International Consortium for Brain Mapping (ICBM) database. This study reveals some correlates of handedness on the size of the sulci located in motor areas, which was not detected previously using standard voxel based morphometry.

... not in women. In this paper, we investigated gender differences in normal subjects in young adulthood by employing a shape analysis of the HC using medial surfaces. For each subject, the most prominent medial manifold of the HC was extracted and flattened. The flattened sheets were then registered using both a rigid and a non-rigid alignment technique, and the medial surface radius was expressed as a height function over them. This allowed for an investigation of the association between subject variables and the local width of the HC. With regard to the effects of age and gender, it could be shown that the previously observed gender differences were mostly due to volume loss in males in the lateral areas of the HC head and tail. We suggest that the analysis of HC shape using medial surfaces might thus serve as a complimentary technique to investigate group differences to the established segmentation protocols for volume quantification in MRI

doi:10.1016/j.neuroimage.2008.10.043

for morphometry of the cortical sulci. These descriptors, which have been introduced more than a decade ago, are invariant relatively to rotations, translations and scale and can be computed for any topology. A rapid insight into the derivation of these invariants is proposed first. Then, their potential to characterize shapes is shown from a principal component analysis of the 12 first invariants computed for 12 different deep brain structures manually drawn for 7 different brains. Finally, these invariants are used to find some correlates of handedness and sex among the shapes of 116 different cortical sulci automatically identified in each of 142 brains of the ICBM database.