In this work, we present a method for exploring the relationship among morphometric variables and the possible anatomic significance of these relationships. The analysis is based on the Jacobian determinant field resulting from the registration of a template to a set of subjects, which is represented as a factorial analytic model. In addition to morphometric variables, information about medical diagnosis is considered in the analytic model and corroborates to exploratory investigation of the relationship between regions of interest and pathologies. The definition of the number of factors to be considered is based on a robust analysis of the statistical fit of the factor model, instead of using as hoc criteria. The advantages of the proposed methodology are demonstrated in a study of shape differences between the corpora callosa of schizophrenic patients and normal controls. We show that the regions where these differences can occur can be determined by unsupervised analysis, indicating the method's potential for exploratory studies.
This paper presents a factor analytic approach to morphometry in which strong intercorrelations among a high-dimensional set of shape-related variables are sought. The correlated variables potentially correspond to substructures of anatomy and thus have a natural interpretation. The analysis is based on information about the pointwise size differences between the anatomy depicted in a template image and the anatomy in a subject image, obtained by registering the template to the subject and then calculating the Jacobian determinant of the registration transformation over the image volume. The method is demonstrated in a preliminary study of shape differences between the corpora callosa of schizophrenic patients and normal controls. We show that the regions where these differences occur can be determined by unsupervised analysis, indicating the method's potential for exploratory studies.
The problem of matching two images can be posed as the search for a displacement field which assigns each point of one image to a point in the second image in such a way that a likelihood function is maximized ruled by topological constraints. Since the images may be acquired by different scanners, the intensity relationship between intensity levels is generally unknown. The matching problem is usually solved iteratively by optimization methods. The evaluation of each candidate solution is based on an objective function which favors smooth displacements that yield likely intensity matches. This paper is concerned with the construction of a likelihood function that is derived from the information contained in the data and is thus applicable to data acquired from an arbitrary scanner. The basic assumption of the method is that the pair of images to be matched is assumed to contain roughly the same proportion of tissues, which will be reflected in their gray-level histograms. Experiments with MRI images corrupted with strong non-linear intensity shading show the method's effectiveness for modeling intensity artifacts. Image matching can thus be made robust to a wide range of intensity degradations.
In this work, we describe an automated approach to morphometry based on spatial normalizations of the data, and demonstrate its application to the analysis of gender differences in the human corpus callosum. The purpose is to describe a population by a reduced and representative set of variables, from which a prior model can be constructed. Our approach is rooted in the assumption that individual anatomies can be considered as quantitative variations on a common underlying qualitative plane. We can therefore imagine that a given individual's anatomy is a warped version of some referential anatomy, also known as an atlas. The spatial warps which transform a labeled atlas into anatomic alignment with a population yield immediate knowledge about organ size and shape in the group. Furthermore, variation within the set of spatial warps is directly related to the anatomic variation among the subjects. Specifically, the shape statistics--mean and variance of the mappings--for the population can be calculated in a special basis, and an eigendecomposition of the variance performed to identify the most significant modes of shape variation. The results obtained with the corpus callosum study confirm the existence of substantial anatomical differences between males and females, as reported in previous experimental work.