From a set of longitudinal three-dimensional scans of the same anatomical structure, we have accurately modeled the temporal shape and size changes using a linear shape model. On a total of 31 computed tomography scans of the mandible from six patients, 14,851 semilandmarks are found automatically using shape features and a new algorithm called geometry-constrained diffusion. The semilandmarks are mapped into Procrustes space. Principal component analysis extracts a one-dimensional subspace, which is used to construct a linear growth model. The worst case mean modeling error in a cross validation study is 3.7 mm.

Article Free AccessFeatures of deformation grids: an approach via singularity theory Share on Author: Fred L. Bookstein Institute of Gerontology, University of Michigan, Ann Arbor, Michigan Institute of Gerontology, University of Michigan, Ann Arbor, MichiganView Profile Authors Info & Claims SCG '98: Proceedings of the fourteenth annual symposium on Computational geometryJune 1998 Pages 214–221https://doi.org/10.1145/276884.276909Online:07 June 1998Publication History 0citation326DownloadsMetricsTotal Citations0Total Downloads326Last 12 Months4Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Quantitative studies of shapes in the real world are often expedited by the tools of morphometrics, a branch of multivariate statistics organized to exploit the origin of such data in real Euclidean geometry. This paper reviews one such tool that has recently been designed for the analysis of corresponding biological outlines of similar shape, such as those that arise from organ or tissue boundaries in medical images. The analysis is a hybrid of two morphometric tools, Procrustes analysis and the thin-plate spline, the properties of which are already well-understood separately. The thin-plate spline optimizes one shape metric, the Procrustes methods another. Their combination permits the averaging of groups of outlines, the rigorous display of sample variation around these averages in full detail, and rigorous multivariate statistical detection and testing of hypotheses linking those patterns to their putative causes or effects. The new tool is demonstrated using outlines of the corpus callosum (connection of the cerebral hemispheres) in mid-sagittal images of 12 normal human brains and 13 brains of schizophrenics.

Landmark points, when they can be located reliably over a sample of medical images, serve both to generate a statistical space of biometric shape variables and to specify an unwarping by which variation of pixel values associated with displacements of the landmarks can be corrected with respect to all landmarks simultaneously. There thus arise two separate spaces of descriptors of the same images: "horizontal" descriptions of the landmark configurations, and "vertical" descriptors, like image averaging or subtraction, applied only after pictures have been unwarped to adjust out this horizontal variation. A large class of image features may be generated by combining these two channels of analysis. In this paper, a series of figure captions, demonstrates their interplay in a little study of brain form in schizophrenia.

The decomposition of deformations by principal warps is demonstrated. The method is extended to deal with curving edges between landmarks. This formulation is related to other applications of splines current in computer vision. How they might aid in the extraction of features for analysis, comparison, and diagnosis of biological and medical images in indicated.>