Non-rigid registration by geometry-constrained diffusion.

. Assume that only partial knowledge about a non-rigid registration is given so that certain points, curves, or surfaces in one 3D image map to certain certain points, curves, or surfaces in another 3D image. We are facing the aperture problem because along the curves and surfaces, point correspondences are not given. We will advocate the viewpoint that the aperture and the 3D interpolation problem may be solved simultaneously by finding the simplest displacement field. This is obtained by a geometry-constrained diffusion which yields the simplest displacement field in a precise sense. The point registration obtained may be used for growth modelling, shape statistics, or kinematic interpolation. The algorithm applies to geometrical objects of any dimensionality. We may thus keep any number of fiducial points, curves, and/or surfaces fixed while finding the simplest registration. Examples of inferred point correspondences in a longitudinal growth study of the mandible are g..

4D Shape-Preserving Modelling of Bone Growth

From a set of temporally separated scannings of the same anatomical structure we wish to identify and analyze the growth in terms of a metamorphosis. That is, we study the temporal change of shape which may provide an understanding of the biological processes which govern the growth process. We subdivide the growth analysis into growth simulation, growth modelling, and finally the growth analysis. In this paper, we present results of growth simulation of the mandible from 3 scannings of the same patient in the age of 9 months, 21 months, and 7 years. We also present the first growth models and growth analyzes. The ultimative goal is to predict/simulate human growth which would be extremely useful in many surgical procedures

Surface-bounded growth modeling applied to human mandibles

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, 14851 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

c Oxford University Press Non-rigid Registration by Geometry-Constrained Diffusion

Assume that only partial knowledge about a non-rigid registration is given: certain points, curves, or surfaces in one 3D image are known to map to certain points, curves, or surfaces in another 3D image. In trying to identify the non-rigid registration field, we face a generalized aperture problem since along the curves and surfaces, point correspondences are not given. We will advocate the viewpoint that the aperture and the 3D interpolation problem may be solved simultaneously by finding the simplest displacement field. This is obtained by a geometryconstrained diffusion, which in a precise sense yields the simplest displacement field. The point registration obtained may be used for segmentation, growth modeling, shape analysis, or kinematic interpolation. The algorithm applies to geometrical objects of any dimensionality. We may thus keep any number of fiducial points, curves, and/or surfaces fixed while finding the simplest registration. Examples of inferred point correspondences in a synthetic example and a longitudinal growth study of the human mandible are given. Keywords: Aperture-problem, automatic landmark detection, simplest displacement field, homology. Received?; revised?; accepted? 1