Approach for the smoothing of three-dimensional reconstructions of the human spine using dual Kriging interpolation

A semi-automated method using interpolation and optimisation for the 3D reconstruction of the spine from bi-planar radiography: a precision and accuracy study

The 3D reconstruction of the spine in upright posture can be obtained by bi-planar radiographic methods, developed since the 1970s. The principle is to identify 4-25 anatomical landmarks per vertebrae and per images. This identification time is hardly manageable in clinical practice. A semi-automated method is used: 3D standard vertebral models are positioned along with a 3D curve (identified all the way through the vertebral bodies). The silhouettes of the models of C7 and L5 vertebrae are first adjusted and the positions of the other vertebrae are interpolated and optimised. The inter- and intra-operator variabilities and the errors between the semi-automated method and the manual identification of six anatomical landmarks per vertebra are evaluated on 20 pairs of X-ray images of subjects with different spinal deformities. The identification time for the semi-automated method is 5 min. For scolitic subjects, the precision is under 2.2 degrees and the accuracy is under 3.2 degrees for all lateral, sagittal and axial rotations.

A semi-automated method using interpolation and optimisation for the 3D reconstruction of the spine from bi-planar radiography: a precision and accuracy study

The 3D reconstruction of the spine in upright posture can be obtained by bi-planar radiographic methods, developed since the 1970s. The principle is to identify 4-25 anatomical landmarks per vertebrae and per images. This identification time is hardly manageable in clinical practice. A semi-automated method is used: 3D standard vertebral models are positioned along with a 3D curve (identified all the way through the vertebral bodies). The silhouettes of the models of C7 and L5 vertebrae are first adjusted and the positions of the other vertebrae are interpolated and optimised. The inter- and intra-operator variabilities and the errors between the semi-automated method and the manual identification of six anatomical landmarks per vertebra are evaluated on 20 pairs of X-ray images of subjects with different spinal deformities. The identification time for the semi-automated method is 5 min. For scolitic subjects, the precision is under 2.2 degrees and the accuracy is under 3.2 degrees for all lateral, sagittal and axial rotations.

Curvilinear Three-Dimensional Modeling of Spinal Curves with Dual Kriging

In spinal deformation studies, three-dimensional reconstruction of the spine is frequently represented as a curve in space fitted to the vertebral centroids. Conventional interpolation techniques such as splines, Bezier and the least squares method are limited since they cannot describe precisely the great variety of spinal morphologies. This article presents a more general technique called dual kriging, which includes two mathematical constituents (drift and covariance) to adjust the interpolated functions to spinal deformity better. The cross-validation technique was used to compare the parametric representations of spinal curves with different combinations of drift and covariance functions. Model validation was performed from a series of analytic curves reflecting typical scoliotic spines. Calculation of geometric torsion, a sensitive parameter, was done to evaluate the accuracy of the kriging models. The best model showed an absolute mean difference of 1.2 x 10(-5) (+/- 7.1 x 10(-5) ) mm(-1) between the analytical and estimated geometric torsions compared to 5.25 x 10(-3) (+/- 3.7 x 10(-2) ) mm(-1) for the commonly used least-squares Fourier series method, a significant improvement in spinal torsion evaluation.

Volume-preserving smoothing of three-dimensional surfaces: application to intravascular ultrasound

A volume-preserving three-dimensional smoothing approach is described that can be directly applied to 3D medical image data consisting of sets of 2D image slices, e.g., segmented intravascular ultrasound image sequences. Two local smoothing filters ℱ and 𝒢 were designed according to different smoothing goals and their performance was compared. Filtering with the ℱ filter of a relatively large frequency window keeps the important local characteristics of the object and results in little shrinkage while removing noise. Filtering with the Gaussian filter G that has an added volume compensation step results in no global shrinkage and may be used for multiscale filtering. The two filters can be easily extended to n-dimensional filtering.