Directional interpolation for magnetic resonance angiography data

Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper, we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the n-dimensional object from a group of (n - 1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for three-dimensional tooth reconstruction.

Subunity coordinate translation with Fourier transform to achieve efficient and quality three-dimensional medical image interpolation

A new approach to the interpolation of three-dimensional (3D) medical images is presented. Instead of going through the conventional interpolation scheme where the continuous function is first reconstructed from the discrete data set and then resampled, the interpolation is achieved with a subunity coordinate translation technique. The original image is first transformed into the spatial-frequency domain. The phase of the transform is then modified with n-1 linear phase terms in the axial direction to achieve n-1 subunity coordinate translations with a distance 1/n, where n is an interpolation ratio, following the phase shift theorem of Fourier transformation. All the translated images after inverse Fourier transformation are then interspersed in turn into the original image. Since windowing plays an important role in the process, different window functions have been studied and a proper recommendation is provided. The interpolation quality produced with the present method is as good as that with the sampling (sinc) function, while the efficiency, thanks to the fast Fourier transformation, is very much improved. The approach has been validated with both computed tomography (CT) and magnetic resonance (MR) images. The interpolations of 3D CT and MR images are demonstrated.

Fast surface and volume estimation from non-parallel cross-sections, for freehand three-dimensional ultrasound

Volume measurements from ultrasound B-scans are useful in many clinical areas. It has been demonstrated previously that using three-dimensional (3-D) ultrasound can greatly increase the accuracy of these measurements. Freehand 3-D ultrasound allows freedom of movement in scanning, but the processing is complicated by having non-parallel scan planes. Two techniques are proposed for volume measurement from such data, which also improve surface and volume estimation from data acquired on parallel planes. Cubic planimetry is a more accurate extension of a volume measurement technique involving vector areas and centroids of cross-sections. Maximal-disc shape-based interpolation is an extension of shape-based interpolation which uses maximal disc representations to adjust the interpolation direction locally and hence improve the quality of the surface generated. Both methods are tested in simulation and in vivo. Volumes estimated using cubic planimetry are more accurate than step-section planimetry, and require fewer cross-sections, even for complex objects. Maximal-disc shape-based interpolation provides a reliable means of reconstructing surfaces from a handful of cross-sections, and can therefore be used to give confidence in the segmentation and hence also the cubic planimetry volume.

Nonlinear filtering approach to 3-D gray-scale image interpolation

Three-dimensional (3-D) images are now common in radiology. A 3-D image is formed by stacking a contiguous sequence of two-dimensional cross-sectional images, or slices. Typically, the spacing between known slices is greater than the spacing between known points on a slice. Many visualization and image-analysis tasks, however, require the 3-D image to have equal sample spacing in all directions. To meet this requirement, one applies an interpolation technique to the known 3-D image to generate a new uniformly sampled 3-D image. The authors propose a nonlinear-filter-based approach to gray-scale interpolation of 3-D images. The method, referred to as column-fitting interpolation, is reminiscent of the maximum-homogeneity filter used for image enhancement. The authors also draw upon the paradigm of relaxation labeling to devise an improved column-fitting interpolator. Both methods are typically more effective than traditional gray-scale interpolation techniques.