Shape-Based Interpolation of Tree-Like Structures in Three-Dimensional Images

Three-dimensional (3-D) images obtainable from many medical-imaging scanners typically have lower resolution in the z direction than in the x or y directions. Before extracting and displaying objects in such images, an interpolated 3-D grayscale image is usually generated via a technique such as linear interpolation to fill in the “missing slices.” Unfortunately, linear interpolation and related schemes produce a 3-D image having blurred object structures. Thus, when objects are extracted and displayed from the interpolated image, the objects often exhibit a blocky and generally unsatisfactory appearance. This problem is particularly acute for thin tree-like structures such as the coronary arteries. Recently, workers in the field have proposed a strategy referred to as shape-based interpolation that offers an improvement to linear interpolation. In shape-based interpolation, the object of interest is first segmented (extracted) from the initial 3-D image to produce a low-z-resolution binary-valued image. Then, the segmented image is interpolated to produce a high-resolution binary-valued 3-D image. These techniques, however, do not use the original Grayscale information and have difficulties with images containing tree-like structures, such as the coronary arteries. We describe two shape-based interpolation methods that generate improved results for tree-like structures. The first method incorporates geometrical constraints and takes as input a segmented version of the original 3-D image. The second method builds upon the first in that it also uses the original Grayscale image as a second input. Tests with 3-D images of the coronary arterial tree demonstrate the efficacy of the methods.