Two-Dimensional Direction-Based Interpolation with Local Centered Moments

Abstract

Interpolation is generally needed to visualize medical images from a limited number of sliced tomographic images such as CT. In this paper, a novel gray-scale image interpolation method, for interpolating two-dimensional images accurately and efficiently, called direction-based interpolation, is investigated. In this method, the digital image is considered a sampling of the underlying continuous function, which is also called the image field. If the image is interpolated along the isovalue curves in the image field, instead of along the coordinate axes, both the edges and the internal structures of the objects in the image are well preserved. Initially, the isovalue direction at each point is calculated from the local centered moments of the image. A specific type of image, called the direction image, is composed from the isovalue directions. Then, the direction image is interpolated into a high-resolution direction image. The isovalue curve through any point in the image field is determined from the high-resolution direction image using a path-finding technique. A high-resolution gray-scale image with satisfactory object structure is then generated by interpolating the original image linearly along the isovalue curves. Experiments on a set of CT images show that this method not only preserves the shapes of complicated structures but also has an efficient computation. The comparison between the digitally reconstructed radiographs generated from the interpolated result using the direction-based interpolation method, the traditional linear interpolation method, and the traditional cubic spline interpolation method shows the promise of the proposed method in radiation treatment planning.