Many three-dimensional (3-D) medical images 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 gray-scale image is usually generated via a technique such as linear interpolation to fill in the missing slices. Unfortunately, when objects are extracted and displayed from the interpolated image, they often exhibit a blocky and generally unsatisfactory appearance, a problem that is particularly acute for thin treelike structures such as the coronary arteries. Two methods for shape-based interpolation that offer an improvement to linear interpolation are presented. 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, and the segmented image is interpolated to produce a high-resolution binary-valued 3-D image. The first method incorporates geometrical constraints and takes as input a segmented version of the original 3-D image. The second method builds on the first in that it also uses the original gray-scale image as a second input. Tests with 3-D images of the coronary arterial tree demonstrate the efficacy of the methods. >

Shape-based interpolation of tree-like structures in three-dimensional images

In this paper, we present a new approach for the interpolation of grey data of arbitrary dimension that generalizes the shape-based method from binary data to grey data. The basic idea here is to express the given n-dimensional image as a (closed) surface in the (n + 1)- dimensional space, to interpolate the surface based on its shape, and then to collapse the new surface back to the image form. This method is more general and flexible in many respects than other methods. In addition to being able to handle data of arbitrary dimension, it allows intermixing operations on structures and images. The traditional shape-based interpolation method becomes a particular case of this new methodology. Our preliminary observation is that in regions of smooth as well as sharp intensity changes, the new method (in its simplest form) performs better than linear grey-level interpolation. In regions of scattered, fractal-like structures its performance seems to be inferior to the linear method.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Shape-based interpolation of multidimensional grey-level images

Morphology-based interpolation for 3D medical image reconstruction

Three-dimensional (3D) visualization in biomedical and other imaging areas is a rapidly emerging discipline. The major developments in this field are described in a unified and concise way. To this end, we introduce an operator notation to describe the basic imaging transforms commonly used in 3D visualization and to identify a comprehensive set of basic transforms. We also introduce several new basic transforms for filtering and interpolating scenes and structures and for rendering surfaces and volumes. We demonstrate not only how the existing visualization methodologies can be described concisely, but we also show how a great variety of new methodologies can be generated using both the existing imaging transforms and the new transforms introduced in this paper. A comprehensive evaluation method to compare objectively rendering methods used in visualization based on task-specific mathematical phantoms is described. We examine in detail separate transform sequences that are best suited for rendering robust and frail structures (ie, structures with well- and poorly defined boundaries).

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Imaging Transforms for Visualizing Surfaces and Volumes

Sectional images generated by medical scanners usually have lower interslice resolution than resolution withinthe slices. Shape-based interpolation is a method of interpolation that can be applied to the segmented 3Dvolume to create an isotropic data set. It uses a distance transform applied to every slice prior to estimationof intermediate binary slices. Gray-level interpolation has been the classical way of estimating intermediateslices. The method reported here is a combination of these two forms of interpolation, using the local gradientas a normalizing factor of the combination. Overall, this combination of the methods performs better thaneither of them applied individually. 1. INTRODUCTION Three-dimensional data created by tomographic medical imaging devices are usually presented as a sequenceof two-dimensional slices. The distance between the slices is typically greater than the distance between thepixels within the slices. An interpolation technique is often applied to convert the data to an isotropic volumewith the same resolution in all three dimensions. Interpolation is also necessary for accurate quantitative

Combining shape-based and gray-level interpolations

The problem of interpolating a high-resolution binary-valued 3-D image given a lower-resolution grayscale 3-D image and a corresponding segmented 3-D image is addressed. Three algorithms for this problem are described. Algorithms 1 and 2 perform shape- and located-based binary interpolation. Algorithm 3, which subsumes algorithms 1 and 2, incorporates grayscale information as well as object shape and slice-to-slice object spatial relationships. Results show that algorithm 3 generates better interpolated objects than the segmented volumes arising from standard grayscale-based interpolation techniques. Algorithm 2, which subsumes algorithm 1, uses only the known presegmented volume to interpolate a new binary-valued volume. the methods show particular merit in cases where the objects to interpolate are thin tube-like structures, such as the coronary arteries. >

E.L. Ritman

Papers

New shape-based interpolation technique for three-dimensional images