A tree data structure for representing multidimensional digital binary images is described. The method is based on recursive subdivision of the d-dimensional space into 2 d hyperoctants. An algorithm for constructing the tree of a d-dimensional binary image from the trees of its (d - 1 )-dimensional cross sections is given. The computational advantages of the data structure and the algorithm are demonstrated both theoretically and in application to a three-dimensional reconstruction of a human brain.

Image reconstruction is the process of recovering a function of two variables from experimentally obtained estimates of its integrals alone certain lines. An important version in medicine is the recovery of the density distribution within a cross-section of the human body from a number of X-ray projections.A computationally efficient technique for image reconstruction is the so-called convolution method.It consists of two steps: (i) data obtained by each of the orojections of the cross-section are separately (discrete) convolved with a fixed function; (ii) the density of the function at any point in the crosssection is estimated as the sum of values (one from each projection) of the convolved projection data.A difficulty is that part (ii) usually requires values of the convolved orojection data at points other than where they have been calculated during part (i). This is usually resolved by interpolation between the calculated values.In this paper we report on a computer experimental study which compares the efficacy of two methods of interpolation (linear interoolation and a modified cubic spline interpolation) when used with the convolution reconstruction method. The two interoolation techniques are examined for their mathematical properties and are compared from the points of view of resolution of fine details, smoothness of the reconstructed cross-sections, sensitivity to noise in the data, the overall nearness of the oriqinal and reconstructed objects, and the cost of implementation. Both methods are illustrated on reconstructions of a mathematically described cross-section of the human head from computer simulated X-ray data.

The Dynamic Spatial Reconstructor (DSR) is a device constructed at the Biodynamics Research Unit of the Mayo Clinic for (among other things) the visualization of the beating heart inside the intact thorax. The device consists of 28 rotating X-ray sources arranged on a circular arc at 6 degrees intervals (total span 162 degrees) and a matching set of 28 imaging systems. The whole thorax of the patient is projected onto the two-dimensional screen of the imaging systems by cone beams of X rays from the sources. All of the X-ray sources are switched on and off within a total period of 10 milliseconds. The Medical Image Processing Group at the State University of New York at Buffalo has developed a software package for the design and evaluation of algorithms to be used by the DSR. In this paper we illustrate the operation of the package and a particular algorithm for the reconstruction of the dynamically changing structure of the heart from data collected by the DSR.

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