Gideon Frieder

The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm

In many three-dimensional imaging applications the three-dimensional scene is represented by a three-dimensional array of volume elements, or voxels for short. A subset Q of the voxels is specified by some property. The objects in the scene are then defined as subsets of Q formed by voxels which are “connected” in some appropriate sense. It is often of interest to detect and display the surface of an object in the scene, specified, say, by one of the voxels in it. In this paper, the problem of surface detection is translated into a problem of traversal of a directed graph, G. The nodes of G correspond to faces separating voxels in Q from voxels not in Q. It is proven that connected subgraphs of G correspond to surfaces of connected components of Q (i.e., of objects in the scene). Further properties of the directed graph are established which allow us to keep the number of marked nodes (needed to avoid loops in the graph traversal) to a small fraction of the total number of visited nodes. This boundary detection algorithm has been implemented. We discuss the interaction between the underlying mathematical theory and the design of the working software. We illustrate the software by some clinical studies in which the input is computed tomographic (CT) data and the output is dynamically rotating three-dimensional displays of isolated organs. Even though the medical application leads to very large-scale problems, our theory and design allows us to use our method routinely on the minicomputer of a CT scanner.

Back-to-Front Display of Voxel Based Objects

This straightforward 3-D display algorithm traverses voxels slice by slice to project each voxel on the screen. No surface detection or z-buffer is needed.

Three-dimensional medical imaging: algorithms and computer systems

This paper presents an introduction to the field of three-dimensional medical imaging It presents medical imaging terms and concepts, summarizes the basic operations performed in three-dimensional medical imaging, and describes sample algorithms for accomplishing these operations. The paper contains a synopsis of the architectures and algorithms used in eight machines to render three-dimensional medical images, with particular emphasis paid to their distinctive contributions. It compares the performance of the machines along several dimensions, including image resolution, elapsed time to form an image, imaging algorithms used in the machine, and the degree of parallehsm used in the architecture. The paper concludes with general trends for future developments in this field and references on three-dimensional medical imaging.

An environment for research in microprogramming and emulation

The development of the research project in microprogramming and emulation at State University of New York at Buffalo consisted of three phases: the evaluation of various possible machines to support this research; the decision to purchase one such machine, which appears to be superior to the others considered; and the organization and definition of goals for each group in the project. Each of these phases is reported, with emphasis placed on the early results achieved in this research.

The architecture and operational characteristics of the VMX host machine

The VMX host machine is a hardware-firmware environment for implementation of actual computer systems with a favorable price performance ratio. The article presents the host framework architecture, together with all units which are used to build actual systems. The advantages and future potential of the architecture is briefly discussed. The notion of memory directives within the frame-work of an active (or “intelligent”) memory unit is introduced. This notion serves as one example of the possibilities that are built into the architecture of the VMX host.

The development of multiple-valued logic as related to computer science

Computer scientists are familiar with options in which there are no middle choices between true and false. The lack of such choices is inconvenient — even critical — for example, when determining whether the status of a computer system is go or no-go. Multiple-valued logic is concerned with these intermediate choices.

Resolution in reconstructing objects from electron micrographs.

Some basic problems associated with the reconstruction of objects from electron micrographs and X-ray photographs are investigated. A precise definition of the problem is given. It is proved that interesting images cannot be uniquely described by any finite number of projections, and thus any reconstruction technique can only hope to give an approximation to the original. The root-mean-square distance is discussed as a measure of the approximation, and it is shown to be sensitive to changes in fine detail. Various suggested ways of measuring resolution are discussed and precise definitions for the resolution of reconstruction techniques are suggested both with and without the use of Fourier transforms. A theoretical explanation is given for the success, from the point of view of resolution, of the algebraic reconstruction techniques using only few projections from a limited range of angles.

Methodology and Clinical Experience with Computed Tomography and a Computer-resident Stereotactic Atlas

We have developed a computer-resident stereotactic atlas of the human brain that quantitatively defines subcortical structures within anatomical landmarks detected on obliquely reconstructed computed tomography (CT) slices. Horizontal stereotactic atlas sections can be stretched and contracted by polar transformation and labeled by a computer to fit within these CT scan-defined landmarks. The stereotactic coordinates of any substructure on the atlas-labeled CT slice may then be calculated by the computer and expressed in mechanical adjustments on a stereotactic surgical frame located in the operating room. We demonstrate the use of this method in the stereotactic treatment of movement disorders as an augmentation to conventional ventriculography and microelectrode recording.

Algorithms for Binary Coded Balanced and Ordinary Ternary Operations

A representation for binary coded ternary (BCT) numbers is proposed. This representation is then used for the introduction of algorithms for ternary addition and subtraction on binary hardware. In the algorithm introduced, distinction is made between basic algorithms, i.e., those which are independent of the type of the arithmetic, and those which are dependent upon it. Some suggestions as to the significance of this approach for nonternary arithmetic are presented.

Ternary computers: part I: motivation for ternary computers

In the first part, motivation is presented for a study of Ternary Computers using emulation. Areas of interest and goals of evaluation are briefly outlined.In the second part, a representation of balanced ternary numbers is presented and examined. Microcode is then written to implement parallel operation on these ternary numbers. Results of experiments are reported in order to demonstrate that the goals outlined in Part I can be achieved via emulation.Part I is based on Project MU report 32-72-MU. Part 2 is based on Project MU report 34-72-MU. These reports are not reproduced here in full for sake of brevity.