ABSTRACTS OF PAPERS ACCEPTED FOR PUBLICATION 217

Dig&d Sjraiglij &gments. SON hIAM. Department of Computer Science, California State University. Northridge, Northridge, California 91330. Received April 23, 1985; revised November 7, 1985.

lt will be proved in this paper that all digital straight segments connecting two given pixels form an area whose lowerbound and upperbound are also the digital straight segments. These two bounds will be simply calculated and have the following properties: one is different to the other by unity in x’ or r-coordinate, and their chain codes of directions reverse from each other. Hence, for practical purposes, these results are used to define general digital straight segments as the digital arcs in this area, and also used to define the convexity and concavity of digital arcs.

NOTES

Oblique Sampling of Projections for Direct Three-Dimensbnal Reconstrction. GEORGE HARAW. Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-lOGO Berlin 33 (Dahlem), West Germany. RICHARD GORDON. Departments of Botany and Radiology, University of Manitoba. Winnipeg, Manitoba, R3T 2N2, Canada. MARIN VAN HEEL. Fritz-Haber-Institut der Max-Planck- Gesellschaft, Faradayweg 4-6, D-1000 Berlin 33 (Dahlem), West Germany. Received August 7, 1985: revised February 5, 1986.

In computerized tomography, a 2dimensional density distribution is calculated from its l-dimensional projections (line integrals). Computationally intensive interpolation procedures can be avoided by using a variable ray width during the calculations. We generalize this concept to direct (true) 3dimensional reconstruction, deriving an oblique tesselation of each 2dimensional projecti’on. This result allows faster computation of direct 3-dimensional reconstructions, as well as of 2-dimensional projections of any 3-dimensional picture stored on a cubic raster.

Theoretical Assessments of Mean Square Errors of Antialiadng Filters. K. KJSHIMOTO. K. ONAGA, AND E. NAKAMAE. Department of Circuits and Systems, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, 724 Japan. Received September 5,198s; revised March 30, 1986.

“The expectation of normalized-square-error-integrals” is proposed as a measure of performance of antialiasing filters for isotropic and piecewise-continuous images on graphic displays with sufficiently many grey levels. This quantity is defined as the average of “normalized-square-error-integrals” over all the possible target images, so that its value does not depend on target images. Its explicit calculation formula is derived for the case of supersampling method, and numericsI examples are given and compared. Using these results, the optimum filtering weight is derived. Interestingly, this optimum filtering indicates that taking too many sampling points has little effect on improving the quality of a graphic image.