A three dimensional (3-D) reconstruction algorithm utilizing both linear interpolation and linear extrapolation was developed for the study of human prostatic cancer. The algorithm was validated by comparing the volumes and shapes of original to reconstructed objects. Synthetic objects of known geometry and wax models with shapes characteristic of prostatic carcinomas were assessed with standard planimetry and by the digital interpolation-extrapolation method. Volume and multifocality measurements obtained by reconstructing excised prostate glands using histologic maps obtained from whole-mount sections were tested. The new algorithm provided greater accuracy in determining tumor volumes than conventional methods. This model provides a basis for mathematical analysis of prostate cancer lesions.

Estimation of lateral and rotational cloud displacement from satellite images is introduced based on various degrees of image abstraction. By using the luminance information, the maximum of the inger product surface of two images serves as a lateral displacement estimator. The peak detectability can be improved by prefiltering with a non-causal inverse filter. If the luminance is fit to a bivariate normal distribution, cloud motion and rotation is estimated from tracing the ellipses of equal density. Finally, the contour of clouds is Fourier transformed. The resulting coefficients reveal information about lateral and rotational displacement as well as size changes.

A method for designing the read-only memories (ROM's) needed for multiplication using logarithms is developed. By defining the word length of the multiplicand, multiplier, and product as n bits and the word length of -the rounded logarithms as m bits, design curves are given that allow various values of n and m to be selected for a given multiplier accuracy. Then a table is used to determine, which combination results in an implementation with the least number of bits.