A new method for reconstruction of the left ventricle from the biplane angiocardiograms is proposed. By dividing the two projection images into parallel slices, the ventricular reconstruction is processed slice by slice stepwise. Each corresponding pair of slices form two one-dimensional projection profiles used to reconstruct a ventricular cross section. Without using predefined binary mask models, we propose to reconstruct the cross section under the assumption that the cross section is regular and a monotonically nondecreasing or nonincreasing equal-divisor curve is available. Instead of solving the binary matrix directly, we need only to obtain the equal-divisor curve. Then the cross section is uniquely determined. The experiments show better results than by any existing direct methods. It also prevents the sensitive selection of mask models.

A unified approach is given for constructing cross entropy and dissimilarity measures between probability distributions, based on a given entropy function or a diversity measure. Special properties of quadratic entropy introduced by Rao [7] are described. In particular it is shown that the square root of the Jensen difference (dissimilarity measure) arising out of a quadratic entropy provides a metric on a probability space. Several characterizations of quadratic entropy are obtained.

Three measures of divergence between vectors in a convex set of an-dimensional real vector space are defined in terms of certain types of entropy functions, and their convexity property is studied. Among other results, a classification of the entropies of degree\alphais obtained by the convexity of these measures. These results have applications in information theory and biological studies.

In an earlier work, the authors introduced a divergence measure, called the first-order Jensen difference, or in short\cal j-divergence, which is based on entropy functions of degree\alpha. This provided a generalization of the measure of mutual information based on Shannon's entropy (corresponding to\alpha = 1). It was shown that the first-order\cal j-divergence is a convex function only when a is restricted to some range. We define higher order Jensen differences and show that they are convex functions only when the underlying entropy function is of degree two. A statistical application requiring the convexity of higher order Jensen differences is indicated.