Delineating Elliptical Objects with an Application to Cardiac Scintigrams

To delineate the myocardium in planar thallium-201 scintigrams of the left ventricle, a method, based on the Hough transformation, is presented. The method maps feature points (X, Y, Y')-where Y' reflects the direction of the tangent in edge point (X,Y)-into the two-dimensional space of the axis lengths of the ellipse. Within this space, a probability density function (pdf) can be estimated. When the center of the ellipse or its orientation are unknown, the 2-D pdf of the lengths of the axes is extended to a 5-D pdf of all parameters of the ellipse (lengths of the axes, coordinates of the center, and the orientation). It is shown that the variance of the edge-point-based estimates of the axis lengths increases when the location error of the center of the supposed ellipse or its orientation error increases. The likelihood of the estimates is expected to decrease with increasing variance. Therefore, local search algorithms can be applied to find the maximum likelihood estimate of the parameters of the ellipse. Curves describing the convergency of the algorithm are presented, as well as an example of the application of the algorithm to real scintigrams. The method is able to detect contours even if they are only partly visualized, as in thallium scintigrams of the myocardium of patients with ischemic heart disease. As long as the number of parameters describing the contour is relatively low, such an algorithm is also suitable for application to differently curved contours.