This paper reports on the clinical application of a system for recovering the time-varying three-dimensional (3-D) left-ventricular (LV) shape from multiview X-ray cineangiocardiograms. Considering that X-ray cineangiocardiography is still commonly employed in clinical cardiology and computational costs for 3-D recovery and visualization are rapidly decreasing, it is meaningful to develop a clinically applicable system for 3-D LV shape recovery from X-ray cineangiocardiograms. The system is based on a previously reported closed-surface method of shape recovery from two-dimensional occluding contours with multiple views. To apply the method to "real" LV cineangiocardiograms, user-interactive systems were implemented for preprocessing, including detection of LV contours, calibration of the imaging geometry, and setting of the LV model coordinate system. The results for three real LV angiographic image sequences are presented, two with fixed multiple views (using supplementary angiography) and one with rotating views. 3-D reconstructions utilizing different numbers of views were compared and evaluated in terms of contours manually traced by an experienced radiologist. The performance of the preprocesses was also evaluated, and the effects of variations in user-specified parameters on the final 3-D reconstruction results were shown to be sufficiently small. These experimental results demonstrate the potential usefulness of combining multiple views for 3-D recovery from "real" LV cineangiocardiograms.

Generally, in the field of industrial design, the measurement data of a clay model are faired, and a 3D model is made in CAD. However, it is a problem that this fairing work takes a long time and requires a great deal of labor. We propose an automatic curve fairing system for the application to reverse engineering technology. The system is constructed by the following five steps. (1) Key-line data are extracted from a clay model by a 3D digitizer. (2) The extracted key-line data are approximated by a spline with a genetic algorithm. (3) The spline curve (key-line) is divided into curves of monotone curvature. (4) The "characteristic" of the curve is analyzed for each monotone-curvature curve. (5) Each monotone-curvature curve is substituted by a visual language based on the result of the analysis mentioned above, and each key-line is reconstructed by the visual language. By using this system, we can easily obtain an aesthetic curve, as intended by a designer, in a short time.

In order to obtain a good spline model from many measurement data, frequently we have to deal with bets as variables. Then the problem to be solved becomes a continuous nonlinear and multivariate optimization problem with many local optima. Therefore, it is difficult to obtain a global optimum. We propose a new method to convert the original problem into a discrete combinatorial optimization problem and solve the converted problem by a genetic algorithm. We construct individuals by considering candidates of the locations of knots as genes, and convert the continuous problem into a discrete problem. We search for the best model among the candidate models by using H. Akaike's (1974) Information Criterion (AIC). Our method can determine appropriate number and locations of knots automatically and simultaneously. We don't need any subjective parameters such as error tolerance or a smoothing factor, and good initial location of knots for iterative search. Numerical examples are given to show the effectiveness of our method.