Elliptic Fourier approximation with application to left ventricular contour analysis

A computer program for the quantitative analysis of left ventricular wall motion, in standard angiography or echography, was developed based on the center-line model. In order to resolve the uncertainties of the previous implementations, the elliptic Fourier approximation was tested on a large set of left ventricular contour pairs, in various pathological conditions. Fitting a function to the center-line (in the middle of end diastolic and end systolic contours) makes it possible to perform multiple tasks at the same time, in an analytical way and without the need of arbitrary parameters, such as search windows. In doing so, the flexibility and accuracy of this method was demonstrated, more in general, for filtering, interpolation and differentiation of noisy 2D or 3D data. A comparison with standard B-spline was carried out, for both open and closed curves, with sparse or equispaced points. The resulting approximation errors were twice as high as those of the elliptic Fourier decomposition, still preserving smooth direction and curvature. Though already described, this methodology deserves more widespread application.