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An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices

Ellipsoid modeling is 
essential in a variety of fields, ranging from astronomy to medicine. Many response 
surfaces can be 
approximated by a hemi-ellipsoid, allowing estimation of shape, magnitude, and 
orientation via orthogonal 
vectors. If the shape of the ellipsoid under investigation changes over time, 
serial estimates of the orthogonal vectors allow time-sequence mapping of these 
complex response surfaces. We have developed a quantitative, analytic method 
that evaluates the dynamic changes of a hemi-ellipsoid over time that takes 
data points from a surface and transforms the data using a kernel function to 
matrix form. A least square analysis minimizes the difference between actual 
and calculated values and constructs the corresponding eigenvectors. With this method, it is 
possible to quantify the shape of a dynamic hemi-ellipsoid over time. Potential 
applications include modeling 
pressure surfaces in a variety of applications including medical.