How to find lengths of three principal axes in an 3D object?

For a region in an binary image, I have calculated co-variance matrix using co-ordinates of region. Using co-variance matrix, I got two eigen values. Later I have calculated major axis length and minor axis length using the formula 4*sqrt(λi) where the λi are the eigenvalues. This formula is mentioned in the below given link http://math.stackexchange.com/questions/911792/3-sigma-ellipse-why-axis-length-scales-with-square-root-of-eigenvalues-of-covar. I have verified lengths of major axis and minor axis with the output of 'regionprops' command in MATLAB. It is exactly matching for 2D object. Now, I want to calculate principal axes lengths (major, middle and minor axis lengths) for 3D object data. For that I want a relation between eigen values obtained from 3D object co-ordinates (using same procedure mentioned above) and principal axes lengths for 3D data. 'regionprops' command in MATLAB do not work for 3D object.

[Ashbub]

Hi Shrikant, have you tried regionprops3 command? I think it works for 3D.