In the previous post, we know how to draw an 2-D ellipse with its center, its major and minor axis, and its orientation. The process can be easily extent to draw N-D multi-dimensional ellipsoid with its center and covariance matrix (of course we can't visualize on N>3).

Now the question is why we need it? Well, mostly for visualization purpose. Check out some following examples.

1. Want to count how many small objects in a given image, such as embryos, and what is their average size?

Given image with small embryos (and a dime for real area reference) |

Ask my 3-yrs-old daughter to do it - she can count up to 10 :). Or write a simple image processing program, and here I show the result:

Detect each embryo, fitting by an ellipse, compute its area |

Elliptic-Shape Clusters in 2-D |

Ellipsoid-Shape Clusters in 3-D |

One who interested in the image processing or clustering techniques used in these examples can give me a note.

Any other thoughts? Comments are always welcome.