  We present a method for registration and visualization of corresponding
supine and prone virtual colonoscopy scans based on eigenfunction analysis and
fold modeling. In virtual colonoscopy, CT scans are acquired with the patient
in two positions, and their registration is desirable so that physicians can
corroborate findings between scans. Our algorithm performs this registration
efficiently through the use of Fiedler vector representation (the second
eigenfunction of the Laplace-Beltrami operator). This representation is
employed to first perform global registration of the two colon positions. The
registration is then locally refined using the haustral folds, which are
automatically segmented using the 3D level sets of the Fiedler vector. The use
of Fiedler vectors and the segmented folds presents a precise way of
visualizing corresponding regions across datasets and visual modalities. We
present multiple methods of visualizing the results, including 2D flattened
rendering and the corresponding 3D endoluminal views. The precise fold modeling
is used to automatically find a suitable cut for the 2D flattening, which
provides a less distorted visualization. Our approach is robust, and we
demonstrate its efficiency and efficacy by showing matched views on both the 2D
flattened colons and in the 3D endoluminal view. We analytically evaluate the
results by measuring the distance between features on the registered colons,
and we also assess our fold segmentation against 20 manually labeled datasets.
We have compared our results analytically to previous methods, and have found
our method to achieve superior results. We also prove the hot spots conjecture
for modeling cylindrical topology using Fiedler vector representation, which
allows our approach to be used for general cylindrical geometry modeling and
feature extraction.
