Modelbased microtubule segmentation

Once the microtubules are localized, the
segmentation can be performed around each microtubule in the enhanced localized
volume. Even so, automatically extracting the microtubule boundaries
remains challenging, since there are still many irrelevant structures and
overlapping materials. Therefore, we use a statistical shape prior method
(active shape model) for segmentation, which is robust against confusing
image features. However, the construction of a statistical shape model of
microtubules in 3D is difficult. To overcome this problem, we characterize
the microtubules by decomposing their shape into crosssectional contours
and longitudinal shapes. The crosssectional contour is modeled with ASM.
The longitudinal shape is modeled with a smoothness constraint using Kalman
filtering.

Segmentation of crosssectional contours with statistical
shape model

The crosssectional
contours are described by a set of boundary points. Training shapes are
obtained from manual delineation of the contours, as shown in the figures
below.


Principal component analysis is then applied
to the training shapes to obtain the mean shape and the modes of shape
variations.

The shape constraints are applied by setting
appropriate limit on b The figure below shows
the effect of individually varying the first three
modes of the microtubule point distribution model. From top row to bottom
row are the first mode, the second mode and the third mode respectively.
Each mode varies to produce the sample shapes in each row


Search crosssectional contours

The
searching for the object contour is an iterative process guided by the
statistical shape model. An image space shape X is found to match a
model space shape x by minimizing
where T is the similarity transform.
The corresponding b in parameter space is obtained as
This b is then constrained to produce valid shape model x.

Combining active shape model with Kalman filtering

Since the microtubule boundary can be easily
corrupted by noise or clutter, segmentation in a single slice may not be
accurate. We therefore utilize the longitudinal shape smoothness of the
microtubules by improving the active shape model with Kalman filtering to
produce more reliable segmentation, assuming that the shape variation
between neighboring slices is small.
The Kalman filtering consists of two steps: state prediction and state
updating. The state prediction is to relate shape parameters s
(including scale factor, transformation parameters and the weights of the
principal components) in neighboring slices
In state updating, the predicted shape and measured shape are
combined to provide an improved shape estimation
Figures below demonstrate the efficacy of the active
shape model combined with Kalman filtering.


(left) a slice in the original volume. (middle) manual
segmentation using IMOD software. (right) automatic segmentation is smooth
due to Kalman filtering. Automatic result is close to the manual result and
reflects the shape of the underlying microtubule.
