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Model-based 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 cross-sectional contours and longitudinal shapes. The cross-sectional contour is modeled with ASM. The longitudinal shape is modeled with a smoothness constraint using Kalman filtering.

Segmentation of cross-sectional contours with statistical shape model

The cross-sectional 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 cross-sectional 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.


Summary | Background | Methods | Results | Publications