where a membrane compartment appears like a solid object with dense material
inside. A method that is still based on edge information and tries to overcome these
issues is based on anisotropic propagation of local structural information using a
tensor-voting algorithm [35]. The initial membrane detection step is based on the
Hessian for line-like membranes [33] and the Structure tensor [36] for membranes
delineating solid-like membrane compartments. The results are fed into a tensor
voting algorithm that enhances the membrane structures further and is capable to
bridge gaps in the membrane efficiently. The method performs well in low
signal-to-noise ratio situations typically found in cryo-tomography.
An alternative to edge-based boundary detection algorithms is the use of
region-based approaches where contiguous regions such as membrane compartments or the inside/outside of the cell are identified by some characteristic such as
texture or intensity (Fig. 12.1). The boundary of the regions then becomes the
output of the segmentation. For example, the immersion based watershed algorithm
[37, 38] has been adapted specifically for electron tomography [39]. The method
can be understood as an analogy with a step-wise flooding of a topological relief,
with dams being built where independent flows meet. The approach is capable of
fully automatic segmentation but, in practice, it is more appropriate to use it in a
semi-automatic fashion, optimizing the few operating parameters. Because the
speed of the algorithm allows interactive refinement of these parameters it has been
implemented in the popular graphics packages Amira [25, 40] and Chimera [41, 42]
for interactive use. Other region-based segmentation approaches that showed promise with electron tomograms are based on fuzzy set theory [43] or on normalized
graph cut methods and eigenvector analysis [44].
There are three principal sources of information that can be used to guide
membrane segmentation algorithms: (i) features that define the outside or inside of a
region; (ii) features that define a boundary point; and (iii) shape information about
the object to be segmented. The segmentation approaches described above use only
one of these information sources at a time. A strength of energy-based methods is
their ability to incorporate shape information in a straight forward manner. This is
the case for strong constraints such as adherence to an absolute shape as well as
weak constraints such as boundary smoothness. While the actual shape of a general
membrane structure is not generally predictable, some distinct geometric properties
are known that can be exploited. For example, template-based iterative boundary
detection combined with elliptic shape models was used to generate high fidelity
segmentations of Caulobacter crescentus cell membranes [46]. The downside of
model-based methods is that the models tend to be highly case specific and need to
be modified for each new application.
Shape information is not as easily incorporated into region-based approaches as it
can be incorporated into energy-based algorithms. Weak constraints such as
boundary smoothness can be imposed into region-based approaches [39, 42], but the
direct inclusion of sophisticated shape models cannot easily be done. An exception is
the watersnake method [47], which combines watershed transforms with active
contours (snakes) into a region growing approach that responds to an energy function, thus allowing inclusion of shape information. The watersnake approach was
304
N. Volkmann
inside. A method that is still based on edge information and tries to overcome these
issues is based on anisotropic propagation of local structural information using a
tensor-voting algorithm [35]. The initial membrane detection step is based on the
Hessian for line-like membranes [33] and the Structure tensor [36] for membranes
delineating solid-like membrane compartments. The results are fed into a tensor
voting algorithm that enhances the membrane structures further and is capable to
bridge gaps in the membrane efficiently. The method performs well in low
signal-to-noise ratio situations typically found in cryo-tomography.
An alternative to edge-based boundary detection algorithms is the use of
region-based approaches where contiguous regions such as membrane compartments or the inside/outside of the cell are identified by some characteristic such as
texture or intensity (Fig. 12.1). The boundary of the regions then becomes the
output of the segmentation. For example, the immersion based watershed algorithm
[37, 38] has been adapted specifically for electron tomography [39]. The method
can be understood as an analogy with a step-wise flooding of a topological relief,
with dams being built where independent flows meet. The approach is capable of
fully automatic segmentation but, in practice, it is more appropriate to use it in a
semi-automatic fashion, optimizing the few operating parameters. Because the
speed of the algorithm allows interactive refinement of these parameters it has been
implemented in the popular graphics packages Amira [25, 40] and Chimera [41, 42]
for interactive use. Other region-based segmentation approaches that showed promise with electron tomograms are based on fuzzy set theory [43] or on normalized
graph cut methods and eigenvector analysis [44].
There are three principal sources of information that can be used to guide
membrane segmentation algorithms: (i) features that define the outside or inside of a
region; (ii) features that define a boundary point; and (iii) shape information about
the object to be segmented. The segmentation approaches described above use only
one of these information sources at a time. A strength of energy-based methods is
their ability to incorporate shape information in a straight forward manner. This is
the case for strong constraints such as adherence to an absolute shape as well as
weak constraints such as boundary smoothness. While the actual shape of a general
membrane structure is not generally predictable, some distinct geometric properties
are known that can be exploited. For example, template-based iterative boundary
detection combined with elliptic shape models was used to generate high fidelity
segmentations of Caulobacter crescentus cell membranes [46]. The downside of
model-based methods is that the models tend to be highly case specific and need to
be modified for each new application.
Shape information is not as easily incorporated into region-based approaches as it
can be incorporated into energy-based algorithms. Weak constraints such as
boundary smoothness can be imposed into region-based approaches [39, 42], but the
direct inclusion of sophisticated shape models cannot easily be done. An exception is
the watersnake method [47], which combines watershed transforms with active
contours (snakes) into a region growing approach that responds to an energy function, thus allowing inclusion of shape information. The watersnake approach was
304
N. Volkmann