results may somewhat depend on the definition of the mask in the general case,
mask-independent scores can be obtained for certain classes of template-matching
problems [68].
Another recent approach employs reduced representation templates [70]. Instead
of using a search model based on the entire density of the template, this approach
reduces the search model to a small number of anchor points that are used to
calculate the scoring function (Fig. 12.3). Advantages include a speed-up in calculations [71], efficient ways to account for conformational variations, and flexibility of defining scoring functions and constraints in real space. Test calculations
indicate that a reduction of false positive hits of about 50% with matched-filter
approaches to below 5% with the reduced representation approach can be achieved
in the full cellular environment [70].
12.4 Segmentation of Filamentous Structures
The third distinct type of features in biological tomograms at the nanometer scale
are filaments. This includes line-like features (actin and intermediate or extra cellular filaments) as well as tubular features (microtubules). Extraction of filament
traces is an active research subject in fluorescence microscopy where the filaments
can be selectively observed through specific fluorescence tags. Many approaches
that have shown promising results for the extraction of filament or bundle center
lines from fluorescence data involve two separate steps of binarization and skeletonization. The simplest way to binarize an image is by applying a threshold value
to assign all voxels that are brighter than the threshold to be part of a filament. This
method almost inevitably leads to binarized images with many artifacts, which need
to be either suppressed by filtering the input or corrected in a subsequent step. The
skeletonization requires thinning of the broadened binarized filaments to a representation of one voxel diameter. To achieve a good skeleton representation, tracing
along the ridges of Euclidean distance maps [75, 76], Hessian-based enhancement
filters [77], constrained diffusion-based methods [78], image decomposition [79],
medial axis determination by distance-ordered homotopic thinning [80], orientation
fields [81], and iterative tensor voting [82], have all been used. Some of these
methods were successfully employed for skeletonization of images [83] and
tomographic reconstructions [84] from scanning electron microscopy, but the
contrast and signal-to-noise ratio in those is much higher than (cryo-)tomograms
from transmission electron microscopy of biological material can provide. For the
latter type of data, methods based on binarization by any type of thresholding tend
to fail [85].
An alternative strategy uses open active contours to segment filaments from
three-dimensional fluorescence data [86, 87]. This approach works well for fluorescence data and approaches based on active contours have also been applied successfully for tracing of microtubules in stained electron tomograms [88, 89]. Because
filaments appear line-like or, in the case of microtubules, as two adjacent lines, very
308
N. Volkmann
mask-independent scores can be obtained for certain classes of template-matching
problems [68].
Another recent approach employs reduced representation templates [70]. Instead
of using a search model based on the entire density of the template, this approach
reduces the search model to a small number of anchor points that are used to
calculate the scoring function (Fig. 12.3). Advantages include a speed-up in calculations [71], efficient ways to account for conformational variations, and flexibility of defining scoring functions and constraints in real space. Test calculations
indicate that a reduction of false positive hits of about 50% with matched-filter
approaches to below 5% with the reduced representation approach can be achieved
in the full cellular environment [70].
12.4 Segmentation of Filamentous Structures
The third distinct type of features in biological tomograms at the nanometer scale
are filaments. This includes line-like features (actin and intermediate or extra cellular filaments) as well as tubular features (microtubules). Extraction of filament
traces is an active research subject in fluorescence microscopy where the filaments
can be selectively observed through specific fluorescence tags. Many approaches
that have shown promising results for the extraction of filament or bundle center
lines from fluorescence data involve two separate steps of binarization and skeletonization. The simplest way to binarize an image is by applying a threshold value
to assign all voxels that are brighter than the threshold to be part of a filament. This
method almost inevitably leads to binarized images with many artifacts, which need
to be either suppressed by filtering the input or corrected in a subsequent step. The
skeletonization requires thinning of the broadened binarized filaments to a representation of one voxel diameter. To achieve a good skeleton representation, tracing
along the ridges of Euclidean distance maps [75, 76], Hessian-based enhancement
filters [77], constrained diffusion-based methods [78], image decomposition [79],
medial axis determination by distance-ordered homotopic thinning [80], orientation
fields [81], and iterative tensor voting [82], have all been used. Some of these
methods were successfully employed for skeletonization of images [83] and
tomographic reconstructions [84] from scanning electron microscopy, but the
contrast and signal-to-noise ratio in those is much higher than (cryo-)tomograms
from transmission electron microscopy of biological material can provide. For the
latter type of data, methods based on binarization by any type of thresholding tend
to fail [85].
An alternative strategy uses open active contours to segment filaments from
three-dimensional fluorescence data [86, 87]. This approach works well for fluorescence data and approaches based on active contours have also been applied successfully for tracing of microtubules in stained electron tomograms [88, 89]. Because
filaments appear line-like or, in the case of microtubules, as two adjacent lines, very
308
N. Volkmann