preservation of globular structures, while if the normal component is selected, this
will lead to enhancement of the tubular structures. The equation u t ¼ Δ ⊥G u is called
mean curvature motion equation [17]. An example is presented in Figure 8.
6. Implementation
The filters described in the present manuscript are implemented in ImageJ as a
set of plug-ins (Table 2). Two implementation strategies have been used: the
integer order filters are implemented in the spatial domain, while the fractional
order filters are implemented in the Fourier domain [21].
1 The plug-ins are distributed under the GNU Lesser General Public License v3.0 and are available as code
repository from the GitHub website [22].
2 The choice of implementation platform
was due to the widespread use of ImageJ in the biomedical and life science
communities.
ImageJ is a public domain image processing program written in Java. Since its
inception in 1997, ImageJ has evolved to become a standard analytical tool in a
Figure 7.
Blob segmentation. Zero-crossing of the LoG decomposition, s = 6 (A) and s = 12 (B). Two blobs are highlighted
for better appreciation. The normal component is in Lap T, tangential component of the Laplacian; Lap O,
normal component of the Laplacian.
Figure 8.
Anisotropic diffusion along principal flow directions. Astrocytes were stained immunohistochemically for glial
fibrillary acidic protein (GFAP) and imaged on a confocal microscope (left). Anisotropic diffusion evolved
according to the orthogonal decomposition of the Laplacian, s = 3, 3 steps—Tangential direction (center) and
along the gradient direction (right). Note the granularity of the right image and its blurred appearance
compared to the central image.
1 The installation procedure of the spatial-domain filters is straightforward, and this is the reason why
only spatial-domain filters are included in the public repository.
2 https://github.com/dprodanov/scalespace.
58
Advances in Neural Signal Processing
will lead to enhancement of the tubular structures. The equation u t ¼ Δ ⊥G u is called
mean curvature motion equation [17]. An example is presented in Figure 8.
6. Implementation
The filters described in the present manuscript are implemented in ImageJ as a
set of plug-ins (Table 2). Two implementation strategies have been used: the
integer order filters are implemented in the spatial domain, while the fractional
order filters are implemented in the Fourier domain [21].
1 The plug-ins are distributed under the GNU Lesser General Public License v3.0 and are available as code
repository from the GitHub website [22].
2 The choice of implementation platform
was due to the widespread use of ImageJ in the biomedical and life science
communities.
ImageJ is a public domain image processing program written in Java. Since its
inception in 1997, ImageJ has evolved to become a standard analytical tool in a
Figure 7.
Blob segmentation. Zero-crossing of the LoG decomposition, s = 6 (A) and s = 12 (B). Two blobs are highlighted
for better appreciation. The normal component is in Lap T, tangential component of the Laplacian; Lap O,
normal component of the Laplacian.
Figure 8.
Anisotropic diffusion along principal flow directions. Astrocytes were stained immunohistochemically for glial
fibrillary acidic protein (GFAP) and imaged on a confocal microscope (left). Anisotropic diffusion evolved
according to the orthogonal decomposition of the Laplacian, s = 3, 3 steps—Tangential direction (center) and
along the gradient direction (right). Note the granularity of the right image and its blurred appearance
compared to the central image.
1 The installation procedure of the spatial-domain filters is straightforward, and this is the reason why
only spatial-domain filters are included in the public repository.
2 https://github.com/dprodanov/scalespace.
58
Advances in Neural Signal Processing