negative, this is an indication for a bright blob-like feature around the point of
reference. In a similar way, if both eigenvalues are positive, there is a dark blob-like
feature around the point of reference.
If the eigenvalues have opposite signs, this is an indication for a saddle point at
the point of reference. Therefore, the zero-crossing of the Laplacian operator can be
used to delimit regions, encompassing blobs. The zero-crossings form the so-called
zero space, which can be used to identify objects. The regions where the Laplacian
changes sign can be extracted by connected component analysis, which are defined
as regions of adjacent pixels that have the same input label. In this regard, different
neighborhoods can be considered for the blobs (4-connected, N4) and for the
contours (8-connected, N8). To compute the connected components of an image,
we first (conceptually) split the image into horizontal runs of adjacent pixels and
then color the runs with unique labels, reusing the labels of vertically adjacent runs
whenever possible. In a second phase, adjacent runs of different colors are then
merged [9].
Figure 3.
The gradient image field. The gradient vector filed is overlaid onto a smoothed and downsampled version of the
original image. The gradient amplitude is encoded by the arrow intensity.
Figure 4.
Connected components of the Laplacian operator’s zero space. The boundary (left) is overlaid on the cell nuclei
image (right). The connected components (center) are calculated from Laplacian of Gaussian, s = 12.
53
Multiscale Segmentation of Microscopic Images
DOI: http://dx.doi.org/10.5772/intechopen.89003
reference. In a similar way, if both eigenvalues are positive, there is a dark blob-like
feature around the point of reference.
If the eigenvalues have opposite signs, this is an indication for a saddle point at
the point of reference. Therefore, the zero-crossing of the Laplacian operator can be
used to delimit regions, encompassing blobs. The zero-crossings form the so-called
zero space, which can be used to identify objects. The regions where the Laplacian
changes sign can be extracted by connected component analysis, which are defined
as regions of adjacent pixels that have the same input label. In this regard, different
neighborhoods can be considered for the blobs (4-connected, N4) and for the
contours (8-connected, N8). To compute the connected components of an image,
we first (conceptually) split the image into horizontal runs of adjacent pixels and
then color the runs with unique labels, reusing the labels of vertically adjacent runs
whenever possible. In a second phase, adjacent runs of different colors are then
merged [9].
Figure 3.
The gradient image field. The gradient vector filed is overlaid onto a smoothed and downsampled version of the
original image. The gradient amplitude is encoded by the arrow intensity.
Figure 4.
Connected components of the Laplacian operator’s zero space. The boundary (left) is overlaid on the cell nuclei
image (right). The connected components (center) are calculated from Laplacian of Gaussian, s = 12.
53
Multiscale Segmentation of Microscopic Images
DOI: http://dx.doi.org/10.5772/intechopen.89003