behavior is determined by a set of rules that control
the pheromone release, the movements and the
variations of the ant energy, a parameter related to
breeding and death. The lung internal structures are
segmented by iteratively deploying ant colonies in
voxels with intensity above a pre-defined threshold
(anthills). Ants live according to the model rules
until the colony extinction: the pheromone
deposition generates pheromone maps. Each voxel
visited by an ant during the life of a colony is
removed from the allowed volume for future ant
colonies. New ant colonies are iteratively deployed
in unvisited voxels that meet the anthill requirement.
By an iterative thresholding of pheromone maps a
list of ROI candidates is obtained. ROIs with a
radius larger than 10 mm are post-processed in order
to disentangle nodules attached to internal lung
structures like vessels and bronchi. The CAM is
iteratively deployed in the right and left lungs,
separately, as a segmentation method for the vessel
tree and the nodule candidates. The first ant colony
segments the vessel tree, starting from an anthill in
the vicinity of its root. The segmented object is then
removed from the original image and the coordinates
of all its voxels are stored as a single Region Of
Interest (ROI). In the remaining image, iteratively,
any voxel with intensity above a predefined
threshold (-700 HU) is a new anthill and a colony
deployed from there generates a pheromone image.
When no more voxels meet the condition to become
an anthill, the information provided by the global
pheromone map is analyzed. The pheromone map
analysis is also iterative: each voxel with a
pheromone content above a minimum accepted
value is used as a seed for a region growing with an
adaptive threshold which is iteratively lowered until
a minimum growth rate of the region is reached.
Every grown region with a radius in the 0.8 − 25
mm range is considered as a nodule candidate.
About 20% of relevant pulmonary nodules are seg-
mented together with a vascular structure they are
connected to. If features were evaluated for the
whole ROI, these nodules would typically be
rejected by further filtering and classification. In
order to address the problem a dedicated algorithm
module was developed. All the structures obtained
from the pheromone map analysis with radius larger
than 10 mm are further analyzed in order to identify
and disentangle spherical-like sub-structures. The 10
mm value was empirically set based on the
minimum size for attached structures that causes a
relevant change in the ROI feature values. Each
voxel that belongs to the structure being analyzed is
averaged with the neighbors inside a sphere of
radius R. Then, the average map is thresholded
again, resulting in a thinner object. Structures with a
diameter smaller than R disappear (e.g., thin vessels
attached to the nodules). However also the nodules
shrink. In order to recover the nodule original size,
the neighbors of each remaining voxel in the average
inside a sphere of radius R/2 with value above 4/3 of
the threshold in the original map are restored as part
of the structure. The procedure is repeated three
times, with spheres of increasing radius (R = 1.5,
2.5, 3.5 mm) that generate sub-structures of
increasing size. The output voxels of the three
iterations are combined in logical OR to generate a
final nodule candidate output mask, which is then
treated as a ROI for further analysis.
2.2.3 Filtering and Classification
The choice of a suitable set of ROI features is a key
to the success of the filtering and classification
stages. Ideally, any computable quantity which is
expected to show a different pattern for true nodules
and false candidates would be a useful feature.
However, the use of a large number of features on a
small training dataset could bias the classifier and
cause a loss of generality. The choice to select a
small number of features for the neural classifier
training aims at optimizing the generality and
keeping the performance stable as the validation
dataset size increases. A set of features was selected
for the nodule candidate analysis, according to the
following criteria: 3D spatial features which are
invariant to rotation and translation and can
disentangle spherical-like structures from ROIs
originating from vessel parts or lung walls; features
based on the voxel HU intensity, so as to capture
density patterns; the fraction of ROI voxels attached
to the walls of the lung volume is crucial in
distinguishing internal and juxta-pleural nodules,
which are characterized by a different shape;
therefore, its use allows the classification of both the
subsamples with the same neural network. The list
of features is reported in Table 1. The average
number of ROIs after the nodule hunting, depending
on the number of slices, ranges between several
hundreds to few thousands per CT scan, a number
far too large to be used as input for a neural network
classifier. The vast majority of findings is easily
rejected with an analytical filter based on
correlations between the radius, the sphericity and
the fraction of voxels connected to the lung mask. In
addition to the sphericity-related selection, two other
filtering conditions were applied to the nodule
candidates: the fraction of voxels connected to lung
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