# Semi-automatic Integrated Segmentation Approaches  and Contour Extraction Applied

Authors: B. Dhalila S. Y. Khoodoruth; Harry C. S. Rughooputh; Wilfrid Lefer
Journal: International Journal of Biomedical Imaging
 (2008)

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## Abstract

We propose to segment two-dimensional CT scans traumatic
brain injuries with various methods. These methods are
hybrid, feature extraction, level sets, region growing, and
watershed which are analysed based upon their parametric
and nonparametric arguments. The pixel intensities, gradient
magnitude, affinity map, and catchment basins of these
methods are validated based upon various constraints evaluations.
In this article, we also develop a new methodology for
a computational pipeline that uses bilateral filtering, diffusion
properties, watershed, and filtering with mathematical
morphology operators for the contour extraction of the lesion
in the feature available based mainly on the gradient
function. The evaluations of the classification of these lesions
are very briefly outlined in this context and are being
undertaken by pattern recognition in another paper work.


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## Body

## 1. Introduction

Segmentation  is
crucial for  image analysis. The segmented features can be used for presurgery
planification or diagnostic purposes as referred to Ciofolo and Barillot [1]. For instance, an irregular
boundary of a segmented subdural haematoma in the parietal lobe indicates the
severity of  the traumatic brain injury as acute stage. Parametric Segmentation
approaches such as feature extraction, hybrid, level-sets,
watershed and region-growing are experimented. These evaluations are performed for traumatic brain injuries
such as brain atropy, subdural hygroma, subdural haematoma, nonhaemorrhagic
contrecoup contusion, and extracranial haematoma.Parametric hybrid approaches such as deformable
models, fuzzy connectedness, and fuzzy voronoi have been experimented, but the
resultant output of the segmented pathological features is less efficient than
those of the nonparametric segmentation approaches. In the case of the
deformable models, the vector field lacks precision to identify the boundary of
the feature. Whilst for the fuzzy connectedness, the binary template has
generated quite effectively some results but not the exact representation of
the segmented lesion. Any voronoi diagram is obtained by the fuzzy voronoi
approach. The feature extraction approach such as hough transform 2D lines
shows no effective result as the hough filter cannot compute the maxima in the
hough map to define a geometry to locate the lesion.The
nonparametric segmentation approaches such as region growing
approaches for confidence connected, connected threshold,
neighbourhood connected are experimented.Level-sets' approaches for threshold segmentation,
fast marching, and shape detection mainly compute and analyse the motion of the
feature under a velocity field which depends on the position, time, and
geometry of the lesion as described in the work of Hong-Kai et al. [2]. Various results have been
obtained with various ranges of constraints. The watershed-based segmentation approach is applied where the
gradient magnitude of intensities of the pixels in the feature
undergoes a transform.The contour extraction of the brain atrophy, subdural
haematoma, nonhemorrhagic contusion, and subdural hygroma is performed by a
computational pipeline from the raw CT scans.Section2 is the state of the art related to
segmentation. Section 3 describes the various approaches of segmentation
applied to the traumatic brain injuries with the validations and evaluations of
constraints. Section 4 describes our approach for the computational pipeline
for the contour extraction. Section 5 concludes part of the work accomplished.


## 2. State of the Art

Basically,
segmentation is the partitioning of the image into nonoverlapping constituent regions
which are homogeneous with respect to some characteristics such as intensity or
texture as described in the work of Bazin and Pham [3]. The
identification of the pixels for a particular lesion is inherently
built-in the segmentation method which can further allow
for a pixel classification and labelling of the structure.The dimensionality of the image is a crucial factor to
be considered before segmentation process because image intensities are
independent of the image domain. As described in the work of Mahrous et
al. [4], the original
vector field can be replaced by a derived segmented data set. The derived set is used to produce separating surfaces in the vector field whereas the CT scans are used for single scalar field.Contour based surface extraction and isosurface
extraction models have been considered for the purpose of implicit
segmentation which is based on intensity threshold where points
are classified as either greater or less than a given intensity as
referred to Pham et al.  [5]. The above is compared to an
explicit segmentation using deformable models by reffering to the
works of Giachetti and Zanetti [6], Colliot et al. [7]. The
purpose is not to modify the image surface by an image vector and
an internal image force.Regarding the work of  Hassouna et al. [8], these slight ambiguities have been encountered by the
intensity regions based on the Hounsfield scale for CT scans. The
purpose is to identify the grayscale range within the lesions. As
stated in the works of   Ritter et al. [9] and Heuberger et al. [10], the threshold
segmentation is efficient for bone segmentation from CT scans.
Since bone tissue attenuates significantly more x-rays during
acquisition. Therefore, these attenuations are represented by much
higher values on the Hounsfield scale compared to soft tissues.  Weber et al. [11] developed an algorithm to modify
a segmentation based on visual examination and obtained
additional information about incorrectly segmented objects.


## 3. Segmentation

The segmentation of these features must be considered based upon either a
geometric approach or a diffusion approach or a fuzzy segmentation with a
statistical approach as stated by Petersch et al., Vidal et al., and John et
al. [12–14]. In the case of nonparametric level set segmentation
methods, a geometric approach such as the distance function with a fast
sweeping function is considered where the distance transform is calculated from
the number of pixels as referred to Sifakis and Tziritas [15]. These segmentation
approaches with different functionalities are experimented using open-source
software insight toolkit [16]
and a viewer.


### 3.1. Methodology

#### 3.1.1. Level Sets

Based upon the excellent review of Osher and Fedkiw [17] on level sets,
the surface Γ is represented as the zero isocontour of a
scalar function (x),
that is, (1)Γ=x:ϕ(x)=0, which represents the curve or boundary of the feature.The various  approaches such as fast marching,
threshold, and shape detection use basically the algorithmic representation of
the level set procedure as described in Algorithm1.Algorithm 1:Algorithmic representation of level
sets procedure.
for each pixel value from seed
points,extract sigmoid function and
propagation term.for each image intensity,apply edge filter,provide threshold,adjust intensity scaling.Algorithm 2:Algorithmic representation of
watershed procedure.
define a slope for each pixelfor each pixel value,calculate topographical distanceestimate gradient for gray-level
values.for each image gradient threshold
identification,perform edge-preserving,represent gradient magnitude,generate merge tree,access segmented image,acquire segmentation tree.Algorithm 3:Algorithmic representation of region
growing procedure.
for each pixel value from seed
points,apply edge-preserving,instantiate smoothing,assign pointer for smoothing and
edge-preserving.Fast Marching Approach
The FastMarchingImageFilter is used in the
Reinitialize LevelSetImageFilter object to create a signed distance function
from the zero level set as referred to [16].
The lower threshold is set to a default value of 0.0
and the upper threshold defines the time snapshot which is taken from the time
crossing map which is set to 85. The CurvatureAnisotropicDiffusionImageFilter
requires TimeStep, NumberOfIterations, and ConductanceParameter are set as
0.125, 5, and 9 so as to detect the boundary of the structures. The
SigmoidImageFilter class requires two parameters, alpha and beta, to define the
linear transformation to the sigmoid argument as illustrated in Figures1(E),
1(F), 1(G), 1(H) or reduction at edges as illustrated in Figures 1(A), 1(B),
1(C), 1(D).
By increasing the value ofβ to 4.00 and decreasing the value α to −0.575 as referred to in Table 1, the size
of the feature gets smaller as illustrated in Figures 1(A), 1(B), 1(C), 1(D)
and expands in Figures 1(E), 1(F), 1(G), 1(H). The shape of the feature gets
distorted as the value of σ increases to 0.325. The threshold is generated
to the time crossing map so as to build the time solution surface Γ of the white matter one grid point at a time
where the feature is situated. Though the time is found for one grid point, but
gets distorted for other nearby values in the features of Figures 1(i) and 1(ii).
The features of Figures1(iii) and 1(iv) as mentioned
in Table 1 show no variation during segmentation by decreasing or increasing
the values of the constraints. The edges of the segmented features as
illustrated in Figures 1(I), 1(J), 1(K), 1(L) are almost identical.  Figures 1(M), 1(N), 1(O),
1(P) illustrate almost identical features. Since the extracranial
haematoma is outside the skull and has a homogeneous tissues density throughout
resulting in no variation of the gradient intensities, the brain atrophy is at
the rim of the right frontal lobe of the skull where the variation of gradient
intensities is almost stagnant. Consequently, the most crucial factor in these
features (iii) and (iv) is the time crossing map, which is set at 0.125 due to
the coil rotation inside the CT scanner.
The fast marching level set segmentation is deduced to
be the most appropriate feature
extraction for the extracranial haematoma and the brain atropy.
The extracranial haematoma is homogeneously
hyperdense, sharply marginated, and consists of solid blood clots found on the
outside border of the skull as referred to [18]. The pixel intensities within this feature are
constant throughout. So, the gradient magnitude intensities computed do not
vary though the σ values are within a range of 0.0005 to 0.325,
the α values are within a range of −0.0005 to
−0.575, and the β values are within a range of 0.0005 to 4.00.
This implies that the sigmoid member class filter has no effect on the time
solution surface Γ which is the zero level set representing the
contour of the feature. The TimeStep of the scanner set at 0.125 and the number
of iterations are crucial parameters to seek the proper edge of the feature.Table 1
Internal constraints for fast marching level sets.
Fast marchingSigma0.0005≤σ≤0.325Alpha−0.0005≥α≥−0.575Beta0.0005≤β≤4.00(A, E, I, M)α=−0.0005,β=0.0005,sigma=0.0005, (B, F, J, N) α=−0.0015,beta=0.0025,σ=0.0125, (C, G, K, O) α=−0.375,β=0.2255,σ=0.0225, (D, H, L, P) α=−0.575,β=4.00,σ=0.0325 are (i) values set for subdural haematoma,
(ii) contrecoup contusion, (iii) extracranial haematoma, and (iv) brain atrophy
by fast marching.Threshold Approach
A range of intensity values are defined for the
feature in the threshold level set segmentation. A propagation term is applied
on the level set equation for the intensity range as referred to [16] and illustrated in Figure  2.
The initial
level set generates the distance map, and a distance function is computed by
applying the lower and upper threshold. In case, the lower threshold is less
than 150, as referred to in Table2, and the higher threshold is greater than
205, the range of intensities for the feature does not determine an initial
surface for the gradient flow resulting in no segmentation.
Values below 4
or greater than 7 for the distance map result in a reduction or expansion of
the initial contour, the zero level set of the feature as the surrounding
region is white matter of homogeneous tissues density. There is very slight change of segmented feature as
illustrated in Figures2(U), 2(V),
2(W), 2(X) and Figures 2(Y), 2(Z), 2(A1), 2(B1) by applying the range of 4 to 7
for the distance map.
The threshold level set segmentation is the
appropriate procedure for segmenting the subdural haematoma and the
nonhemorrhagic contusion.
Since the subdural haematoma is in an acute stage, it
is hyperdense because of the attenuating properties of the haemoglobin
molecules found in the blood clots. The stage of density takes weeks before
being isodense. The lower and upper limits of the thresholds are set at 140 and
205 so as to consider only gradient magnitude intensities within the feature
forbidding surrounding regions which can be hypodense or isodense. By lowering
the limit of the threshold, lower gradient magnitude densities are acquired for
which the distance function does not clearly mark the edge of the feature. The
hyperdense area of the feature can be clearly demarcated by the proper
threshold setting. When the  threshold is increased  to the corresponding gradient magnitude densities applied to the distance function,  a proper segmented feature is obtained without any distortion of the initial
surface of the zero level set.
Whilst the nonhemorrhagic contrecoup contusion is an
area of higher densities of tissues sorrounded by  areas of lower densities  of tissues, the varying range of the minimum and maximum of
the threshold values is adjust to the varying range of gradient magnitude
densities. Consequently, the initial zero level set surface is computed by the
adjustments of the corresponding densities and distance map resulting in a
proper feature extraction.Table 2
Internal constraints for threshold level sets.
Threshold level setInitial distance4≤ initial distance ≤ 7Lower threshold150≤ lower ≤ 175Upper threshold175≤ upper ≤ 205(U, Y)distance=4,lower=150,upper=175, (V, Z) distance=5,lower=155,upper=185, (W, A1) distance=6,lower=160,upper=195, (X, B1) distance=7,lower=175,upper=205 are (vi) values set for the subdural haematoma
and (vii) contrecoup contusion by threshold approach.Shape Detection Approach
Finally in the shape detection level set segmentation
method, fast marching level set segmentation is used to define the initial
level set based upon a distance map as referred to [16].
Though a wide range of parameter values are set for
this approach, no exact segmented feature is obtained, as referred to in Table3. The relative weightings of the propagation and curvature terms between these
two parameters do not adjust to produce the shape boundaries of the feature. Consequently,
zero level set leaks may have been produced through the feature's regions of
low gradient along the boundaries of the pathological feature itself as
illustrated in Figures 3(C1), 3(D1), 3(E10), 3(F1) and Figures
3(G1), 3(H1), 3(I1), 3(J1).Table 3
Internal constraints for shape detection level sets.
Shape detectionInitial distance3≤ initial distance ≤9Sigma0.45≤σ≤1.1Alpha−0.25 ≥α≥−0.55Beta1.85≤β≤3.25Propagation scaling0.005≤ propagation ≤ 0.07Curvature scaling0.9≤ curvature ≤ 1.5Table 4
Internal constraints for watershed.
WatershedConductante term2≤ conductance ≤ 7Iterations10≤ iterations ≤ 20Lowerthreshold0.001≤ Threshold ≤ 0.1Output scale level0.15≤ Scale level ≤ 0.30(C1, G1) distance=3,α=−0.25,σ=0.45,β=1.85,
propagation
=0.005,curvature=0.9,(D1,H1)distance=5,α=−0.35,σ=0.65,β=2.15,propagation=0.035,curvature=1.1,(E1,I1)distance=7,α=−0.45,σ=0.95,β=2.9,propagation=0.05,curvature=1.3,(F1,J1)distance=9,α=−0.55,σ=1.1,β=3.25,propagation=0.07,curvature=1.5 are values set for (viii) the contrecoup
contusion and (ix) subdural haematoma by shape detection approach.


#### 3.1.2. Watershed

As described in
the work of Grau et al. [19], and the excellent review of Roerdink and Meijster [20], the method is based on the
topographical distance applied on these discrete two-dimensional medical images
where basically the algorithmic representation is used.Two important parameters, threshold and level control
the output of this watershed segmentation, as referred to in Table5. The
purpose of the threshold parameter is to set the absolute minimum height value.
The level parameter controls the depth of metaphorical flooding of the image.
Raising and lowering the level influence the number of segments in the basic
segmentation that are merged to produce the final output. A level of 1.0 is
analogous to flooding the image up to a depth that is 100 percent of the
maximum value in the image. Level values of interest are typically low as
illustrated in Figure 4, that is, less than about 0.40 since higher
values will quickly undersegment the image.Table 5
Internal constraints for region growing.
Confidence connectedMultiplier0.05≤ multiplier ≤ 2.5Connected thresholdLower threshold150≤ lower ≤ 175Upper threshold175≤ upper ≤ 205NeighbourhoodLower threshold140≤ lower ≤ 175Upper threshold170≤ upper ≤ 205(column
K1) Values set for the subdural hygroma(x) are conductance=2.5,iterations=11,lower=0.015,scalelevel=0.15 by watershed approach.The threshold parameter cannot exceed the value of 0.1
as illustrated in Figure4(K1) to represent the gradient magnitude of
intensities which are a percentage of the maximum depth of the feature so as to
avoid oversegmentation.


#### 3.1.3. Region Growing

In this
approach, a seed is selected from the data set manually, and the algorithm
engulfs the relevant region up to its boundary using some connectedness
approach to the surrounding pixels as referred to [16]. Basically, the algorithmic
representation of the region growing procedure is used for the confidence
connected, connected threshold, and neighbourhood approaches.The NumberOfIterations and TimeStep which are set as
default values of 5 and 0.125 for 2D images, as referred to in Table6. The
itkConfidenceConnectedImageFilter class is used for the segmentation itself.
This requires the definition of two parameters. The factor f which determines the extent of the range of intensities
and the number of iterations specifies the homogeneity of the structure to be
segmented. In this context, the multiplier factor is more important than the
number of iterations, to avoid the region to engulf the entire image as
illustrated in Figure 5(L1).Table 6
Tables of required constraints for contour extraction of pathological features.
Computational pipelineConductante term2Iterations10Lower threshold0.05Output scale level0.15Domain sigma0.015Range sigma0.85Time step0.125(L1)multiplier=2.5, (M1) multiplier=2.0, (N1) multiplier=1.5, (O1) multiplier=1.0, (P1) lower=140,upper=170, (Q1) lower=150,upper=180, (R1) lower=155,upper=190, (S1) lower=160,upper=195 are (xi) values set for the contrecoup
contusion by confidence connected, for (xii) contrecoup contusion by
neighbourhood connected.The range of
values for the lower threshold and upper threshold varies between the minimum
of 140 and maximum of 205. This allows for the usage of various pixel
intensities to be identified for the computation of the gradient magnitude
intensities due to its sensitivity to thresholds. As illustrated in Figure5(P1), a minimum value of threshold 140 and maximum value of threshold 170 show
a compression of the segmented feature, and the most exact representation of
the segmented feature is illustrated in Figure 5(Q1) with a minimum of 150 and
maximum of 180. No segmented feature expansion is obtained through this range,
but still a compressed segmented feature is obtained with the minimum of 160
and maximum of 195 as illustrated in Figure 5(S1).The nonhemorrhagic contusion is well segmented by the
neighbourhood connected threshold approach. The varying range of minimum and
maximum values of threshold of 140 and 205 allows the neighbouring filter to
consider neighbouring pixels intensities instead of only the current pixel
intensity. This is done by also accepting or rejecting small structures found
inside or outside the lesion. Since the lesion is heterogeneous, the
structuring element of the feature is well surrounded by the exact evaluation
of gradient magnitude densities resulting in the exact segmented feature.


### 3.2. Constraints

The influence
of each constraint has a direct impact on each lesion type, which is the most
crucial part of the work undertaken. The segmented lesions types vary
differently or constantly depending upon the range of the applied constraint.
These variations are also assessed by the numerical evaluations and comparisons
of the results.


#### 3.2.1. Numerical Constraints Evaluations

Herewith is the
sets of constraints associated to the segmented lesion types after segmentation
process.The Sigma Constraint
The sigma “σ” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value.
Two ranges of values such as0.0005≤σ≤0.325 and 0.45 ≤σ≤ 1.1 have been experimented. Negative and null
values are forbidden resulting in leakages at the edges of the feature since
the pixel type is of unsigned short type. Values less than 0.0005 result in
expansion and values greater than 1.1 result in reduction of the segmented
feature. According to Figure 1, the most appropriate result for the segmented
feature lies in columns (B, F, J, N) and (C, G, K, O) within a range of 0.0125 to
0.0225.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is 0.0100 which
explains the closeness and narrowness of the lesion to an edge.The Alpha Constraint
The alpha “α” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma, and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value till a
threshold is applied to a time crossing map to the white matter.
Two ranges of values such as−0.0005≤α≤−0.575 and  −0.25≤α≤−0.55 have been experimented. Negative and
null values are used according to the requirements though the pixel is of
unsigned short type. Values less than −0.0005 result in expansion, and values
greater than −0.55 result in reduction of the segmented feature. According to
Figure 1, the most appropriate result for the segmented feature lies in columns
(B, F, J, N) and (C, G, K, O) within a range of −0.0015 to −0.375.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is −0.360 which
explains the closeness and narrowness of the lesion to an edge.The Beta Constraint
The beta “β” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma, and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value.
Two ranges of values such as0.0005≤β≤4.00 and 1.85≤β≤3.2 have been experimented. Negative and null
values are forbidden resulting in leakages at the edges of the feature since
the pixel type is of unsigned short type. Values less than 0.0005 result in
expansion, and values greater than 4.00 result in reduction of the segmented
feature. According to Figure 1, the most appropriate result for the segmented
feature lies in columns (B, F, J, N) and (C, G, K, O) within a range of 0.0025 to
0.2255.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is 0.2230 which
explains the closeness and narrowness of the lesion to an edge.The Distance Constraint
The initial distance “initial distance” constraint is
efficient for the segmentation of the subdural haematoma and nonhemorrhagic
contrecoup contusion. The initial distance is the distance between the initial
surface and the boundary of the feature which is assigned a numerical value.
Two ranges of values such as 4≤ initial distance ≤ 7 and 3 ≤ initial distance ≤ 9 have been experimented. Negative and null
values are forbidden because this constraint is a crucial requirement to locate
the lesion. Values less than 3 result in expansion, and values greater than 9
result in reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 6 to 7.
As illustrated in Figure2, these two lesion types are
located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 1 which explains the closeness and narrowness of the lesion
to an edge.The Lower Threshold Constraint
The lower threshold “lower” constraint is efficient
for the segmentation of the subdural haematoma, and nonhemorrhagic contrecoup
contusion has been experimented. The lower threshold accesses current pixel
intensities within the feature.
The ranges of values such as 150≤ lower ≤ 175 and 140 ≤ lower ≤ 175 have been experimented. Negative and null
values are forbidden because if not the feature will not be selected at all.
Values less than 150 result in expansion, and values greater than 175 result in
reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 160 and 175.
As illustrated in Figure2, these two lesions types
are located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 15, which explains the closeness and narrowness of the
lesion to an edge.The Upper Threshold Constraint
The upper threshold “upper” constraint is efficient
for the segmentation of the brain atrophy, extracranial haematoma, subdural
haematoma and nonhemorrhagic contrecoup contusion. The upper threshold
accesses neighbouring pixel intensities of similar intensities within the
feature.
Two ranges of values such as 175≤ upper ≤ 205 and 170 ≤ upper ≤ 205 have been experimented. Negative and null
values are forbidden because if not the feature won't be selected at all.
Values less than 140 result in expansion, and values greater than 175 result in
reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 195 to 205.
As illustrated in Figure2, these two lesions types are
located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 10 which explains the closeness and narrowness of the
lesion to an edge.The Conductance Constraint
The conductance constraint is efficient for the
segmentation of the subdural hygroma. This constraint helps for a proper
definition of the boundary of the lesion.
The range of values such as 2≤ conductance ≤ 7 has been experimented. Negative and null
values are forbidden because if not the feature's boundary will not be selected
at all. Values less than 2 result in undersegmentation, and values greater than
7 result in oversegmentation of the feature. According to Figure 4, the most
appropriate result for the segmented feature lies in column (K1) with a value
of 2.5.The Iterations Constraint
The iterations constraint is efficient for the
segmentation of the brain atrophy, extracranial haematoma, subdural haematoma,
and nonhemorrhagic contrecoup contusion. This constraint determines the mean
and standard variance of the neighbouring pixels to be calculated and
consequently the number of times to repeat the segmentation.
The range of values such as 10≤ iterations ≤ 20 has been experimented. Negative and null
values are forbidden so as to obtain the best segmentation result. Values less
than 0.0005 result in expansion, and values greater than 4.00 result in
reduction of the segmented feature.


#### 3.2.2. Comparison of Various Results for Constraints Evaluations

(i) The Sigma Constraint
These values 0.0005, 0.0125, 0.0225, and 0.0325 are
illustrated in Figure1, and these values 0.45, 0.65, 0.95, and 1.1 are
illustrated in Figure 3.(ii) The Alpha Constraint
These values−0.0005, −0.0015, −0.375, and −0.575 are
illustrated in Figure 1, and these values −0.25, −0.35, −0.45, and  −0.55 are
illustrated in Figure 3.(iii) The Beta Constraint
These values 0.0005, 0.0025, 0.2255, and 4.00 are
illustrated in Figure1, and these values 1.85, 2.15, 2.9, and 3.25 are
illustrated in Figure 3.(iv) The Initial Distance Constraint
These values 4, 5, 6, and 7 are illustrated in Figure2, and these values 3, 5, 7, and 9 are illustrated in Figure 3.(v) The Lower Threshold Constraint
These values 150, 155, 160, 175 are illustrated in
Figure2, and these values 140, 150, 155, 160 are illustrated in Figure 5.(vi) The Upper Threshold Constraint
These values 175, 185, 195, 205 are illustrated in
Figure2, and these values 170, 180, 190, 195 are illustrated in Figure 5.


#### 3.2.3. Requirements

The traumatic
brain injuries segmented are brain atrophy, subdural hygroma, subdural
haematoma, nonhemorrhagic contrecoup contusion, and extracranial haematoma
obtained from a set of 5 patients.These axial CT scans obtained from Centre Hospitalier
De Bayonne are of dimension512×512 and thickness 2.5 mm varying in between 38
to 182 slices effected from different medical practitioners which have been
converted into 256×256. These slices show varying levels of intensities
depending on the intra and intervisual perception of these practitioners.Before segmentation proceeds, these images are
preprocessed by the bilateral image filter which is an edge preserving
smoothing filter. Smoothing is performed by using domain and range
neighbourhoods. Pixels that are close to a pixel in the image domain and
similar to a pixel in the image range are used to calculate the filtered value
as referred to Tomasi and Manduchi [21].


## 3.1. Methodology

### 3.1.1. Level Sets

Based upon the excellent review of Osher and Fedkiw [17] on level sets,
the surface Γ is represented as the zero isocontour of a
scalar function (x),
that is, (1)Γ=x:ϕ(x)=0, which represents the curve or boundary of the feature.The various  approaches such as fast marching,
threshold, and shape detection use basically the algorithmic representation of
the level set procedure as described in Algorithm1.Algorithm 1:Algorithmic representation of level
sets procedure.
for each pixel value from seed
points,extract sigmoid function and
propagation term.for each image intensity,apply edge filter,provide threshold,adjust intensity scaling.Algorithm 2:Algorithmic representation of
watershed procedure.
define a slope for each pixelfor each pixel value,calculate topographical distanceestimate gradient for gray-level
values.for each image gradient threshold
identification,perform edge-preserving,represent gradient magnitude,generate merge tree,access segmented image,acquire segmentation tree.Algorithm 3:Algorithmic representation of region
growing procedure.
for each pixel value from seed
points,apply edge-preserving,instantiate smoothing,assign pointer for smoothing and
edge-preserving.Fast Marching Approach
The FastMarchingImageFilter is used in the
Reinitialize LevelSetImageFilter object to create a signed distance function
from the zero level set as referred to [16].
The lower threshold is set to a default value of 0.0
and the upper threshold defines the time snapshot which is taken from the time
crossing map which is set to 85. The CurvatureAnisotropicDiffusionImageFilter
requires TimeStep, NumberOfIterations, and ConductanceParameter are set as
0.125, 5, and 9 so as to detect the boundary of the structures. The
SigmoidImageFilter class requires two parameters, alpha and beta, to define the
linear transformation to the sigmoid argument as illustrated in Figures1(E),
1(F), 1(G), 1(H) or reduction at edges as illustrated in Figures 1(A), 1(B),
1(C), 1(D).
By increasing the value ofβ to 4.00 and decreasing the value α to −0.575 as referred to in Table 1, the size
of the feature gets smaller as illustrated in Figures 1(A), 1(B), 1(C), 1(D)
and expands in Figures 1(E), 1(F), 1(G), 1(H). The shape of the feature gets
distorted as the value of σ increases to 0.325. The threshold is generated
to the time crossing map so as to build the time solution surface Γ of the white matter one grid point at a time
where the feature is situated. Though the time is found for one grid point, but
gets distorted for other nearby values in the features of Figures 1(i) and 1(ii).
The features of Figures1(iii) and 1(iv) as mentioned
in Table 1 show no variation during segmentation by decreasing or increasing
the values of the constraints. The edges of the segmented features as
illustrated in Figures 1(I), 1(J), 1(K), 1(L) are almost identical.  Figures 1(M), 1(N), 1(O),
1(P) illustrate almost identical features. Since the extracranial
haematoma is outside the skull and has a homogeneous tissues density throughout
resulting in no variation of the gradient intensities, the brain atrophy is at
the rim of the right frontal lobe of the skull where the variation of gradient
intensities is almost stagnant. Consequently, the most crucial factor in these
features (iii) and (iv) is the time crossing map, which is set at 0.125 due to
the coil rotation inside the CT scanner.
The fast marching level set segmentation is deduced to
be the most appropriate feature
extraction for the extracranial haematoma and the brain atropy.
The extracranial haematoma is homogeneously
hyperdense, sharply marginated, and consists of solid blood clots found on the
outside border of the skull as referred to [18]. The pixel intensities within this feature are
constant throughout. So, the gradient magnitude intensities computed do not
vary though the σ values are within a range of 0.0005 to 0.325,
the α values are within a range of −0.0005 to
−0.575, and the β values are within a range of 0.0005 to 4.00.
This implies that the sigmoid member class filter has no effect on the time
solution surface Γ which is the zero level set representing the
contour of the feature. The TimeStep of the scanner set at 0.125 and the number
of iterations are crucial parameters to seek the proper edge of the feature.Table 1
Internal constraints for fast marching level sets.
Fast marchingSigma0.0005≤σ≤0.325Alpha−0.0005≥α≥−0.575Beta0.0005≤β≤4.00(A, E, I, M)α=−0.0005,β=0.0005,sigma=0.0005, (B, F, J, N) α=−0.0015,beta=0.0025,σ=0.0125, (C, G, K, O) α=−0.375,β=0.2255,σ=0.0225, (D, H, L, P) α=−0.575,β=4.00,σ=0.0325 are (i) values set for subdural haematoma,
(ii) contrecoup contusion, (iii) extracranial haematoma, and (iv) brain atrophy
by fast marching.Threshold Approach
A range of intensity values are defined for the
feature in the threshold level set segmentation. A propagation term is applied
on the level set equation for the intensity range as referred to [16] and illustrated in Figure  2.
The initial
level set generates the distance map, and a distance function is computed by
applying the lower and upper threshold. In case, the lower threshold is less
than 150, as referred to in Table2, and the higher threshold is greater than
205, the range of intensities for the feature does not determine an initial
surface for the gradient flow resulting in no segmentation.
Values below 4
or greater than 7 for the distance map result in a reduction or expansion of
the initial contour, the zero level set of the feature as the surrounding
region is white matter of homogeneous tissues density. There is very slight change of segmented feature as
illustrated in Figures2(U), 2(V),
2(W), 2(X) and Figures 2(Y), 2(Z), 2(A1), 2(B1) by applying the range of 4 to 7
for the distance map.
The threshold level set segmentation is the
appropriate procedure for segmenting the subdural haematoma and the
nonhemorrhagic contusion.
Since the subdural haematoma is in an acute stage, it
is hyperdense because of the attenuating properties of the haemoglobin
molecules found in the blood clots. The stage of density takes weeks before
being isodense. The lower and upper limits of the thresholds are set at 140 and
205 so as to consider only gradient magnitude intensities within the feature
forbidding surrounding regions which can be hypodense or isodense. By lowering
the limit of the threshold, lower gradient magnitude densities are acquired for
which the distance function does not clearly mark the edge of the feature. The
hyperdense area of the feature can be clearly demarcated by the proper
threshold setting. When the  threshold is increased  to the corresponding gradient magnitude densities applied to the distance function,  a proper segmented feature is obtained without any distortion of the initial
surface of the zero level set.
Whilst the nonhemorrhagic contrecoup contusion is an
area of higher densities of tissues sorrounded by  areas of lower densities  of tissues, the varying range of the minimum and maximum of
the threshold values is adjust to the varying range of gradient magnitude
densities. Consequently, the initial zero level set surface is computed by the
adjustments of the corresponding densities and distance map resulting in a
proper feature extraction.Table 2
Internal constraints for threshold level sets.
Threshold level setInitial distance4≤ initial distance ≤ 7Lower threshold150≤ lower ≤ 175Upper threshold175≤ upper ≤ 205(U, Y)distance=4,lower=150,upper=175, (V, Z) distance=5,lower=155,upper=185, (W, A1) distance=6,lower=160,upper=195, (X, B1) distance=7,lower=175,upper=205 are (vi) values set for the subdural haematoma
and (vii) contrecoup contusion by threshold approach.Shape Detection Approach
Finally in the shape detection level set segmentation
method, fast marching level set segmentation is used to define the initial
level set based upon a distance map as referred to [16].
Though a wide range of parameter values are set for
this approach, no exact segmented feature is obtained, as referred to in Table3. The relative weightings of the propagation and curvature terms between these
two parameters do not adjust to produce the shape boundaries of the feature. Consequently,
zero level set leaks may have been produced through the feature's regions of
low gradient along the boundaries of the pathological feature itself as
illustrated in Figures 3(C1), 3(D1), 3(E10), 3(F1) and Figures
3(G1), 3(H1), 3(I1), 3(J1).Table 3
Internal constraints for shape detection level sets.
Shape detectionInitial distance3≤ initial distance ≤9Sigma0.45≤σ≤1.1Alpha−0.25 ≥α≥−0.55Beta1.85≤β≤3.25Propagation scaling0.005≤ propagation ≤ 0.07Curvature scaling0.9≤ curvature ≤ 1.5Table 4
Internal constraints for watershed.
WatershedConductante term2≤ conductance ≤ 7Iterations10≤ iterations ≤ 20Lowerthreshold0.001≤ Threshold ≤ 0.1Output scale level0.15≤ Scale level ≤ 0.30(C1, G1) distance=3,α=−0.25,σ=0.45,β=1.85,
propagation
=0.005,curvature=0.9,(D1,H1)distance=5,α=−0.35,σ=0.65,β=2.15,propagation=0.035,curvature=1.1,(E1,I1)distance=7,α=−0.45,σ=0.95,β=2.9,propagation=0.05,curvature=1.3,(F1,J1)distance=9,α=−0.55,σ=1.1,β=3.25,propagation=0.07,curvature=1.5 are values set for (viii) the contrecoup
contusion and (ix) subdural haematoma by shape detection approach.


### 3.1.2. Watershed

As described in
the work of Grau et al. [19], and the excellent review of Roerdink and Meijster [20], the method is based on the
topographical distance applied on these discrete two-dimensional medical images
where basically the algorithmic representation is used.Two important parameters, threshold and level control
the output of this watershed segmentation, as referred to in Table5. The
purpose of the threshold parameter is to set the absolute minimum height value.
The level parameter controls the depth of metaphorical flooding of the image.
Raising and lowering the level influence the number of segments in the basic
segmentation that are merged to produce the final output. A level of 1.0 is
analogous to flooding the image up to a depth that is 100 percent of the
maximum value in the image. Level values of interest are typically low as
illustrated in Figure 4, that is, less than about 0.40 since higher
values will quickly undersegment the image.Table 5
Internal constraints for region growing.
Confidence connectedMultiplier0.05≤ multiplier ≤ 2.5Connected thresholdLower threshold150≤ lower ≤ 175Upper threshold175≤ upper ≤ 205NeighbourhoodLower threshold140≤ lower ≤ 175Upper threshold170≤ upper ≤ 205(column
K1) Values set for the subdural hygroma(x) are conductance=2.5,iterations=11,lower=0.015,scalelevel=0.15 by watershed approach.The threshold parameter cannot exceed the value of 0.1
as illustrated in Figure4(K1) to represent the gradient magnitude of
intensities which are a percentage of the maximum depth of the feature so as to
avoid oversegmentation.


### 3.1.3. Region Growing

In this
approach, a seed is selected from the data set manually, and the algorithm
engulfs the relevant region up to its boundary using some connectedness
approach to the surrounding pixels as referred to [16]. Basically, the algorithmic
representation of the region growing procedure is used for the confidence
connected, connected threshold, and neighbourhood approaches.The NumberOfIterations and TimeStep which are set as
default values of 5 and 0.125 for 2D images, as referred to in Table6. The
itkConfidenceConnectedImageFilter class is used for the segmentation itself.
This requires the definition of two parameters. The factor f which determines the extent of the range of intensities
and the number of iterations specifies the homogeneity of the structure to be
segmented. In this context, the multiplier factor is more important than the
number of iterations, to avoid the region to engulf the entire image as
illustrated in Figure 5(L1).Table 6
Tables of required constraints for contour extraction of pathological features.
Computational pipelineConductante term2Iterations10Lower threshold0.05Output scale level0.15Domain sigma0.015Range sigma0.85Time step0.125(L1)multiplier=2.5, (M1) multiplier=2.0, (N1) multiplier=1.5, (O1) multiplier=1.0, (P1) lower=140,upper=170, (Q1) lower=150,upper=180, (R1) lower=155,upper=190, (S1) lower=160,upper=195 are (xi) values set for the contrecoup
contusion by confidence connected, for (xii) contrecoup contusion by
neighbourhood connected.The range of
values for the lower threshold and upper threshold varies between the minimum
of 140 and maximum of 205. This allows for the usage of various pixel
intensities to be identified for the computation of the gradient magnitude
intensities due to its sensitivity to thresholds. As illustrated in Figure5(P1), a minimum value of threshold 140 and maximum value of threshold 170 show
a compression of the segmented feature, and the most exact representation of
the segmented feature is illustrated in Figure 5(Q1) with a minimum of 150 and
maximum of 180. No segmented feature expansion is obtained through this range,
but still a compressed segmented feature is obtained with the minimum of 160
and maximum of 195 as illustrated in Figure 5(S1).The nonhemorrhagic contusion is well segmented by the
neighbourhood connected threshold approach. The varying range of minimum and
maximum values of threshold of 140 and 205 allows the neighbouring filter to
consider neighbouring pixels intensities instead of only the current pixel
intensity. This is done by also accepting or rejecting small structures found
inside or outside the lesion. Since the lesion is heterogeneous, the
structuring element of the feature is well surrounded by the exact evaluation
of gradient magnitude densities resulting in the exact segmented feature.


## 3.1.1. Level Sets

Based upon the excellent review of Osher and Fedkiw [17] on level sets,
the surface Γ is represented as the zero isocontour of a
scalar function (x),
that is, (1)Γ=x:ϕ(x)=0, which represents the curve or boundary of the feature.The various  approaches such as fast marching,
threshold, and shape detection use basically the algorithmic representation of
the level set procedure as described in Algorithm1.Algorithm 1:Algorithmic representation of level
sets procedure.
for each pixel value from seed
points,extract sigmoid function and
propagation term.for each image intensity,apply edge filter,provide threshold,adjust intensity scaling.Algorithm 2:Algorithmic representation of
watershed procedure.
define a slope for each pixelfor each pixel value,calculate topographical distanceestimate gradient for gray-level
values.for each image gradient threshold
identification,perform edge-preserving,represent gradient magnitude,generate merge tree,access segmented image,acquire segmentation tree.Algorithm 3:Algorithmic representation of region
growing procedure.
for each pixel value from seed
points,apply edge-preserving,instantiate smoothing,assign pointer for smoothing and
edge-preserving.Fast Marching Approach
The FastMarchingImageFilter is used in the
Reinitialize LevelSetImageFilter object to create a signed distance function
from the zero level set as referred to [16].
The lower threshold is set to a default value of 0.0
and the upper threshold defines the time snapshot which is taken from the time
crossing map which is set to 85. The CurvatureAnisotropicDiffusionImageFilter
requires TimeStep, NumberOfIterations, and ConductanceParameter are set as
0.125, 5, and 9 so as to detect the boundary of the structures. The
SigmoidImageFilter class requires two parameters, alpha and beta, to define the
linear transformation to the sigmoid argument as illustrated in Figures1(E),
1(F), 1(G), 1(H) or reduction at edges as illustrated in Figures 1(A), 1(B),
1(C), 1(D).
By increasing the value ofβ to 4.00 and decreasing the value α to −0.575 as referred to in Table 1, the size
of the feature gets smaller as illustrated in Figures 1(A), 1(B), 1(C), 1(D)
and expands in Figures 1(E), 1(F), 1(G), 1(H). The shape of the feature gets
distorted as the value of σ increases to 0.325. The threshold is generated
to the time crossing map so as to build the time solution surface Γ of the white matter one grid point at a time
where the feature is situated. Though the time is found for one grid point, but
gets distorted for other nearby values in the features of Figures 1(i) and 1(ii).
The features of Figures1(iii) and 1(iv) as mentioned
in Table 1 show no variation during segmentation by decreasing or increasing
the values of the constraints. The edges of the segmented features as
illustrated in Figures 1(I), 1(J), 1(K), 1(L) are almost identical.  Figures 1(M), 1(N), 1(O),
1(P) illustrate almost identical features. Since the extracranial
haematoma is outside the skull and has a homogeneous tissues density throughout
resulting in no variation of the gradient intensities, the brain atrophy is at
the rim of the right frontal lobe of the skull where the variation of gradient
intensities is almost stagnant. Consequently, the most crucial factor in these
features (iii) and (iv) is the time crossing map, which is set at 0.125 due to
the coil rotation inside the CT scanner.
The fast marching level set segmentation is deduced to
be the most appropriate feature
extraction for the extracranial haematoma and the brain atropy.
The extracranial haematoma is homogeneously
hyperdense, sharply marginated, and consists of solid blood clots found on the
outside border of the skull as referred to [18]. The pixel intensities within this feature are
constant throughout. So, the gradient magnitude intensities computed do not
vary though the σ values are within a range of 0.0005 to 0.325,
the α values are within a range of −0.0005 to
−0.575, and the β values are within a range of 0.0005 to 4.00.
This implies that the sigmoid member class filter has no effect on the time
solution surface Γ which is the zero level set representing the
contour of the feature. The TimeStep of the scanner set at 0.125 and the number
of iterations are crucial parameters to seek the proper edge of the feature.Table 1
Internal constraints for fast marching level sets.
Fast marchingSigma0.0005≤σ≤0.325Alpha−0.0005≥α≥−0.575Beta0.0005≤β≤4.00(A, E, I, M)α=−0.0005,β=0.0005,sigma=0.0005, (B, F, J, N) α=−0.0015,beta=0.0025,σ=0.0125, (C, G, K, O) α=−0.375,β=0.2255,σ=0.0225, (D, H, L, P) α=−0.575,β=4.00,σ=0.0325 are (i) values set for subdural haematoma,
(ii) contrecoup contusion, (iii) extracranial haematoma, and (iv) brain atrophy
by fast marching.Threshold Approach
A range of intensity values are defined for the
feature in the threshold level set segmentation. A propagation term is applied
on the level set equation for the intensity range as referred to [16] and illustrated in Figure  2.
The initial
level set generates the distance map, and a distance function is computed by
applying the lower and upper threshold. In case, the lower threshold is less
than 150, as referred to in Table2, and the higher threshold is greater than
205, the range of intensities for the feature does not determine an initial
surface for the gradient flow resulting in no segmentation.
Values below 4
or greater than 7 for the distance map result in a reduction or expansion of
the initial contour, the zero level set of the feature as the surrounding
region is white matter of homogeneous tissues density. There is very slight change of segmented feature as
illustrated in Figures2(U), 2(V),
2(W), 2(X) and Figures 2(Y), 2(Z), 2(A1), 2(B1) by applying the range of 4 to 7
for the distance map.
The threshold level set segmentation is the
appropriate procedure for segmenting the subdural haematoma and the
nonhemorrhagic contusion.
Since the subdural haematoma is in an acute stage, it
is hyperdense because of the attenuating properties of the haemoglobin
molecules found in the blood clots. The stage of density takes weeks before
being isodense. The lower and upper limits of the thresholds are set at 140 and
205 so as to consider only gradient magnitude intensities within the feature
forbidding surrounding regions which can be hypodense or isodense. By lowering
the limit of the threshold, lower gradient magnitude densities are acquired for
which the distance function does not clearly mark the edge of the feature. The
hyperdense area of the feature can be clearly demarcated by the proper
threshold setting. When the  threshold is increased  to the corresponding gradient magnitude densities applied to the distance function,  a proper segmented feature is obtained without any distortion of the initial
surface of the zero level set.
Whilst the nonhemorrhagic contrecoup contusion is an
area of higher densities of tissues sorrounded by  areas of lower densities  of tissues, the varying range of the minimum and maximum of
the threshold values is adjust to the varying range of gradient magnitude
densities. Consequently, the initial zero level set surface is computed by the
adjustments of the corresponding densities and distance map resulting in a
proper feature extraction.Table 2
Internal constraints for threshold level sets.
Threshold level setInitial distance4≤ initial distance ≤ 7Lower threshold150≤ lower ≤ 175Upper threshold175≤ upper ≤ 205(U, Y)distance=4,lower=150,upper=175, (V, Z) distance=5,lower=155,upper=185, (W, A1) distance=6,lower=160,upper=195, (X, B1) distance=7,lower=175,upper=205 are (vi) values set for the subdural haematoma
and (vii) contrecoup contusion by threshold approach.Shape Detection Approach
Finally in the shape detection level set segmentation
method, fast marching level set segmentation is used to define the initial
level set based upon a distance map as referred to [16].
Though a wide range of parameter values are set for
this approach, no exact segmented feature is obtained, as referred to in Table3. The relative weightings of the propagation and curvature terms between these
two parameters do not adjust to produce the shape boundaries of the feature. Consequently,
zero level set leaks may have been produced through the feature's regions of
low gradient along the boundaries of the pathological feature itself as
illustrated in Figures 3(C1), 3(D1), 3(E10), 3(F1) and Figures
3(G1), 3(H1), 3(I1), 3(J1).Table 3
Internal constraints for shape detection level sets.
Shape detectionInitial distance3≤ initial distance ≤9Sigma0.45≤σ≤1.1Alpha−0.25 ≥α≥−0.55Beta1.85≤β≤3.25Propagation scaling0.005≤ propagation ≤ 0.07Curvature scaling0.9≤ curvature ≤ 1.5Table 4
Internal constraints for watershed.
WatershedConductante term2≤ conductance ≤ 7Iterations10≤ iterations ≤ 20Lowerthreshold0.001≤ Threshold ≤ 0.1Output scale level0.15≤ Scale level ≤ 0.30(C1, G1) distance=3,α=−0.25,σ=0.45,β=1.85,
propagation
=0.005,curvature=0.9,(D1,H1)distance=5,α=−0.35,σ=0.65,β=2.15,propagation=0.035,curvature=1.1,(E1,I1)distance=7,α=−0.45,σ=0.95,β=2.9,propagation=0.05,curvature=1.3,(F1,J1)distance=9,α=−0.55,σ=1.1,β=3.25,propagation=0.07,curvature=1.5 are values set for (viii) the contrecoup
contusion and (ix) subdural haematoma by shape detection approach.


## 3.1.2. Watershed

As described in
the work of Grau et al. [19], and the excellent review of Roerdink and Meijster [20], the method is based on the
topographical distance applied on these discrete two-dimensional medical images
where basically the algorithmic representation is used.Two important parameters, threshold and level control
the output of this watershed segmentation, as referred to in Table5. The
purpose of the threshold parameter is to set the absolute minimum height value.
The level parameter controls the depth of metaphorical flooding of the image.
Raising and lowering the level influence the number of segments in the basic
segmentation that are merged to produce the final output. A level of 1.0 is
analogous to flooding the image up to a depth that is 100 percent of the
maximum value in the image. Level values of interest are typically low as
illustrated in Figure 4, that is, less than about 0.40 since higher
values will quickly undersegment the image.Table 5
Internal constraints for region growing.
Confidence connectedMultiplier0.05≤ multiplier ≤ 2.5Connected thresholdLower threshold150≤ lower ≤ 175Upper threshold175≤ upper ≤ 205NeighbourhoodLower threshold140≤ lower ≤ 175Upper threshold170≤ upper ≤ 205(column
K1) Values set for the subdural hygroma(x) are conductance=2.5,iterations=11,lower=0.015,scalelevel=0.15 by watershed approach.The threshold parameter cannot exceed the value of 0.1
as illustrated in Figure4(K1) to represent the gradient magnitude of
intensities which are a percentage of the maximum depth of the feature so as to
avoid oversegmentation.


## 3.1.3. Region Growing

In this
approach, a seed is selected from the data set manually, and the algorithm
engulfs the relevant region up to its boundary using some connectedness
approach to the surrounding pixels as referred to [16]. Basically, the algorithmic
representation of the region growing procedure is used for the confidence
connected, connected threshold, and neighbourhood approaches.The NumberOfIterations and TimeStep which are set as
default values of 5 and 0.125 for 2D images, as referred to in Table6. The
itkConfidenceConnectedImageFilter class is used for the segmentation itself.
This requires the definition of two parameters. The factor f which determines the extent of the range of intensities
and the number of iterations specifies the homogeneity of the structure to be
segmented. In this context, the multiplier factor is more important than the
number of iterations, to avoid the region to engulf the entire image as
illustrated in Figure 5(L1).Table 6
Tables of required constraints for contour extraction of pathological features.
Computational pipelineConductante term2Iterations10Lower threshold0.05Output scale level0.15Domain sigma0.015Range sigma0.85Time step0.125(L1)multiplier=2.5, (M1) multiplier=2.0, (N1) multiplier=1.5, (O1) multiplier=1.0, (P1) lower=140,upper=170, (Q1) lower=150,upper=180, (R1) lower=155,upper=190, (S1) lower=160,upper=195 are (xi) values set for the contrecoup
contusion by confidence connected, for (xii) contrecoup contusion by
neighbourhood connected.The range of
values for the lower threshold and upper threshold varies between the minimum
of 140 and maximum of 205. This allows for the usage of various pixel
intensities to be identified for the computation of the gradient magnitude
intensities due to its sensitivity to thresholds. As illustrated in Figure5(P1), a minimum value of threshold 140 and maximum value of threshold 170 show
a compression of the segmented feature, and the most exact representation of
the segmented feature is illustrated in Figure 5(Q1) with a minimum of 150 and
maximum of 180. No segmented feature expansion is obtained through this range,
but still a compressed segmented feature is obtained with the minimum of 160
and maximum of 195 as illustrated in Figure 5(S1).The nonhemorrhagic contusion is well segmented by the
neighbourhood connected threshold approach. The varying range of minimum and
maximum values of threshold of 140 and 205 allows the neighbouring filter to
consider neighbouring pixels intensities instead of only the current pixel
intensity. This is done by also accepting or rejecting small structures found
inside or outside the lesion. Since the lesion is heterogeneous, the
structuring element of the feature is well surrounded by the exact evaluation
of gradient magnitude densities resulting in the exact segmented feature.


## 3.2. Constraints

The influence
of each constraint has a direct impact on each lesion type, which is the most
crucial part of the work undertaken. The segmented lesions types vary
differently or constantly depending upon the range of the applied constraint.
These variations are also assessed by the numerical evaluations and comparisons
of the results.


### 3.2.1. Numerical Constraints Evaluations

Herewith is the
sets of constraints associated to the segmented lesion types after segmentation
process.The Sigma Constraint
The sigma “σ” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value.
Two ranges of values such as0.0005≤σ≤0.325 and 0.45 ≤σ≤ 1.1 have been experimented. Negative and null
values are forbidden resulting in leakages at the edges of the feature since
the pixel type is of unsigned short type. Values less than 0.0005 result in
expansion and values greater than 1.1 result in reduction of the segmented
feature. According to Figure 1, the most appropriate result for the segmented
feature lies in columns (B, F, J, N) and (C, G, K, O) within a range of 0.0125 to
0.0225.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is 0.0100 which
explains the closeness and narrowness of the lesion to an edge.The Alpha Constraint
The alpha “α” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma, and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value till a
threshold is applied to a time crossing map to the white matter.
Two ranges of values such as−0.0005≤α≤−0.575 and  −0.25≤α≤−0.55 have been experimented. Negative and
null values are used according to the requirements though the pixel is of
unsigned short type. Values less than −0.0005 result in expansion, and values
greater than −0.55 result in reduction of the segmented feature. According to
Figure 1, the most appropriate result for the segmented feature lies in columns
(B, F, J, N) and (C, G, K, O) within a range of −0.0015 to −0.375.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is −0.360 which
explains the closeness and narrowness of the lesion to an edge.The Beta Constraint
The beta “β” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma, and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value.
Two ranges of values such as0.0005≤β≤4.00 and 1.85≤β≤3.2 have been experimented. Negative and null
values are forbidden resulting in leakages at the edges of the feature since
the pixel type is of unsigned short type. Values less than 0.0005 result in
expansion, and values greater than 4.00 result in reduction of the segmented
feature. According to Figure 1, the most appropriate result for the segmented
feature lies in columns (B, F, J, N) and (C, G, K, O) within a range of 0.0025 to
0.2255.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is 0.2230 which
explains the closeness and narrowness of the lesion to an edge.The Distance Constraint
The initial distance “initial distance” constraint is
efficient for the segmentation of the subdural haematoma and nonhemorrhagic
contrecoup contusion. The initial distance is the distance between the initial
surface and the boundary of the feature which is assigned a numerical value.
Two ranges of values such as 4≤ initial distance ≤ 7 and 3 ≤ initial distance ≤ 9 have been experimented. Negative and null
values are forbidden because this constraint is a crucial requirement to locate
the lesion. Values less than 3 result in expansion, and values greater than 9
result in reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 6 to 7.
As illustrated in Figure2, these two lesion types are
located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 1 which explains the closeness and narrowness of the lesion
to an edge.The Lower Threshold Constraint
The lower threshold “lower” constraint is efficient
for the segmentation of the subdural haematoma, and nonhemorrhagic contrecoup
contusion has been experimented. The lower threshold accesses current pixel
intensities within the feature.
The ranges of values such as 150≤ lower ≤ 175 and 140 ≤ lower ≤ 175 have been experimented. Negative and null
values are forbidden because if not the feature will not be selected at all.
Values less than 150 result in expansion, and values greater than 175 result in
reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 160 and 175.
As illustrated in Figure2, these two lesions types
are located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 15, which explains the closeness and narrowness of the
lesion to an edge.The Upper Threshold Constraint
The upper threshold “upper” constraint is efficient
for the segmentation of the brain atrophy, extracranial haematoma, subdural
haematoma and nonhemorrhagic contrecoup contusion. The upper threshold
accesses neighbouring pixel intensities of similar intensities within the
feature.
Two ranges of values such as 175≤ upper ≤ 205 and 170 ≤ upper ≤ 205 have been experimented. Negative and null
values are forbidden because if not the feature won't be selected at all.
Values less than 140 result in expansion, and values greater than 175 result in
reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 195 to 205.
As illustrated in Figure2, these two lesions types are
located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 10 which explains the closeness and narrowness of the
lesion to an edge.The Conductance Constraint
The conductance constraint is efficient for the
segmentation of the subdural hygroma. This constraint helps for a proper
definition of the boundary of the lesion.
The range of values such as 2≤ conductance ≤ 7 has been experimented. Negative and null
values are forbidden because if not the feature's boundary will not be selected
at all. Values less than 2 result in undersegmentation, and values greater than
7 result in oversegmentation of the feature. According to Figure 4, the most
appropriate result for the segmented feature lies in column (K1) with a value
of 2.5.The Iterations Constraint
The iterations constraint is efficient for the
segmentation of the brain atrophy, extracranial haematoma, subdural haematoma,
and nonhemorrhagic contrecoup contusion. This constraint determines the mean
and standard variance of the neighbouring pixels to be calculated and
consequently the number of times to repeat the segmentation.
The range of values such as 10≤ iterations ≤ 20 has been experimented. Negative and null
values are forbidden so as to obtain the best segmentation result. Values less
than 0.0005 result in expansion, and values greater than 4.00 result in
reduction of the segmented feature.


### 3.2.2. Comparison of Various Results for Constraints Evaluations

(i) The Sigma Constraint
These values 0.0005, 0.0125, 0.0225, and 0.0325 are
illustrated in Figure1, and these values 0.45, 0.65, 0.95, and 1.1 are
illustrated in Figure 3.(ii) The Alpha Constraint
These values−0.0005, −0.0015, −0.375, and −0.575 are
illustrated in Figure 1, and these values −0.25, −0.35, −0.45, and  −0.55 are
illustrated in Figure 3.(iii) The Beta Constraint
These values 0.0005, 0.0025, 0.2255, and 4.00 are
illustrated in Figure1, and these values 1.85, 2.15, 2.9, and 3.25 are
illustrated in Figure 3.(iv) The Initial Distance Constraint
These values 4, 5, 6, and 7 are illustrated in Figure2, and these values 3, 5, 7, and 9 are illustrated in Figure 3.(v) The Lower Threshold Constraint
These values 150, 155, 160, 175 are illustrated in
Figure2, and these values 140, 150, 155, 160 are illustrated in Figure 5.(vi) The Upper Threshold Constraint
These values 175, 185, 195, 205 are illustrated in
Figure2, and these values 170, 180, 190, 195 are illustrated in Figure 5.


### 3.2.3. Requirements

The traumatic
brain injuries segmented are brain atrophy, subdural hygroma, subdural
haematoma, nonhemorrhagic contrecoup contusion, and extracranial haematoma
obtained from a set of 5 patients.These axial CT scans obtained from Centre Hospitalier
De Bayonne are of dimension512×512 and thickness 2.5 mm varying in between 38
to 182 slices effected from different medical practitioners which have been
converted into 256×256. These slices show varying levels of intensities
depending on the intra and intervisual perception of these practitioners.Before segmentation proceeds, these images are
preprocessed by the bilateral image filter which is an edge preserving
smoothing filter. Smoothing is performed by using domain and range
neighbourhoods. Pixels that are close to a pixel in the image domain and
similar to a pixel in the image range are used to calculate the filtered value
as referred to Tomasi and Manduchi [21].


## 3.2.1. Numerical Constraints Evaluations

Herewith is the
sets of constraints associated to the segmented lesion types after segmentation
process.The Sigma Constraint
The sigma “σ” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value.
Two ranges of values such as0.0005≤σ≤0.325 and 0.45 ≤σ≤ 1.1 have been experimented. Negative and null
values are forbidden resulting in leakages at the edges of the feature since
the pixel type is of unsigned short type. Values less than 0.0005 result in
expansion and values greater than 1.1 result in reduction of the segmented
feature. According to Figure 1, the most appropriate result for the segmented
feature lies in columns (B, F, J, N) and (C, G, K, O) within a range of 0.0125 to
0.0225.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is 0.0100 which
explains the closeness and narrowness of the lesion to an edge.The Alpha Constraint
The alpha “α” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma, and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value till a
threshold is applied to a time crossing map to the white matter.
Two ranges of values such as−0.0005≤α≤−0.575 and  −0.25≤α≤−0.55 have been experimented. Negative and
null values are used according to the requirements though the pixel is of
unsigned short type. Values less than −0.0005 result in expansion, and values
greater than −0.55 result in reduction of the segmented feature. According to
Figure 1, the most appropriate result for the segmented feature lies in columns
(B, F, J, N) and (C, G, K, O) within a range of −0.0015 to −0.375.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is −0.360 which
explains the closeness and narrowness of the lesion to an edge.The Beta Constraint
The beta “β” constraint is efficient for the segmentation
of the brain atrophy, extracranial haematoma, subdural haematoma, and
nonhemorrhagic contrecoup contusion. The edge of the segmented feature is kept
linearly constant by the proper assignment of its numerical value.
Two ranges of values such as0.0005≤β≤4.00 and 1.85≤β≤3.2 have been experimented. Negative and null
values are forbidden resulting in leakages at the edges of the feature since
the pixel type is of unsigned short type. Values less than 0.0005 result in
expansion, and values greater than 4.00 result in reduction of the segmented
feature. According to Figure 1, the most appropriate result for the segmented
feature lies in columns (B, F, J, N) and (C, G, K, O) within a range of 0.0025 to
0.2255.
As illustrated in Figure1, these four lesions types
are located either at the rim of the dura matter or just at the outline of the
bone skull with a slight varying range of pixels intensities within each lesion
type. The very slight range for an efficient segmented lesion is 0.2230 which
explains the closeness and narrowness of the lesion to an edge.The Distance Constraint
The initial distance “initial distance” constraint is
efficient for the segmentation of the subdural haematoma and nonhemorrhagic
contrecoup contusion. The initial distance is the distance between the initial
surface and the boundary of the feature which is assigned a numerical value.
Two ranges of values such as 4≤ initial distance ≤ 7 and 3 ≤ initial distance ≤ 9 have been experimented. Negative and null
values are forbidden because this constraint is a crucial requirement to locate
the lesion. Values less than 3 result in expansion, and values greater than 9
result in reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 6 to 7.
As illustrated in Figure2, these two lesion types are
located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 1 which explains the closeness and narrowness of the lesion
to an edge.The Lower Threshold Constraint
The lower threshold “lower” constraint is efficient
for the segmentation of the subdural haematoma, and nonhemorrhagic contrecoup
contusion has been experimented. The lower threshold accesses current pixel
intensities within the feature.
The ranges of values such as 150≤ lower ≤ 175 and 140 ≤ lower ≤ 175 have been experimented. Negative and null
values are forbidden because if not the feature will not be selected at all.
Values less than 150 result in expansion, and values greater than 175 result in
reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 160 and 175.
As illustrated in Figure2, these two lesions types
are located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 15, which explains the closeness and narrowness of the
lesion to an edge.The Upper Threshold Constraint
The upper threshold “upper” constraint is efficient
for the segmentation of the brain atrophy, extracranial haematoma, subdural
haematoma and nonhemorrhagic contrecoup contusion. The upper threshold
accesses neighbouring pixel intensities of similar intensities within the
feature.
Two ranges of values such as 175≤ upper ≤ 205 and 170 ≤ upper ≤ 205 have been experimented. Negative and null
values are forbidden because if not the feature won't be selected at all.
Values less than 140 result in expansion, and values greater than 175 result in
reduction of the segmented feature. According to Figure 2, the most appropriate
result for the segmented feature lies in columns (W, A1) and (X, B1) within a
range of 195 to 205.
As illustrated in Figure2, these two lesions types are
located at the rim of the dura matter with a slight varying range of pixels
intensities within each lesion type. The very slight range for an efficient
segmented lesion is 10 which explains the closeness and narrowness of the
lesion to an edge.The Conductance Constraint
The conductance constraint is efficient for the
segmentation of the subdural hygroma. This constraint helps for a proper
definition of the boundary of the lesion.
The range of values such as 2≤ conductance ≤ 7 has been experimented. Negative and null
values are forbidden because if not the feature's boundary will not be selected
at all. Values less than 2 result in undersegmentation, and values greater than
7 result in oversegmentation of the feature. According to Figure 4, the most
appropriate result for the segmented feature lies in column (K1) with a value
of 2.5.The Iterations Constraint
The iterations constraint is efficient for the
segmentation of the brain atrophy, extracranial haematoma, subdural haematoma,
and nonhemorrhagic contrecoup contusion. This constraint determines the mean
and standard variance of the neighbouring pixels to be calculated and
consequently the number of times to repeat the segmentation.
The range of values such as 10≤ iterations ≤ 20 has been experimented. Negative and null
values are forbidden so as to obtain the best segmentation result. Values less
than 0.0005 result in expansion, and values greater than 4.00 result in
reduction of the segmented feature.


## 3.2.2. Comparison of Various Results for Constraints Evaluations

(i) The Sigma Constraint
These values 0.0005, 0.0125, 0.0225, and 0.0325 are
illustrated in Figure1, and these values 0.45, 0.65, 0.95, and 1.1 are
illustrated in Figure 3.(ii) The Alpha Constraint
These values−0.0005, −0.0015, −0.375, and −0.575 are
illustrated in Figure 1, and these values −0.25, −0.35, −0.45, and  −0.55 are
illustrated in Figure 3.(iii) The Beta Constraint
These values 0.0005, 0.0025, 0.2255, and 4.00 are
illustrated in Figure1, and these values 1.85, 2.15, 2.9, and 3.25 are
illustrated in Figure 3.(iv) The Initial Distance Constraint
These values 4, 5, 6, and 7 are illustrated in Figure2, and these values 3, 5, 7, and 9 are illustrated in Figure 3.(v) The Lower Threshold Constraint
These values 150, 155, 160, 175 are illustrated in
Figure2, and these values 140, 150, 155, 160 are illustrated in Figure 5.(vi) The Upper Threshold Constraint
These values 175, 185, 195, 205 are illustrated in
Figure2, and these values 170, 180, 190, 195 are illustrated in Figure 5.


## 3.2.3. Requirements

The traumatic
brain injuries segmented are brain atrophy, subdural hygroma, subdural
haematoma, nonhemorrhagic contrecoup contusion, and extracranial haematoma
obtained from a set of 5 patients.These axial CT scans obtained from Centre Hospitalier
De Bayonne are of dimension512×512 and thickness 2.5 mm varying in between 38
to 182 slices effected from different medical practitioners which have been
converted into 256×256. These slices show varying levels of intensities
depending on the intra and intervisual perception of these practitioners.Before segmentation proceeds, these images are
preprocessed by the bilateral image filter which is an edge preserving
smoothing filter. Smoothing is performed by using domain and range
neighbourhoods. Pixels that are close to a pixel in the image domain and
similar to a pixel in the image range are used to calculate the filtered value
as referred to Tomasi and Manduchi [21].


## 4. Contour Extraction

In our
approach, the contour is a feature tracking of the lesions as referred to
Loncaric et al., Deriche, and Roover et al. [22–24]. CT scans have a static scalar field of vision as
mentioned in Sohn and Bajaj [25]. Diffusion properties have been applied in our
computational pipeline preceded by smoothing and edge-preserving from a
bilateral filter using open-source software insight Toolkit (ITK) [16]. The diffusion data
enhances the properties of the components in these CT  scan images as mentioned in
Breen et al. [26] and Straka et al.  [26, 27]. The gradient magnitude of the diffusion anisotropy is
analysed by the watershed transform by graphing a function to create the merge
tree. The gradient magnitude of the watershed pixels is transformed into the
gradient magnitude of the diffusion anisotropy.Mathematical morphology grayscale operators such as
dilation and erosion use the merge tree of these connected flood levels of
varying values. Each intersection node of the connected flood levels is used to
create a graph. The higher values of the flood levels receive the maximum
values of the dilation operator as referred to the work of Droogenbroeck [28], Droogenbroeck and Talbot [29], and   Vardavoulia et al. [30] and the lower values of the flood levels receive the
minimum values of the erosion operator. The nodes connect the intersection
points which are linked so as to represent the contours corresponding to their
features. Finally, some smoothing   has been  performed in a viewer for
edge-preserving of the eroded output images.


### 4.1. Methodology

After the raw
CT scans are preprocessed by the bilateral filter. Theh(x) components of the output image move to the
gradient anisotropic diffusion image filter. The anisotropic diffusion measures
the diffusion properties of the water molecules in the cerebral tissues C where D is the diffusion coefficient: (2)δCδt=∇⋅(D∇C),D=(DxxDxyDyxDyy). The invariants are the
eigenvalues of diffusion D which are the roots of corresponding characteristic: (3)λ3−C1⋅λ2+C2⋅λ−C3=0, with coefficients (4)C1=λ1+λ2+λ3,C2=λ1λ2+λ1λ3+λ2λ3,C3=λ1λ2λ3, which are proportional to the
sum of the radii and surface area of the pathological feature. The data set is
described as (C1,C2,C3) since Ci are the coefficients of the characteristic
equation. Considering the dimensionless combination C1C2/C3,
it becomes (5)C1C2C3=3+λ2+λ3λ1+λ1+λ3λ2+λ1+λ2λ3, where a new dimensionless
anisotropy measure is defined as (6)Ca=16[C1C2C3−3] for a linear, directional diffusion (λ1≫λ2≈λ3) is equal to (7)Calimit≈13[1+λ1λ3+λ3λ1]. Thus, Ca is always ∼λmax/λmin and measures the gradient magnitude of the
diffusion anisotropy.The watershed transform is calculated on the absolute
value of the gradient with high values at features' contours. Calculation of
the watershed transform using arc weights in a graph allows the substitution of
the usual gradient estimation by absolute differences of gray level calculated
directionally during the flooding process to achieve a higher resolution. The
lower slope is redefined as(8)LS(p)=maxq∈NG(p)∪p(g(p,q)d(p,q)), where g(p,q) is a new function for the link (p,q).
An equivalent function is calculated for the lower neighbours from (9)Γ(p)={p′∈N(p)∣g(p,p′)=maxp′′∈NG(p)∪pg(p,p′′)}. This condition allows the use of the directional
diffusion anisotropy gradient magnitude value in substitution of the absolute
value of the gradient resulting in (10){p∈N,g(p,q)=g(p,Ci)}, where the neighbor space N is referred to as a set Z in which the component q of the function link is substituted by the
component Ci.The discrete morphological gradient is(11)δ(f)−ε(f). The erosion and dilation functions by a gray-scale
structuring element as referred to Droogenbroeck, and Darbon et
al. [28, 31], g:G→Z are applied to the new links {g(p,Ci)} such that (12)ε(f)=(f⊖g)(x), where (13)(f⊖g)(x)=miny∈G⁡{f(x+y)+g(y)},δ(f)=(f⊕g)(x), where (14)(f⊕g)(x)=maxy∈G,x−y∈F⁡{f(x−y)+g(y)}, respectively, where x,y∈Z2 are the spatial coordinates. F,G⊆Z2 are the domains of the grayscale image
(function) and grayscale structuring element.


### 4.2. Program Flowchart for Contour Extraction

Letf(x) be the original grayscale image defined in the
domain Di and let g(x) be the output image as illustrated in Figure 6.Program flowchart for contour extraction.
(a)(b)


### 4.3. Implementation and Results

The contour
extraction traced out the  exact feature as illustrated in
Figure7 and Table 6 of constraints.k-means classification.(T1) contour extraction of subdural
haematoma and nonhemorrhagic contusion (xiii), (U1) contour extraction of
subdural hygroma (xiv), slice 17, (V1) contour extraction of subdural hygroma (xv),
slice 15, (W1)contour extraction of subdural hygroma (xvi), slice 16, (X1) contour
extraction applied to brain atropy on left frontal lobe (xvii).


### 4.4. Reasons for Contour Extraction Technique Compared to Active Contour Model

The CT scans
are from an “8-barrette” CT scanner. The removal of noise and filtering
are a tedious task to get an optimized contrast of
these CT images.Since the active
econtour geodesic/geometric models as referred to the work of Yoon et al. [32]   are sensitive to these above fluctuations, the experimented technique has been implemented and
preferred to active contour model because of the varying strength of the edges
of these CT scans.The speed at which the contours have been extracted by
the experimented technique is fast compared to another model. Since the
calculation of the speed of convergence with active contour model will require
other parameters to be implemented.


## 4.1. Methodology

After the raw
CT scans are preprocessed by the bilateral filter. Theh(x) components of the output image move to the
gradient anisotropic diffusion image filter. The anisotropic diffusion measures
the diffusion properties of the water molecules in the cerebral tissues C where D is the diffusion coefficient: (2)δCδt=∇⋅(D∇C),D=(DxxDxyDyxDyy). The invariants are the
eigenvalues of diffusion D which are the roots of corresponding characteristic: (3)λ3−C1⋅λ2+C2⋅λ−C3=0, with coefficients (4)C1=λ1+λ2+λ3,C2=λ1λ2+λ1λ3+λ2λ3,C3=λ1λ2λ3, which are proportional to the
sum of the radii and surface area of the pathological feature. The data set is
described as (C1,C2,C3) since Ci are the coefficients of the characteristic
equation. Considering the dimensionless combination C1C2/C3,
it becomes (5)C1C2C3=3+λ2+λ3λ1+λ1+λ3λ2+λ1+λ2λ3, where a new dimensionless
anisotropy measure is defined as (6)Ca=16[C1C2C3−3] for a linear, directional diffusion (λ1≫λ2≈λ3) is equal to (7)Calimit≈13[1+λ1λ3+λ3λ1]. Thus, Ca is always ∼λmax/λmin and measures the gradient magnitude of the
diffusion anisotropy.The watershed transform is calculated on the absolute
value of the gradient with high values at features' contours. Calculation of
the watershed transform using arc weights in a graph allows the substitution of
the usual gradient estimation by absolute differences of gray level calculated
directionally during the flooding process to achieve a higher resolution. The
lower slope is redefined as(8)LS(p)=maxq∈NG(p)∪p(g(p,q)d(p,q)), where g(p,q) is a new function for the link (p,q).
An equivalent function is calculated for the lower neighbours from (9)Γ(p)={p′∈N(p)∣g(p,p′)=maxp′′∈NG(p)∪pg(p,p′′)}. This condition allows the use of the directional
diffusion anisotropy gradient magnitude value in substitution of the absolute
value of the gradient resulting in (10){p∈N,g(p,q)=g(p,Ci)}, where the neighbor space N is referred to as a set Z in which the component q of the function link is substituted by the
component Ci.The discrete morphological gradient is(11)δ(f)−ε(f). The erosion and dilation functions by a gray-scale
structuring element as referred to Droogenbroeck, and Darbon et
al. [28, 31], g:G→Z are applied to the new links {g(p,Ci)} such that (12)ε(f)=(f⊖g)(x), where (13)(f⊖g)(x)=miny∈G⁡{f(x+y)+g(y)},δ(f)=(f⊕g)(x), where (14)(f⊕g)(x)=maxy∈G,x−y∈F⁡{f(x−y)+g(y)}, respectively, where x,y∈Z2 are the spatial coordinates. F,G⊆Z2 are the domains of the grayscale image
(function) and grayscale structuring element.


## 4.2. Program Flowchart for Contour Extraction

Letf(x) be the original grayscale image defined in the
domain Di and let g(x) be the output image as illustrated in Figure 6.Program flowchart for contour extraction.
(a)(b)


## 4.3. Implementation and Results

The contour
extraction traced out the  exact feature as illustrated in
Figure7 and Table 6 of constraints.k-means classification.(T1) contour extraction of subdural
haematoma and nonhemorrhagic contusion (xiii), (U1) contour extraction of
subdural hygroma (xiv), slice 17, (V1) contour extraction of subdural hygroma (xv),
slice 15, (W1)contour extraction of subdural hygroma (xvi), slice 16, (X1) contour
extraction applied to brain atropy on left frontal lobe (xvii).


## 4.4. Reasons for Contour Extraction Technique Compared to Active Contour Model

The CT scans
are from an “8-barrette” CT scanner. The removal of noise and filtering
are a tedious task to get an optimized contrast of
these CT images.Since the active
econtour geodesic/geometric models as referred to the work of Yoon et al. [32]   are sensitive to these above fluctuations, the experimented technique has been implemented and
preferred to active contour model because of the varying strength of the edges
of these CT scans.The speed at which the contours have been extracted by
the experimented technique is fast compared to another model. Since the
calculation of the speed of convergence with active contour model will require
other parameters to be implemented.


## 5. Conclusions

We have presented a new methodology through the
gradient calculation for the feature sets further enhanced by
mathematical morphology grayscale operators. This computational pipeline technique is
applied to CT scan images illustrating a subdural haemorrhage, a nonhemorrhagic
contusion, a subdural hygroma, and a brain atrophy. In the case of the subdural
hygroma, this technique demonstrates similar or superior performance to manual
segmentation by experts. Without any doubt, the precision and accuracy of the
segmented features in the contour tracking are reliable for diagnostic or
presurgery purposes.The deductions of the particular pathological feature extraction by particular segmentation procedures are mostly relevant in the
selection process. The validation of the constraints settings of each
segmentation procedure based upon the particular characteristics of trauma
lesions is the determinant factors to be considered.Finally, the
substitution of one constituent of the link component in the gradient function
of the watershed transform in the computational pipeline by the constituent of
linear directional diffusion anisotropy gradient magnitude is one of the new
methodology brought forward. The classification of these lesions by pattern
recognition is tackled in another paper work.



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*Source: 759354-2008-10-27.xml*