3.4 Global Thresholding Techniques
3.4.2 Global Thresholding
3.4.2.3 Inverse Difference Moment (IDM)-Based Thresholding . 42
Image signal statistics, particularly first- and second-order statistics, are good tex- ture feature descriptors used for supervised segmentation techniques. Moments, first-
Figure 3.8: CLAHE and ISODATA thresholding technique with different filters. (a) DRIVE coloured retinal image.(b) DRIVE database gold standard image. (c) Seg- mented vessels using ISODATA threshold with Gaussian filter. (d) Segmented vessels using ISODATA threshold with average filter. (e) Segmented vessels using ISODATA threshold with adaptive filter. (f) Segmented vessels using ISODATA threshold with combination of average and Gaussian filters.
statistics such as grey level co-occurrence matrix (GLCM) are concerned with individual pixel properties as well as the spatial inter-dependency of the two pixels at particular relative positions.
GLCM is popularly known for its usage in texture image segmentation [168]. Har- alick features [168] computed from GLCM have been used for both supervised [169], [170] and unsupervised [171], [172], [173] [174] image segmentation techniques. Six of the features proposed by Haralick et. al.[168] were considered to be the most rel- evant [175]. The features considered are Energy (ENER), Entropy (ENT), Contrast (CONTR), Variance (VAR), Correlation (COR) and Inverse Difference Moment (IDM).
Some other unsupervised grey level co-occurrence based segmentation techniques have also been proposed in the literature [175], [176], [177].
Although IDM was originally used in [168] for supervised segmentation, this re- search utilises it for an unsupervised segmentation approach. The IDM texture infor-
mation applied in this research is computed using the GLCM of the grey scale of the retinal fundus image. Due to the large variation in the widths of the vessels [47], a multi-scale approach is adopted for the computation of a global threshold to segment the vessel network. The GLCM for the retinal fundus image is computed using the relative distance ‘d’ between the pixel pair and their relative orientation ‘Φ’ across four directions (horizontal: 00, diagonal: 450, vertical: 900 and anti-diagonal: 1350) as
Ci,j =
M−1
X
x=0 N−1
X
y=0
(P{V(x, y) =i&V(x±dΦ1, y±dΦ2) =j}) (3.20) whereV(x, y) =i, meansiis the grey level of the pixel (x, y), and P is defined as
P(x) =
1 if x is true 0 Otherwise
(3.21)
The IDM feature across the different distances, ‘d’, and varying relative orienta- tions, ‘Φ’, is defined as
IDM(d,Φ)=X
i,j
p(i,j)/(1 + (i+j)2) (3.22)
where p(i,j) is the (i, j)th entry in a normalised grey scale spatial dependence matrix C(i,j)/Rand R is the number of neighboring resolution cell pairs.
A Multi-Scale IDM-Feature measurement across the varying distance ‘d’ and relative orientation ‘Φ’ is used in the computation of an IDM feature matrix as:
F =
f11 f12 f13 f14 f21 f22 f23 f24
f31 f32 f33 f34 f41 f42 f43 f44
(3.23)
where fij = IDMdi,Φj with orientations (Φj)i=1,...,4, such that Φ1= 0o, Φ2= 45o, Φ3= 90oand Φ4= 135o, with distances (di)i=1,...,4. Since the width of retinal vessels can vary from very large (15 pixels) to very small (3 pixels)[47], the multi-scale approach adopted investigates the distances (di)i=1,...,4 across the four orientations as it covers adequate spectrum of vessel texture information (4 × 4 = 16) to compute the global
threshold. The range measure of F is given below as:
RΦ = max
1≤j≤4(fij)− min
1≤j≤4(fij) (3.24)
where 1≤i≤4 andRΦ is a row vector containing the range of each column of matrix (F).
The threshold value that will be used for the binarisation of the output image from the phase congruence and average filter is computed as:
Th =max(RΦ) +mean(RΦ) (3.25) Figures 3.9 and 3.10 show the segmented vessels obtained from phase congru- ence and IDM-based global thresholding after post-processing on DRIVE and STARE databases respectively.
Figure 3.9: Retinal images and the segmented vessels obtained through phase con- gruence using different global-based thresholding techniques. Images (a) and (e) are DRIVE database gold standards. Images (b) and (f) are images segmented using IDM- based threshold values while images (c) and (g) are images segmented using ISODATA threshold values. Images (d) and (h) are images segmented using Otsu threshold values.
Figure 3.10: (a) STARE database ground truth. (b) Pre-processed image using Phase Congruence. (c) Retinal Image Mask (d) Segmented vessel network using Phase Congruence-Based global thresholding approach.
3.4.2.4 Sum Entropy-Based Thresholding
Entropy has been one of the few major Haralick features that has often been used for unsupervised segmentation. Different entropy based thresholding such as global, local, joint and relative entropy have been proposed in [171], [172], [173] and [174].
The unsupervised segmentation approach applied in this research is different from the previously proposed methods [171], [172], [173] and [174] in that a multi-scale approach is applied in this thesis to compute a global threshold based on sum entropy information to segment the vessel network. A grey-level threshold value based on GLCM sum entropy feature information is computed for the segmentation of the retinal vasculature from the background using the image output from phase congruence technique. The GLCM for the retinal fundus image is computed as described in equation (3.20). The sum entropy feature across the varying distances, ‘d’, and relative orientation, ‘Φ’, is defined as
Entr+(d,Φ)=−
2Ng
X
i=2
px+y(k)log{px+y(k)} (3.26) wherepx+y(k) =PNg
i=1
PNg
j=1p(i, j)
(i+j=k)
and p(i,j) is the normalised matrix.
A multi-scale feature measurement of the sum entropy across the varying dis- tance ‘d’ and relative orientation ‘Φ’ to manage the variation in the widths of the vessels [47] is applied in the computation of a feature matrix as:
E = (eij),1≤i, j ≤4 (3.27)
where
eij =Entr(d+
i,Φj),1≤i, j≤4 (3.28) Such that Φ1= 0o, Φ2= 45o, Φ3= 90o and Φ4 = 135o, with distances (di)i=1,...,4.
Distances (di)i=1,...,4 across the four orientations are considered as adequate spec- trum of vessel texture information (4× 4 = 16) is also covered to compute the global threshold based on sum entropy.
The threshold value used for the segmentation of the vessels using the output image from the phase congruence and a mean filter is computed as
Th = max
1≤i≤4k max
1≤j≤4(eij)− min
1≤j≤4(eij)k (3.29)
Hence, the segmented image is given as
Sim=
0, ifF(x, y)≤Th 1, otherwise
(3.30)
where F(x,y) is the output image of the pre-processing phase.
Figures 3.11 and 3.12 show the segmented vessels obtained from phase congruence and sum entropy-based thresholding technique after post-processing on DRIVE and STARE databases respectively.
Figure 3.11: (a) Coloured Retinal Image (b) Drive Gold Standard (c) Segmented Vessels Using GLCM Sum-Entropy Threshold Combined with Phase Congruence