SECTOR ATENCIÓN A POBLACIÓN VULNERABLE

There are a number of image decomposition techniques available as described in Chap- ter 3 (Sub-section 3.5.3) of this thesis. With respect to the work described in this chapter, a new image decomposition technique is proposed. The proposed image de- composition approach is performed in a recursive and hierarchical manner as commonly used by other established image decomposition techniques [72, 169, 185]. The novelty of the proposed approach is that a circular partitioning, interleaved with an angular

partitioning, is used. In angular partitioning, the decomposition is defined by two radii (spokes) and an angle describing an arc on the circumference of the image “disc”. Cir- cular decomposition is defined by a set of concentric circles with different radii radiating out from the centre of the retinal disc. Individual regions identified during the decom- position are thus delimited by a tuple comprising a pair of radii and a pair of arcs. The main advantage of this technique (with regard to retinal images) is that more image detail is captured from the central part of the retina disc image that is likely to contain most of the relevant image information (therefore contributing to the production of a better classifier) with respect to AMD screening. Figure 7.2(a) shows an example of the proposed partitioning; Figure 7.2(b) shows the associated tree storage structure. Note that a numbering convention is used to label individual regions described by nodes in the tree structure. The decomposition commences with an angular decomposition to divide the image into four equal sectors. If the pixels making up a sector have approx- imately uniform colour intensity no further decomposition is undertaken (for example the sector labelled ‘0’ in the upper left hand side of the decomposition shown in Figure 7.2(a) has not been decomposed any further). All further decomposition is undertaken in a binary form by alternating between circular and angular decomposition. In the example, sectors that are to be decomposed further are each divided into two regions by applying a circular decomposition. The decomposition continues in this manner by alternatively applying angular and circular partitioning until uniform sub-regions are arrived at, or a desired maximum level of decomposition,Dmax, is reached.

Algorithm 2 shows how the interleaved circular and angular partitioning is per- formed. Before the partitioning is commenced, the centre of the retina disc has to be defined. To achieve this, the GetCentroids method in line 4 uses the retinal image mask, M, to identify the centroid of the retina disc (centre of the circle in the tree de- composition). TheGetImageBackgroundmethod in line 5 generates a binary format background image, imbg, to be used to distinguish the background (areas outside of the field of view of the fundus) pixels and the blood vessel pixels,RV, from the retinal pixels. Both the generation of the image mask,M, and the blood vessel pixels image,

RV, were described in detail in Chapter 4. The image background,imbg, is defined as:

imbg=M∩RV (7.1) M(x) = 1, ifx is a retinal pixel 0, otherwise (7.2) RV(x) =

0, ifx is a blood vessels pixel,

ROI 0 1 2 3 10 11 20 21 30 31 100 101 110 111 310 311 1000 1001 1100 1101 (a) (b)

0

20

21

30

Figure 7.2: An example of: (a) the angular and circular image decomposition, and (b) the associate tree data structure.

Algorithm 2: ImageDecomposition

Data: Coloured retinal fundus image I, retinal image maskM, retinal blood vessels binary image RV and Dmax

Result: Image decomposition treeTf inal

1 c count←1; 2 a count←1;

3 T ← {null, null, null};

4 centroid←GetCentroid(M);

5 imbg←GetImageBackground(M, RV); 6 roi←GetROI(imbg, centroid);

7 for k←0 to 2do // Generate trees for each colour channel

8 for i←1 tomaxDepthdo // Generate trees for each tree level

9 if mod(i/2) = 0then

10 t←CircularP artitioning(roi, imbg, c count, centroid);

11 c count←c count+ 1;

12 else

13 t←AngularP artitioning(roi, imbg, a count, centroid);

14 a count←a count+ 1;

15 end

16 tree←U pdateT ree(tree, t);

17 end

18 T_k←tree;

19 end

where 0 < x ≤ X, and M and RV are both of size X pixels. The image ROI was then identified using the GetROI method. The partitioning commences with Angu- larPartitioning (line 13 of Algorithm 2). On the next iteration CircularPartitioning will be applied. BothAngularPartitioning andCircularPartitioning will then be called alternately until theDmax tree level is reached or only regions of uniform intensity are left. Throughout the process the tree data structure is continuously appended to itself (line 16). Each identified sub-region is represented as a “node” in the tree data struc- ture, whilst the relationship between each sub-region and its parent are represented by the edges. Note that each node holds the average intensity value of the sub-region it represents.

Algorithm 3: CircularPartitioning

Data: Retinal image roi, image background imbg,c count and centroid

Result: An array of circular partitioned image regions B

1 m←2c count ; // To calculate number of circles

2 R←GetRadius(imbg, centroid, m) ; // To calculate radii values

3 B ←SplitImage(roi, imbg, R, centroid); 4 return B

The RGB (red, green and blue) colour model was used to extract the pixel intensity values, which means each pixel will have three intensity values (red, green, blue) asso- ciated with it, hence three trees are generated initially. Using all three colour channels will serve to capture more colour information. The algorithm ends with the merging of the three trees in T, using the MergeTrees method (line 20), to form a single tree,

Tf inal. The initial size of Tf inal is set to the maximum number of nodes that could possibly be generated, thus [PDmax

i=1 (2i+1)] + 1 unique nodes (Dmax must be a value of greater than zero). The merging is done by calculating the Average Intensity Values (AIV) for the nodes inT, defined as:

AIVy = 1 n 3 X k=1 (Tky) (7.4)

where T comprises the red, green and blue colour trees, y is a unique node identifier (or label) inTf inal,Tky is the average intensity values of nodey in tree k, andnis the

occurrences of nodeyin the set of treesT. The value ofnis increased by 1 every time a node labeledy is found in Tk, with the possible minimum and maximum value of 0 (y does not exist in any trees ofT) and 3 (yexist in all three trees). Empty nodes were then pruned fromTf inal.

Algorithm 3 describes theCircularP artitioningmethod. First, we need to identify how many circles, m, are required for the current iteration, as given in line 1. Then, a set of new radii, R = {ρ0, ρ1, ..., ρm} that describe a sequence of concentric circles,

is calculated using theGetRadius method. A set of new additional nodes,B, are then generated (if necessary) using theSplitImage method (line 3) and returned. Note that a “termination criterion” is used in theSplitImage method to determine if nodes splitting is required. Details of the termination criterion used in this chapter are presented in Sub-section 7.2.1.

The AngularPartitioning method, described in Algorithm 4, begins by identifying the number of radii (m) that are required (line 1). The radii define the angular parti- tions which in turn are presented in terms of a set of circular arcsA={α0, α1, . . . , αm}. Each arc α is defined by an angle θ = 2π/m, used in the GetTheta method (line 2). As in the case of theCircularPartitioning algorithm, the SplitImage method is called to decompose the image, as indicated, to produce an appropriate set of nodesB.

Algorithm 4: AngularPartitioning

Data: Retinal image roi, image background imbg,a countand centroid

Result: An array of angular partitioned image regions B

1 m←2×2a count ; // To calculate number of angular lines

2 θ←GetT heta(m) ; // To calculate the angle between angular lines

3 B ←SplitImage(roi, imbg, m, θ, centroid); 4 return B

7.2.1 Termination Criterion

As noted in the above, the nature of the termination criterion is important in any image decomposition technique. For the work described here a similar termination criterion as described in [72] was adopted. However, colour intensity values were considered instead of energy (extracted from the image texture information) due to the difficulties in identifying drusen. Therefore, the homogeneity of a parent region, ω, was defined according to how well a parent region represents its child regions’ intensity values. If the intensity value, which is derived from the average intensity values of all pixels in a particular region, of a parent is similar (less than a predefined homogeneity threshold,

τ) to all of its child regions, the parent region is regarded as being homogeneous and is not decomposed further. Otherwise, it will be further partitioned. Calculation of the

ω value for a child region iof a parent region pcan be formalised as:

ωi =

|(µp−µi)|

µp

(7.5)

where µp is the average intensity value for the parent region and µi is the average intensity value for child regioni. Note that a lowerτ value will make the decomposition process more sensitive to colour intensity variations in the image, and will produce a larger tree as more nodes will be kept (but it is limited to the maximum number of

nodes that can be produced by a predefined tree’s maximum level of depth, Dmax). The decomposition process is performed iteratively until it has reached theDmaxvalue or all sub-regions are homogeneous.