2.2.1. Feature Extraction

To extract the discriminative features from SRs, we focus on the shape features. The common shape features can be categorized into region-based and boundary-based features. Concerning the rotation and translation issues, we select some shape features which demonstrate the best resistance against these factors. Moreover, we define new features based on the extracted SRs that are described in the details in the following.

2.2.1.1. Region-based Shape Features

Some simple region-based shape features such as minor and major axis length, solidity, eccentricity can not stand alone to describe a shape but they can be used to describe a shape along with other shape features [33]. Hence, we use these shape features to filter the enrolled SRs and find the best candidates in the matching step while they are partly resistant against the rotation and translation problems to some extends. Table 1 obtains the details of extracted region-based shape features from the marked SR in Fig. (3-a).

2.2.1.2. Boundary-based Shape Features

The boundary-based shape features provide a more detailed description of boundary of the target regions as far as these boundaries are the blood vessels around the SRs. We define the features such as angle of SR corner points, centroid distance, differential tangent angle, and weighted corner angle which provide more rotation and translation invariant properties in comparison to region-based shape features. In the following, we describe them in the details.

2.2.1.3. Angle of sr Corners

As previously mentioned, the SRs are located in the crossover or branches of vessels (mostly thick vessels). Hence, we define the corners of a SR as the points that belong to the boundary of selected SR and have been located in a crossover or a bifurcation. To extract these corner points, we propose an efficient algorithm based on the morphological properties of the SRs that are described in the following,

1) Perform the morphological dilation on (binary image of SR) using a disk shape structure element ( ) with the size of 5 pixels as, (Fig. (4-b)).

2) Perform , where (Fig. (4-c)) is a binary image obtained by subtracting from and (Fig. (4-d)) represents the skeleton of extracted blood vessels. Fig. (4-e) shows the result of this process ( ).

3) Find the nonzero pixels in the image which have more than 3 nonzero pixels in their neighborhoods (in an 8-connected neighborhood) as the candidates of corner points (Marked points in Fig. (4-f)). Since, some candidates are caused by the thin vessels outside of the selected region and could not satisfy our definition of the corner points of SR, so they should be eliminated as will be described in the next step.

4-a) Move the extracted candidate points in the outward orientation of selected SR through the skeleton segmented image ( ) for 10 pixels. The moved candidate corner points are shown by marked points in Fig. (4-g).

4-b) Cut the connectivity of selected SR with blood vessel tree by subtracting the dilated image (Fig. (4-b)) from segmented blood vessel image, , (Fig. (3-b)) as, (Fig. (4-g)).

4-c) Label the nonzero components of and remove the small components with area less than 100 pixels. So, smaller components that represent the thin vessels are removed (Fig. (4-h)).

4-d) Eliminate the candidate corner points which the value of its corresponding moved point is zero in the image of (Fig. (4-i)). By using this strategy, the extracted corner points which happened on thin vessels around the selected SR are removed.

5) Merge the corner points which are close to each other (three pixels).

6) Find the closest point on the boundary to the resulted point and replace it by this point on the boundary. Fig. (4-j) shows the resulted corner point with blue star.

7) Calculate the angle of corner points on the selected SR boundary as in the following. Assume be a set of the corner points of the selected SR in clockwise direction, ( ), where is the number of extracted corner points. For each corner point, , the angle between the left side vector and the right side vector is then computed as,

(3)

where and are obtained by averaging ten left-handed neighborhood pixels and ten right-handed neighborhood pixels of concerned corner point ( ), respectively. As a result, a set of corner angles is gained. Fig. 4 shows the middle results of our algorithm to extract the feature of angle of SR corners.

To extract other shape features from each SR, we should soften the boundary of selected SR to reduce the effect of noise in the boundary segmentation process. For this purpose, we apply a moving average filter on all pixels of SR’s boundary. Assume that , , denotes the coordinates of boundary pixels of the selected SR as a closed sequence with boundary pixels. By applying this filter, new coordinates of the filtered boundary points, , , are calculated as follows,

, (4)

where is the size of filter. Hereinafter, we extract the shape features from the filtered sequence instead of the pixel coordinates.

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j)

Fig. 4: Extraction of the feature of angle of SR corners. (a) A sample of the selected SR, (b) Dilated version of the selected SR in (a), (c) Subtraction of (a) from (b), (d) Skeleton segmented image of blood vessels, (e) Skeleton of extracted blood vessels around SR, (f) Corner point candidates of SR, (g) Moved candidate corner points for 10 pixels, (h) Removing small components of vessel tree corresponding thin vessels around selected SR, (i) Eliminating candidate corner points on thin vessels and (j) Calculating the angle of corner points of SR as it is described in Eq. (3).