Subsampling strategies in learning-based vessel segmentation

The original practical motivation of the efforts discussed so far in this chapter was the recognition of human appearance in thermal videos. However, we have investigated whether these sampling strategies can be exploited also in other application fields to speed up computations. Accord-ingly, in this section, we present some results on applying these approaches in a learning-based environment dedicated to the segmentation of retinal vessels (see also section 1.4).

Algorithms for segmenting the vascular system of the retina have high importance in automatic systems for detecting diseases (such as diabetic retinopathy) based on digital retinal (fundus) images. Using an accurately segmented vascular system, we have better chances to locate other anatomical parts (e.g. optic disc and macula/fovea) of the retina and explore the disorders of the vascular system itself. State-of-the-art segmentation algorithms are usually based on machine learning, with a subsequent classification step to decide whether the pixels belong to the vascular system or to its retinal complement. We can highlight the method presented in [116] as a typical approach in this field with good performance having reported. Figure 2.22 depicts an original fundus image, a manually segmented vascular system for the training phase, the confidence results of the classification step and the detected vascular system, respectively. The classification of a pixel is done by thresholding the confidence map.

In our screening system DRSCREEN (see also the Introduction) for diabetic retinopathy, we investigated how this type of segmentation algorithms can be further improved. For efficient classification, a representative sample of vascular pixels is needed. However, the corresponding literature lacks the suitable selection of the training sample. Both to avoid overtraining and to save computational time, a sampling of the manually segmented vascular systems is desired during the training step. The most obvious selection of the points is random sampling. However, it seems also natural that a more adaptive sampling should lead to better overall segmentation performance.

Thus, we have tested such approaches that can guarantee more homogeneous representation of the original object. For an objective comparison, we calculated the symmetric difference of the test images and the vascular system found by involving the investigated sampling strategies.

Sampling strategies

We have tested whether the random sampling can be outperformed by using more homogeneous sampling approaches based on the centroidal Voronoi (CVT) or the constrained centroidal Voronoi

(a) (b)

(c) (d)

Figure 2.22: Components of a learning-based vessel segmentation algorithm; (a) input retinal im-age, (b) manual segmentation for training, (c) confidence values to classify as vessel, (d) segmented vascular system.

(CCVT) tessellation. Since CVT does not sample the boundary of the sets, and CCVT may emphasize it too much, we also combined them with having a union of half number of points using CVT and CCVT, separately. For an illustrative result of these strategies on retinal vessels see Figure 2.23.

Experimental setup

As for preprocessing, the segmentation algorithm we have selected works on the green channel of the fundus images. Moreover, we applied adaptive histogram equalization (CLAHE) described in section 1.6.1.

Our training database contained 10 fundus images from the publicly available DRIVE database (see section 1.5.6). This database also contains the manually segmented vascular system for each of the images to support quantitative comparison of different segmentation algorithms. For the elements of the test database we have selected 4 other images from the DRIVE database.

For vessel extraction, we considered the robust vessel segmentation method presented in [116].

This approach considers a kNN classifier based on learnt feature vectors for both vascular and

(a) (b)

(c) (d)

Figure 2.23: Result of sampling strategies shown for a part of the vascular system; (a) random sampling, (b) CVT, (c) CCVT, (d) CVT and CCVT combined.

retinal background pixels. The method composes the feature vectors from the green level intensity of the pixels, and from the responses of 0th, 1st and 2nd order derivatives of Gaussian masks having different standard deviations.

In our experimental tests, we compared the performance of the following sampling strategies:

• random,

• centroidal Voronoi tessellation based (CVT),

• constrained centroidal Voronoi tesselation based (CCVT),

• a combination of the CVT and CCVT sampling.

We performed our tests using the following levels of sampling: 0.05%, 0.5%, 1%, 5%, 10%. For example, level 5% means that 5% of the pixels are retained from the object for training. These sampling levels were applied to both the vessel and background pixels.

We defined a quantitative measure for an objective comparison of the segmentation results of different sampling strategies, and levels. Namely, we calculated the normalized symmetric difference S of the vascular system A found by the segmentation algorithm and the manually segmented oneB that we had for all the test images

S(A,B) = ^|A\B|+|B\A|

|A∪B| , (2.23)

where the symbol \ denotes the set difference operator. Notice that S(A,B) = 0, if A and B coincide, while S(A,B) = 1, if they have no common points at all. To show the performance of segmentation, we consider the goodness value G(A,B) = 1−S(A,B). Thus, to summarize our experimental setup, it was prepared in a way to be able to compare sampling strategies and levels objectively.

Results

In our experiments, we were looking for the answer to the following questions:

• which sampling approach from the investigated ones leads to the best segmentation results?

• how does the segmentation accuracy drop with the level of sampling?

• how does the computational time drop with the level of sampling?

Figure 2.24 depicts the comparative results of the investigated sampling approaches (random, CVT, CCVT, combined) for several levels (0.05%, 0.5%, 1%, 5%, 10%) of sampling.

Figure 2.24: Segmentation performance of different sampling strategies regarding the level of simplification.

From Figure 2.24 we can see that CVT outperformed the other strategies in the case of the smallest level of sampling. However, as the sampling level increased, in all of our test cases CCVT provided the best performance. Moreover, as expected, random sampling is the less reliable one and the performance of the combination of CVT and CCVT is somewhere between these two. It is also to be noticed that random sampling is able to outperform CVT in some cases that suggests the importance of training pixels close to the object boundary. From Figure 2.24 we can also see that below the sampling level 1% the accuracy falls considerably.

In Figure 2.25, we present the global performance of the sampling approaches (random, CVT, CCVT, combined). To have an overall goodness value, we calculated the average performance for the sampling levels. We can conclude that CCVT provided the most representative sampling.

We collected the computational times of the vessel segmentation algorithm for all the test images. Naturally, we ran all of our tests on the same computer with a 2.4GHz Intel Pentium Dual-Core CPU and 2GB RAM. Our experiments indicated that only the level of sampling affected the segmentation time. Thus, we do not present computational results for the sampling methods separately. Instead, Figure 2.26 depicts the average segmentation times of all the test images and sampling methods for fixed sampling levels. We can see that a reasonable amount of computation can be saved by using a smaller number of training pixels.

Figure 2.25: Average segmentation performance of different sampling strategies.

Figure 2.26: Segmentation times regarding the level of simplification.

Chapter 3

Piecewise linear digital curve