Detection of uveal melanoma using fuzzy and neural networks classifiers

ABSTRACT


INTRODUCTION
The traditional image processing is used to solve problems like quality improvement, restoration, highlight features, among others.Currently, with the emergence of branches such as fuzzy logic and neural networks, image processing is also being used to address problems related to diseases.Among them is the uveal melanoma (UM), a subtype of ocular melanoma (OM) [1] a type of intraocular cancer that arises in the melanocytes of the coloured part of the eye (iris), circle of muscle tissue (ciliary body) or in the largest part of the uvea track (choroid) which is located beneath the retina in the back part of the eye.Mostly, ocular melanomas appear within the choroid and come from the melanocytes, which are the cells of the body that produce pigment [2].Early diagnosis and local treatment are crucial since survival rates correlate with the size of the primary tumour.However, approximately 50% of patients will develop metastases with a survival rate of 6-12 months from diagnosis [3].
Using modern tools like ultrasonography, fluorescein angiography, and optical coherence tomography can significantly aid in diagnosis [4,5], roughly 3 out of 4 people with ocular melanoma survive for at least 5 years.Survival rates tend to be better for cancer detection in earlier stages than for those in later stages.When cancer is confined to the eye, the relative survival rate at 5 years is around 80%.For people with eye melanomas that have spread to distant parts of the body, the 5-year relative survival rate is around 15% [6] and 1-year survival rate is 10% to 15% [7][8][9].
In related works, a large number of projects associated with the iris have been developed.There are two main applications: identification of people through unique patterns [10][11][12] and detection of diseases where Iridology is found, which is a branch of alternative medicine that is responsible for examining patterns, colours, and other characteristics of the iris to determine the health of patients [13,14].For example [15], where the iris is employed for the detection of Alzheimer.
In [16] is shown how to detect diseases in the iris using the Gabor filter.Among the classified diseases are corneal oedema, iridotomies, and conjunctivitis.Moreover, in [17], through techniques of Iridology and the Watershed transform diseases are identified, reaching an accuracy of 87.5% in the detection of kidney problems.In [18], using unique iris features and advanced encryption standard (AES) images are encrypted, achieving high levels of security.
As shown in [2,5] there is no approved therapy to treat metastatic uveal melanoma and considering that its early detection significantly increases the chances of survival, there was developed a method to identify UM.The proposed method integrates algorithms used in work related to iris segmentation and proposes a methodology for UM detection from the fuzzy logic and neural network approach, as well as present a variation of the algorithm proposed by Wildes in [19].The variation implements additional logic to increase the accuracy as well as implementing data structures like a red-black tree and disjoint set with the union by rank and path compression to reduce the turnaround time.
The shown algorithm employed to detect UM consists of: 1) preprocess images with and without UM, 2) apply a segmentation algorithm to each of these preprocessed images to find the region of interest (ROI), 3) transform the ROI to another space that allows an analysis with less noise, 4) obtain descriptors of the ROIs to generate a training dataset, 5) a fuzzy and a neural network classifier are created based on the training dataset, and finally in 6) the results of the classifiers are analysed and compared.

IMAGE PROCESSING
Humans are very good at detecting patterns but unlike machines, we are not good at processing large amounts of data, then, if the machine is taught to identify patterns it is possible to automate many specialized tasks such as disease detection.For the present case study, Hough circular transform, adaptive binarizations, filters, Hu moments, among others techniques are used to train the classifiers to identify UM, a brief description of those algorithms is provided.

Hough circular transform
Hough circular transform (HCT) is an algorithm to search circles in images, this approach is used because it provides robustness to the presence of noise, occlusion and variation of illumination [20].This algorithm has three fundamental phases: 1. Accumulator array computation 2. Center estimation

Radius estimation
The HCT is used to transform a set of characteristics of points in the space of the image, (1) to a set of votes accumulated in the space of the parameters (2).These votes are integer values that are stored in an array.The position of the arrangement that contains the most votes indicates the presence of a circle.The (1) represents a circle, where  is the radius and ( 0 ,  0 ) are the coordinates of the centre of the circle.
The (2) represents the parametrization of the circle where ( 0 ,  0 ) are the coordinates of the centre of the circle and  is the angle of inclination.That equation allows transforming a circle into a rectangle.

Adaptive thresholding
Conventional thresholding methods use a threshold for all pixels, while adaptive thresholding (AT) changes the threshold value dynamically on the image.The AT has shown better results with respect to the traditional thresholding since the illumination and the shadows change depending on the position of the image [21].Within the thresholding methods used in this article are: Gaussian thresholding (represented by (3)) and mean thresholding.In (4) is depicted an example of a Gaussian window.
TELKOMNIKA Telecommun Comput El Control  Detection of uveal melanoma using fuzzy and neural networks classifiers (Daniel F. Santos)

Hu moments
The Hu Moments allow to obtain image features used in the classification process.The following definition is important in this regard.Definition 1 (Moment of an image): A measure that provides a generic representation of an object, with simple or complex figures [21].
There are a considerable number of used and well-known moments within which we can include geometric moments [23], Zernike moments [24], rotational moments [25], and complex moments [26].The invariants of the moment were introduced by Hu in [23], these are very useful properties that can be extracted from an image because they are not only independent to position, size and orientation but also to parallel projection, thus they have been widely used to perform pattern recognition, image registration and image reconstruction [23,[27][28][29].

Invariant moments
A two-dimensional moment of order ( + ) is defined by the (5).
If the function (, ) is defined in parts, the moments of all orders exist and the sequence of moments   is only determined by the function (, ), but those moments in the ( 5) may not be invariant to translation, rotation or scale, thus the invariant Hu moments can be calculated using the central moments, which are defined by (6).
The moments   are calculated using the image (, ), these are equivalent to   whose centre has been moved to the centroid of the image, therefore, the moments are invariant to translation [23].Where the pixel ( ′ ,  ′ ) is the centroid of the image and: With the use of the normalization of the moments the invariance to scale can be obtained.This moment can be defined by: Based on those moments, Hu in [23] presented the seven moment invariants shown below: It is important to mention that the noise generated by different factors, such as the type of camera and file formatting, can produce errors when calculating moments.In other words, moments can vary with the geometric transformation of the image [29].In the case of a scale transformation or rotation of the image, a rounding of pixel positions or interpolation is generated which causes that at a digital level the invariants of the moment also change [30].

RESEARCH METHOD
This section describes the algorithm (see Figure 1), each sub-section represents each stage as follows: the first one corresponds to the image processing; next, refers to the detection of the region of interest; afterwards comes the filtration and transformation of those regions to finally perform the feature extraction.

Image pre-processing
This is the first phase and it is of vital importance to facilitate the detection of the ROI, in which enters an image (, ) whose output is the image (, ). Figure 2 shows the stages through which the image passes.Using Figure 3 it is shown how this stage works, this image corresponds to an eye affected with uveal melanoma [31].The sequence of algorithms that facilitate the detection of the ROI: -Grayscale transformation: First, an image with three channels RGB is received and transformed into a grayscale image; this is mainly due to the fact that a grayscale image is easier to process than an RGB image (see Figure 4).-Apply median filter: The image is smoothed by applying a median filter, this will decrease the noise, helping to make the ROI clearer.The result of this process is shown in Figure 5. -Apply binarization: With this stage the boundaries are clearly defined, the binarization used was the Adaptive Mean Thresholding and the Adaptive Gaussian Thresholding.Figure 6 shows the result obtained in this step.-Image dilation: Again, a process is done to reduce noise, in this case, pepper type noise, using dilation.
The respective result obtained in this step is shown in Figure 7.

Detection of the region of interest
The region of interest is the iris, this is also a crucial stage for the detection of UM since an inappropriate location of the ROI can result in extraction of characteristics from non-relevant parts, generating a training with noise and therefore an erroneous classification.Based on the literature of iris segmentation algorithms, it was decided to use a variation of the wildes algorithm due to its ease of implementation, computational efficiency and suitable properties.
-Algorithm of ROI detection Algorithm 1 receives the image of Figure 7, calculates the width and height of the image to make an estimate of the maximum radius and minimum radius that the iris can have, the minimum is calculated based on a  pre-established.As the function of the Hough transform receives as argument the image and the radius, this procedure is carried out within an iteration varying the  from  to  and at the same time it is executed twice since two types of binarization are used.Because the algorithm is executed several times a set is used to store unique ROIs.The set stores the ROIs in a red-black tree that will allow to access the elements quickly and avoiding duplicates.At the end of this stage, there is a set of possible regions of interest, as seen in Figure 8.  ← (ℎ(), ℎℎ()) 3: ← / 4: ← { } 5: for  ←    do 6: circles.insert(houghTransform(,radius)) 7: return circles

Filtering of regions of interest
As can be seen in Figure 8 a large number of regions of interest were detected, some valid and others not, some with noise or very similar, thus it is necessary a filtering stage.Reducing the number of ROIs reduces the processing stage.Algorithm 2 discards invalid circles.Since the performance of the algorithm deteriorates under uncontrolled conditions [19], and there is a large number of similar ROIs, Algorithm 3 was made to join similar ROI, this last one uses disjoint set with union by rank and path compression that by means of a δ of distance joins similar ROI.The results of this stage can be seen in Figure 9.

Transformation of the region of interest
With the detection of the ROI it is applied a transformation that reduces noise in order to isolate the iris and to obtain the features.The scheme of Figure 10 was used to carry out the process of unwrapping the iris.The iris region is transformed into a confined rectangular area, recognizing the boundaries is possible to apply a transformation from Polar coordinates (, ) to Cartesian coordinates (, ), according to ( 8) and ( 9), where  ∈ [0, 2], (  ,   ) represents the direction of the pupil region which is being transformed and (  ,   ) is the new location of that iris element.The results showed in Figures 11 and 12

Feature extraction
For the features extraction, the Hu moments were selected due to their properties mentioned in detail in section 2.4.The extraction was performed in a total of 1622 images that are divided according to Table 1.With these images, the characteristics were extracted and stored in a comma-separated value (csv) file, which will be later used to train the classifiers.

Fuzzy model
The ranges that differentiate healthy and unhealthy iris sets are established using the data set (csv-file); with this processing, the membership functions were built in a Mamdani fuzzy system (Figure 13).Considering the seven Hu moments ℎ 1 , ℎ 2 , ℎ 3 , ℎ 4 , ℎ 5 , ℎ 6 , ℎ 7 for each moment it was decided to use triangle functions to implement the antecedents shown in Figure 13, while Gaussian functions are implemented for the consequent; this represents a numerical value that identifies if the image is healthy or unhealthy, as shown in Figure 14.The result of this model can be seen in Table 2 in which it was obtained 76% of correct classification.

Neural networks
Because the proposed fuzzy system has a success rate of 76%, it was decided to perform a neural network classifier.Supported by an experimental design; different configurations of neural networks were implemented to obtain the accuracy of the classifier.The neural networks parameters that are changed can be seen in Table 2.The inputs of the neural network are the seven Hu moments ℎ 1 , ℎ 2 , ℎ 3 , ℎ 4 , ℎ 5 , ℎ 6 , ℎ 7 and the outputs are two: healthy and unhealthy.Figure 15 shows a sample configuration with 7 inputs, 2 hidden layers with 3 neurons each one and 2 outputs.Below are the results with three types of neural networks, each configuration was executed four times, the results of one of the executions are shown below; finally, statistical measures are shown each configuration.Figure 16 represents the mean squared error (MSE) for each type of neural network, varying the number of layers and the number of neurons based on the parameters of Table 2.These graphs and Table 3 present the conditions in which the UM is most likely to be detected.The configurations with low MSE outcomes are the ones with less than 6 neurons per layer and less than 5 layers.

RESULTS AND DISCUSSION
As an experimental result, the accuracy rates of the fuzzy system and the neural network system are shown.In the confusion matrix of Table 4 are shown the results of the fuzzy classifier, the function that was used to perform the classification can be seen in the (10) where  is the fuzzy system created,  is the function that obtains the values of Hu and  is the image to be tested.As can be seen in the confusion matrix of Table 4, the fuzzy system generates better results with healthy images.The hypothesis of these results is based on the fact that the entry dataset is larger for healthy iris than for unhealthy iris.Given the last table is possible to compute some measures like accuracy, error rate, sensitivity and precision that can give more insights of the model, the results are 0.76633, 0.23366, 0.88847, and 0.83917, respectively.Regarding the precision and sensitivity can be shown that the system is prone to detect healthy images.After executing the different configurations of neural networks, a statistical analysis was performed on four data-sets corresponding to the results of each configuration;   represents the standard deviation of the results of the execution number .The results obtained are shown in Table 5, where it can be seen that the network that produces the best results is the feed forward network with a success rate of 96.04%.

𝐶(𝐼) = {
(()) > 0 ℎℎ  (()) < 0 ℎℎ Finally, judging from the results collected through the different executions, it can be seen that the feed forward network produces the best accuracy of 96.04% with standard deviation of 0.008 which can be improved from different approaches such as increasing the size of the data set, incrementing the number of descriptors, e.g Gabor descriptor or using other techniques, e.g ANFIS, convolutional networks or genetic algorithms.

CONCLUSION
The proposed methodology was tested using different configurations, the experimental results show that fuzzy logic and neural networks classifiers provide a suitable system to detect uveal melanoma, achieving 76% in the fuzzy classifier and for the neural network classifier which performs better with an accuracy of 96.04% using a Feed Forward Net.For the segmentation of the ROI it was proposed a new algorithm built over the principles of Wildes algorithm, this new algorithm was done to improve the success ratio of well-segmented regions of interest (ROIs) as well as the integration of data structures like disjoint-set with path and range compression to reduce the processing time.As a result of the pre-processing stage, it was possible to perform detection of the regions of interest.The stage of transformation and use of data structures was decisive to reduce the noise in the data set and the processing time for the feature extraction.In order to improve the performance of the classifiers, it is considered to expand the number of images used, as well as the integration of more descriptors into the training data set such as Gabor descriptors.In a future work the methodology and the algorithm proposed could be implemented in smarthphones

Figure 1 .
Figure 1.Stages for image feature extraction

Figure 2 .Figure 3 .Figure 4 .Figure 6 .Figure 7 .
Figure 2. The sequence of algorithms that facilitate the detection of the ROI

Figure 8 .Figure 9 .
Figure 8. Possible regions of interest detected using Algorithm 1, obtained from the dilated images

Figure 13 .Figure 14 .
Figure 13.Block diagram of the fuzzy inference system

Figure 16 .
Figure 16.Neural networks results (a) performance feed forward net, (b) performance cascade forward net, (c) performance FitNet

Table 1 .
The number of images for feature extraction

Table 2 .
Parameters and ranges that varied for the neural network test

Table 3 .
Results of neural network configurations

Table 4 .
Confusion matrix using the proposed fuzzy system

Table 5 .
Standard deviation and MSE