The problem of improving the efficiency of medical diagnostics is continuously present in the medical practice. The feasibility of using the mathematical tools for fuzzy logic as applied to the tasks of medical radiological images analysis is under investigation. The paper considers a new approach to the application of the fuzzy clustering technique for analysis and processing of medical images having various structures. The results of practical application of the new approach with the use of real medical images are shown.
The ultrasonic imagining is one of the main and common methods of medical
diagnostics [
Another distinctive feature of ultrasound diagnostics is the fact that the boundaries of the anatomical regions are “blurred” on the ultrasonic images, since the acoustical impedances of adjacent biological structures may be close or continuous variable. This fact necessitates the application of the fuzzy clustering techniques. The fuzzy clustering introduces the notion of fuzzy clusters and the function of membership of
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the objects thereto, which varies in the interval [
Recently, one of the urgent directions of the development of computer technology in medicine is the processing of digital images: improving image quality, restoring damaged images, recognizing individual elements. Ultrasonic (ultrasound) technique is the most common and allows you to diagnose a large number of dangerous conditions of human health.
To date, many leading research centers and laboratories have developed many image processing algorithms, including medical ones. When processing and analyzing images, the following main stages are distinguished: filtering, pre-processing, segmentation, recognition and diagnostics. The effectiveness of the subsequent stages of image processing directly depends on the results of filtering and pre-processing.
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The advantage of the proposed algorithm is the minimization of the level of errors, ensuring the finding of most boundaries; maximum accuracy of selection, that is, ensuring a minimum distance between the detected and actual boundaries; the only response in a place where there is only one border.
The Canny algorithm has a two-level threshold for trimming redundant information. This drawback does not allow the Canny algorithm to be used in automatic mode, since the required participation of the user in setting the upper and lower thresholds is required.
In [
Proposed by the authors, the method has high speed image processing and relatively low computational complexity. In addition, for this method, parallelization of calculation processes is easily applicable. High speed, ease of calculation, parallelization of processes gives a great advantage in the application of this method for processing data in layers.
The disadvantage of this method is that the value of the relative number of
erroneously determined contour pixels of this method decreases nonlinearly. A
mathematical model of noise is proposed in [
Based on the table of reduced MSE values for 5 different images, it is concluded that the model proposed by the authors is more accurate than standard multiplicative noise.
It should be noted that the proposed model does not have a normal distribution, by technical means, at the moment, it is impossible to completely suppress it, therefore, the approach to the development of methods based on artificially created images is theoretically poorly justified.
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The main advantage is the short processing time, since this algorithm does not require re-smoothing the image to obtain a pronounced peak. The disadvantage of this algorithm is that it does not give a single, precisely defined contour of the object, but makes the boundaries of strong brightness differences more noticeable.
Approaches to binarization of images are no less diverse than to cleaning from
noise. There are a huge number of histogram conversion algorithms, adaptive local
and global threshold filters based on various statistics and parameters. In [
The disadvantage of the algorithm is the limited class of application, since the main requirement for its use is the continuity and smoothness of the contour of the desired object.
In [
The advantage of the proposed method is that the method allows to reduce the width of the contour line and increase the accuracy of its localization.
The disadvantage of the proposed method is an increase in processing time and an
increase in memory, since the algorithm works with two images (input and blurry). In
[
The main advantage is that the algorithm provides high segmentation accuracy based on the analysis of local histogram statistics, since the obtained limit line has a less complex shape, does not contain gaps, and there are no random "holes".
The disadvantage of this method is the low visual information content, which does not make it possible to widely apply it.
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The disadvantage is that when you select a smaller mask, the image becomes grainy, erroneous contours appear.
Another algorithmic approach to segmentation was proposed in [
An important advantage of the algorithm is that it allows you to automatically determine the threshold value as a result of approximating a portion of a three-peak histogram, this indicates its adaptive nature. That is, this allows you to apply it not only for threshold processing, but also for highlighting the image outline.
The disadvantage is that the principle of selecting the size of the Gaussian filter mask is not specified, nor is the formula for obtaining the set of intersection points of the original and the smoothed image based on which a three-peak histogram constructed. It is proposed to set the brightness threshold value equal to the brightness corresponding to the maximum value of the average peak of the three-peak histogram.
An adaptive filter based on the anisotropic diffusion method was proposed in [
The advantage of an adaptive filter based on anisotropic diffusion using an adaptive threshold value and a function of the number of iterations allows you to obtain an image with preserved edges of small objects even at a noise level of 90% of the signal amplitude. The disadvantage of the proposed method is the occurrence of computational complexity in the context of lowering the speed of the algorithm depending on the number of iterations.
In [
The advantage of the algorithm under consideration is that it allows achieving a segmentation quality close to expert for a given ultrasound image (90% match).
The disadvantage of the parallel genetic algorithm is that it allows with a high degree of certainty (probability ≥ 0.8) to obtain the desired processing result, provided that the parameters of the given image are close enough to the parameters of any image from the training sample.
In [16], a method of secondary processing of various types of images is proposed,
which makes it possible to distinguish contours characterized by a maximum value of
the brightness difference. When visualizing ultrasound images, the bulk of the
information is contained in the differences in brightness. In this case, the psychophysical
properties of vision are such that the contrast sensitivity depends on the intensity of
the surrounding background and, therefore, the reaction of the eye to a change in
illumination is non-linear [
This method can significantly reduce the systematic errors of the geometric measurements of the heart associated with the psychophysical features of a person’s vision.
However, the application of this method in medical practice leads to the fact that for different types of images characterized by texture features and saturation, the efficiency of border extraction can be different. In [17], the results of experimental studies of the influence of features of human vision on the measurement error of the geometric dimensions of objects with a blurred outline are presented. The study was conducted in a group of 11 operators. Each participant was asked to choose the point at which, in their opinion, the maximum value of the brightness difference is observed in several test images. Images were offered to operators in a loop in order to average the error value on the same image. The results of the study confirm the need to create supporting software designed to reduce the subjectivity of expert analysis of ultrasound images.
In [18], segmentation is performed on an ultrasound image of layers of artery tissue in order to measure their thickness. The experiments were carried out on 100 ultrasound longitudinal images of the coronary artery, the results of computer calculations were compared with the measurements of two experts, and no significant differences were found in the computer and expert assessment. Testing of the method was carried out as follows. On each of the images, a region containing the artery wall was manually selected. The selected area was filtered to eliminate noise using the filters described in, then it was binarized, the binarized image was dilated over a 3x3 set, the borders at the bottom of the selected area were eliminated, and a contour was drawn using B-splines. As a result, selected tissue boundaries were obtained. Statistical calculations of deviations in computer and expert assessment of tissue thicknesses in various ultrasound images of the artery are also presented. However, the results of the proposed method were not presented for less “good” cases of ultrasound of the arteries, on which there is no such clear difference in the brightness of the layers of the artery. As a result, selected tissue boundaries were obtained.
In [19], a GA was proposed for obtaining effective threshold detectors for signal identification, which is also applicable in image processing and machine vision problems. GA is used to study compound operators used in the task of identifying objects. The proposed results show that GA is one of the methods for synthesizing complex operators that allow recognition of objects. In order to generate noise / target classification rules and object identification rules, the GA algorithm is also used. The algorithm is used to extract dependent features from a plurality of predefined sets of image features. The algorithm is used to obtain automatic object recognizers. In [20], the statement of the problem of segmentation of medical magnetic resonance images is presented. A hybrid ant algorithm for its solution is proposed, which allows to improve the quality and speed of image processing. In solving the problem, the methodology of swarm intelligence, cluster analysis, the theory of evolutionary calculations, mathematical statistics, computer modeling and programming are used. The authors present the results of experiments obtained on the basis of data from a library of medical MRI images. The optimal values of the parameters determining the behavior and efficiency of the algorithm are established.
Advantages of the algorithm: the comparative simplicity of the actions performed, the possibility of a highly efficient implementation for multiprocessor architectures, guaranteed convergence (although the convergence time is not defined).
The disadvantages are mainly associated with not always optimal settings. Meanwhile, the objects on MRI images have a high degree of complexity and multifactoriality, which imposes high requirements on the reliability and accuracy of their research.
In [21], the implementation and analysis of a mixed algorithm for segmentation of K-medium and ant colonies was performed, and a software system for visualizing and testing the developed algorithm was implemented. The developed algorithm was tested on public benchmarks (Berkeley benchmark was used). The output processed images are obtained, as well as the values of the heuristic coefficients of the developed algorithm.
As can be seen from the results presented by the authors, the proposed method coped quite well with the task. The advantage of the algorithm is the correct separation of parts of the image from the background. However, as can be seen from the presented results, in order to achieve the optimum, the method still needs the correct selection of heuristic parameters. The study of the functions and features of modern specialized systems for the analysis and processing of medical images for various purposes has shown that these systems have several disadvantages. The main drawback seems to be that most of the systems contain only a wide range of image analysis and processing methods available to the researcher, without indicating which method should be applied to achieve the conversion goal. In this regard, the following problems were identified: it is impossible to guarantee the optimal (in the sense of achieving the conversion goal) the choice of a method (or combination of methods) for image processing, since this choice is based only on the knowledge and experience of the user; it is impossible to search all the methods available to the researcher (and their combinations) to achieve the best processing result, since it will be too timeconsuming. 3
The result of the Fuzzy C-Means algorithm is that each pixel in an image is assigned a vector of the function of membership to each class, with reference to which we can make a conclusion about the nature of the object, but subject to the previous neutralization of the influence of the noise factors. Currently, there is no single approach to the task solution. In [22] it is suggested that Wiener filtering is used, and in [23] the use of adaptive anisotropic filtration is proposed. The main problem is the fact that apriori knowledge of spectral characteristics of both noise and noise-free (i.e. ideal) images is required for optimal filtering. In this regard, the method of selective singular decomposition of automorphic visualization (AVSSDM) [24-26] of noisy images is of interest, because this method does not require a-priori knowledge of spectral characteristics, but only approximate knowledge of the noise correlation interval.
AVSSDM is relating to the image analysis framework methods with the size of the square frame corresponding to the correlation interval. A multidimensional array is formed on the basis of AVSSDM, to which a procedure for decorrelation transformation is applied with the formation of a new array of “own” images. The first “own” image corresponding to the highest singular value is taken as the filtered image.
The experimental findings given in [27] were applicable to the analysis of geophysical fields images. The informational capabilities of the method as applied to the analysis of ultrasonic pulse-echo images remained unclear.
Therefore, for the further improvement of efficiency of medical diagnostics, it is necessary to investigate the information capabilities of AVSSDM and fuzzy FCM clustering as applied to the tasks of medical ultrasonic pulse-echo image segmentation.
The fuzzy clustering is a generalized version of the traditional C-means algorithm overcoming the constraints of group membership of the samplings. The fuzzy clustering uses a fuzzy set in order to specify the degree of membership of the samplings to only one group. The numerical value of the degree of membership lies in the range [28-30], so that the sum of all values of membership of one element (pixel) to all groups is equal to unity.
The fuzzy clustering algorithm is based on the use of procedure for iterative minimization of the objective function
J (U , V ) c N m i1 n1uin xn vi 2 where V={ν1,…,νc} – cluster centers; U=[uin] – matrix of order cN, where uin is the membership function i of n entry xn, m[1,∞) – fuzzification parameter, c – assigned cluster count. The values of the membership functions should satisfy the following constraints: c i1uin 1 ,
n 1,2,..., N ;
N 0 n1uin N , i 1,2,..., c .
This iterative algorithm is based on the sequential computation of the following equations: uin
1/(m1) ; i 1,2,..., c , n 1,2,..., N . 1
N m m n1uin xin , i 1,2,..., c ;
1/(m1) vi N
n1uin 1 xn vi 2
c 1 j1 xn v j 2
For each pixel in the ensemble of images, the value of its membership function for each cluster depends on the distance to the corresponding center of the cluster. The fuzzification parameter m reduces the influence of low values of the membership function. The advantages of the Fuzzy C-Means algorithm can include its flexibility, which allows to work with values of membership functions. The disadvantages include the need to assign a-priori cluster count and the theoretical uncertainty of the choice of initial values and fuzzification parameter, resulting in the variant results of clusterization, as well as noise sensitivity.
The Figure 1 a-d shows the ultrasonic pulse-echo image of the child’s brain (a) and the first three “own” AVSSDM images (b-d) in “space-time” coordinates. Such echoimpulse images are usually considered as a set of signal paths (image columns). It is apparent that the original image on the Figure 1a is noisy, whereas on the first “own” AVSSDM image (Fig. 1b) the influence of modulation distortion is virtually neutralized. When considering the amplitude-time slices (Fig. 2 a and b) of the 50th impulse line (50th column of the Figures 1a and 1b), one can see removing excessive noise from a signal (Fig. 2b) (rapidly changing amplitudes in peaks and declines (Fig. .2a)).
The Figure 2 c and d shows the amplitude-time slices of the second and third “own” AVSSDM images (Fig. 1c, d) corresponding to the noise components, and their rejection is actually equivalent to the adaptive filtration effect, since no assump(2) (3) (4) (5) (6) tions were made about the spectral and statistical characteristics of the modulation noise [31-33].
The Figure 3 depicts the results of the application of the fuzzy clustering technique for segmentation of Fig. 1a and Fig. 1b into seven classes
It follows from the comparison of Fig. 1a and Fig. 3a that the application of the fuzzy clustering technique for segmentation of the noisy image actually accomplishes nothing, whereas its application to the filtered image (Fig. 3 b) allows to facilitate the procedure for visual analysis and interpretation of diagnostic results e.g. by varying the number of classes [34 - 39]. 4
The fuzzy clustering technique is a fairly simple and convenient method for improving the efficiency of the procedure for visual analysis of medical ultrasonic pulseecho images. The neutralization of the influence of modulation noises is an indispensable prerequisite for the successful application of the fuzzy clustering technique. The method of selective singular decomposition of automorphic visualization of noisy images is an effective method of modulation noise filtering, because this method does not require a-priori knowledge of spectral and statistical characteristics
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