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Each year millions of Americans are diagnosed with foot ulcers that present a risk of amputation. The rate of ulceration is particularly high among diabetics. Because the risk of diabetes is significantly related to obesity, which is reaching epidemic proportions in the United States, the number of Americans with foot ulcers will increase in the coming years. Unfortunately, current methods to assess skin, including visual inspection and palpation, seldom detect changes in skin integrity until an ulcer has already developed. This paper proposes a methodology based on the asymmetry analysis and a genetic algorithm to analyze the thermal distributions of the feet in order to predict foot ulcers. Experimental results suggest that the proposed technique can be reliable and effective in detecting inflammation and, hence, predicting potential ulceration.
Keywords: Foot Ulcers, Thermal Imaging, Asymmetry Analysis, Automatic Thresholding, Genetic Algorithms
Foot ulcers affect millions of Americans annually. One of the most common mechanisms in the development of foot ulcerations involves a cumulative effect of unrecognized repetitive trauma at pressure points on the sole of the foot over the course of several days [1-3]. Areas that are likely to ulcerate have been associated with increased local skin temperatures due to inflammation and enzymatic autolysis of tissue [4-6]. This inflammation is mainly characterized by five signs: redness, heat, swelling, pain, and loss of function. Some of these signs are difficult to assess objectively by clinicians; however, temperature measurements can provide quantitative information that has been shown to be predictive of impending ulceration [4, 7-10].
Conventional noninvasive methods to assess foot skin, including inspection and palpation, may be valuable diagnostic tools, but usually they do not detect changes in skin integrity until skin breakdown has already occurred. Additionally, manual thermal thermometers used in clinics can only provide a mean value over a large area of the foot. In this research work, thermal imaging is used to monitor the temperature distribution of the foot skin. However, there is no standard distribution of the skin-surface temperature of a healthy foot because it is affected by many factors, such as ambient and internal thermal conditions, age, sex, weight, etc. One way to eliminate this variability is to compare the thermal skin distributions of two feet of the same subject [11, 12]. This comparison, asymmetry analysis, is combined with a segmentation technique based on a genetic algorithm to achieve higher efficiency in the detection of inflammation and, hence, prediction of ulcers before they can develop. The methodology proposed involves three steps: segmentation, geometric transformation, and asymmetry analysis.
In this research work, a high resolution thermal camera, FLIR A320, is used to record the temperature foot skin distributions after patients have removed their socks and shoes. The resulting thermal images are then analyzed using an approach shown in Fig. 1 that involves the following three steps:
Segmentation extracts the feet from the background.
Geometric transformation adjusts the left and the right feet so they are in the same positions in the image.
Asymmetry analysis subtracts the intensity level of each pixel in the left foot from the intensity level of the symmetric pixel of the right foot to detect potential ulcerous areas.
Fig. 1. Flowchart of the proposed methodology.
2.1 Automatic thresholding
In the proposed methodology, automatic thresholding of the thermal images is an important step to minimize the noise and decrease the detection of false inflammation. This step presents some challenges. First, some patients have feet that present areas with low temperatures, which are close to the temperatures of the images background levels. Second, the heat transfer from the legs and other body parts increases the temperature between the feet, resulting in highly non-uniform background levels. Figs. 6a, 6b, and 6c show three examples of thermal images that present non-uniform background levels mainly due to the transfer of heat from the legs and other body parts.
Therefore, it is important to find a suitable thresholding technique for these types of thermal images. Examples of thresholding techniques have been addressed in a number of papers [13-21]. These techniques can be classified into several groups including
Histogram shape-based methods
Object attribute-based methods
In this paper, we implemented one algorithm of each category and compared their performances. These algorithms are described below.
2.1.1 Histogram shape-based methods
This category of methods achieves image thresholding through the characteristics of the image histogram, such as peaks, valleys, and curvatures [14, 15]. One of the most referenced methods is Otsu's technique . Otsu suggested minimizing the weighted sum of within-class variances of the foreground and background pixels to establish an optimum threshold given by
Where and represent the mean values of the background and foreground, respectively, as functions of the thresholding level T; and represent the variance values of the background and foreground, respectively, as functions of the thresholding level T. represents the cumulative probability as function of the thresholding level T. This probability is defined as
2.1.2 Clustering-based methods
In clustering-based methods, the gray-level samples are clustered in two parts, background and foreground [16, 17]. One example of this category is Ridler's technique , which presents one of the first iterative schemes based on two-class Gaussian mixture models. At each iteration n, a new threshold Tn is established using the average of the foreground and the background class means. The iteration terminates when the difference |Tn - Tn+1| becomes sufficiently small. The final optimal threshold level is given by
Here, represents an intensity level of the image;
represents the probability mass function (PMF) of the image;
and represent the probability mass functions of the foreground and background, respectively;
and represent the mean of the foreground and background, respectively.
2.1.3 Entropy-based thresholding methods
Entropy-based methods use the entropy of the foreground and background regions as well as the cross-entropy between the original and binarized images [18, 19]. An example of such techniques was developed by Kapur et al. , in which the image's foreground and background are considered two different signal sources, so that when the sum of the two class entropies reaches its maximum, the image is said to be optimally thresholded. The optimal threshold is given by
, , , , , and refer to the same variables as in section 2.1.2.
2.1.4 Object attribute-based thresholding methods
Object attribute-based methods search a measure of similarity between the gray-level and the binarized images, such as fuzzy shape similarity and edge coincidence [20, 21]. An example of such techniques is the moment preserving introduced by Tsai  who considers the gray-level image as the blurred version of an ideal binary image. The thresholding is established so that the ¬rst three gray-level moments match the ¬rst three moments of the binary image:
Again,, , , , , and refer to the same variables as in section 2.1.2.
2.1.5 Genetic algorithms-based thresholding techniques
Genetic algorithms are optimization algorithms based on biological mechanics of natural selection through a set of operations, such as chromosome, population size, cross rate, mutation rate, and maximum generation [12, 22].
The fitness is evaluated by
Where and are the numbers of foreground and background pixels, respectively.
, the mean intensity of foreground pixels, is given by
Where is the sum of intensities of foreground pixels.
is the mean intensity of background pixels given by
Where is the sum of intensities of background pixels.
The best threshold is determined by the following equation:
Where represents a threshold level.
The main steps of the proposed genetic algorithm are summarized below:
Assign the length of chromosome, population size, cross rate, mutation rate, and maximum generation.
Initialize population of the first generation, with each individual being a random eight bits binary string, representing a specific intensity level.
Evaluate the fitness of the whole population.
Generate the next population by performing selection, crossover and mutation operations.
Go to step 3 if the desired number of generations is not reached.
Reduce the cross rate and mutation rate after half of the desired generation number is reached.
Segment the image using the optimal threshold level when the desired number of generation is reached.
2.2 Geometry transformation
The ultimate goal is to compare the thermal skin distributions of a healthy foot to the thermal distributions of a foot with abnormal areas. This comparison is achieved by subtracting the intensity levels of left foot from those of the right foot in the segmented image. However, the feet in the image are rarely in symmetric positions. Therefore, a geometric transformation is needed to adjust the positions of the feet. Assuming that the sizes of the feet are the same in the image, a simple translation and rotation around two feature points can achieve this purpose. The centroid and the furthest point from the centroid to the heel edge are chosen as references for the adjustment of each foot. Based on these two feature points, the relative position and angle differences between the two feet are calculated. Then, a rotation and a translation are performed to put each foot in the middle of the image with the characteristic line in the vertical direction. The geometric transformation procedure is described as follows:
Separate the original feet image into two images corresponding to the left foot and the right foot.
Identify the centroid and the furthest heel points of each foot.
Calculate the angle of the characteristic line with respect to the vertical direction.
Perform the translation and the rotation to adjust the feet in the middle of the image. First, each foot is shifted by moving the position of all pixels inside the foot to the center of the image. Then, the foot is rotated to make the characteristic line in the vertical direction.
Figs. 2, 3, 4, and 5 illustrate the geometric transformation steps to adjust the feet in symmetric positions. Fig. 2 shows an example of initial foot positions. Fig. 3 shows the translation to adjust the left foot to the middle of the image. Fig. 4 shows the rotation of the left foot around the characteristic line to the vertical position. Fig. 5 shows the final output images corresponding to the right and the left feet.
Fig. 2. Example of original image. Fig. 3. Translation of the left foot.
Fig. 4. Rotation of the left foot. Fig. 5. Output images of the adjusted feet.
2.3 Asymmetry analysis
In this step, the potential ulcerous areas are identified by analyzing the asymmetry between the adjusted feet images. Once the feet are adjusted in symmetric positions by using the geometric transformation algorithm, the left foot pixels intensities are subtracted from the corresponding right foot pixels intensities. If the difference exceeds a specific threshold the intensity is shown as abnormality in the image difference.
To assess the effectiveness of the developed technique, we accessed a set of 80 thermal images corresponding to patients' feet with and without inflammation. Some examples of thermal images are illustrated in Figs. 6a - 6c. Figs. 6a and 6b show examples of thermal images of healthy feet, while Fig. 6c shows another example of an thermal image in which the right foot contains a high temperature area, indicating the presence of inflammation. As can be seen from these images, the heat transfer from the legs in the thermal images generates a non-uniform background.
Examples of results after applying the five aforementioned thresholding techniques are shown in Figs. 7a - 7e. The most important criteria to assess these techniques are removing the noise resulting from the heat transfer around the feet and preserving their shapes. Based on these criteria, assessing a set of thresholded images indicates that the genetic algorithm provides better results than the other implemented techniques do.
However, no technique completely removed the noise between the feet. One of the solutions used to increase the efficiency of the thresholding techniques is separating the feet from the other parts of the body by using a light weight metallically painted shield. An example of the results is shown in Fig. 8. As observed, the quality of the thresholded image is greatly improved and the noise around the feet is completely removed. Fig. 9 represents the output images with adjusted feet after applying the geometric transformation to the thresholded image of Fig. 3. Fig. 10 shows the grayscale image representing the result of the asymmetry analysis. In this image, the white spot represents the location of the abnormal area.
Fig. 11 shows the results of the asymmetry analysis (output images after overlapping and subtracting) for different inflammation diameters ranging from 1cm to 0.2381cm. As can be seen from this figure, inflammation, with diameter as small as 2mm, can be detected. Furthermore, Figs. 12 and 13 illustrate the accuracy of the technique by showing linear relationships between the inflammation areas and their corresponding spots areas in the images resulting from the asymmetry analyses. This relationship will allow clinicians to accurately estimate the area of the inflammation and take action before an ulcer develops.
a b c
Fig. 6. Example of thermal images corresponding to
a. healthy feet with cold temperatures areas;
b. healthy feet with non-uniform background due to the heat transfer around the feet;
c. foot with an abnormal area
b c d e
Fig. 7. Some results of the thresholding techniques:
a. grayscale image corresponding to the thermal image of Fig. 6b
b. output image after applying moment preserving method
c. output image after applying maximum entropy method
d. output image after applying Otsu's method
e. output image after applying the genetic algorithm
Fig. 8. Output image after applying Fig. 9. Output images after applying the
the genetic algorithm on Fig. 1c geometry transformation technique on Fig. 3
Fig. 10. Output image resulting from
the asymmetry analysis of Fig. 8
Fig. 11. Results of the asymmetry analysis corresponding to different inflammation diameters
Fig. 12. Area of the inflammation vs. area of the spot Fig.13. Width of the inflammation vs. width
of the spot in the image
We developed a technique to investigate the thermal distributions of the feet in order to detect inflammation and, hence, predict foot ulcers. The experimental results suggest that this technique is effective in identifying small size of inflammations and, hence, predicting potential ulcerations. Our objectives, in the future, are 1) to develop a technique that scans and compares symmetric pixels whatever the shape, size, and position of the feet and 2) to use the developed techniques and system to screen diabetes patients in the Altru Wound Clinic .