Fully Automatic Measurement of Intima-Media Thickness in Ultrasound Images of the Common Carotid Artery Based on Improved Otsu’s Method and Adaptive Wind Driven Optimization

Abstract

The intima media thickness (IMT) of the common carotid artery (CCA) can be used to predict the risk of atherosclerosis. Many image segmentation techniques have been used for IMT measurement. However, severe noise in the ultrasound image can lead to erroneous segmentation results. To improve the robustness to noise, a fully automatic method, based on an improved Otsu’s method and an adaptive wind-driven optimization technique, is proposed for estimating the IMT (denoted as “improved Otsu-AWDO”). First, an advanced despeckling filter, i.e., “ Nagare’s filter” is used to address the speckle noise in the carotid ultrasound images. Next, an improved fuzzy contrast method (IFC) is used to enhance the region of the intima media complex (IMC) in the blurred filtered images. Then, a new method is used for automatic extraction of the region of interest (ROI). Finally, the lumen intima interface and media adventitia interface are segmented from the IMC using improved Otsu-AWDO. Then, 156 B-mode longitudinal carotid ultrasound images of six different datasets are used to evaluate the performance of the automatic measurements. The results indicate that the absolute error of proposed method is only 10.1 ± 9.6 (mean ± std in μm). Moreover, the proposed method has a correlation coefficient as high as 0.9922, and a bias as low as 0.0007. From comparison with previous methods, we can conclude that the proposed method has strong robustness and can provide accurate IMT estimations.

Keywords

common carotid arteries intima-media thickness improved Otsu’s method adaptive wind driven optimization

Introduction

Cardiovascular disease (CVD) has been become a “first killer,” and is harmful to human health.¹ Atherosclerosis is a major source of CVD.² The common carotid artery (CCA) is a common site for atherosclerosis. Research has proven that the intima media thickness (IMT) is an effective parameter for predicting cardiovascular risk, as an increase of the IMT indicates a higher risk of atherosclerosis.^3–7

As can be seen in Figure 1, there are three layers in the CCA wall. From the innermost to the outermost, they are the intima, media, and adventitia. These three layers can be seen in a longitudinal cut of the human carotid artery, over the near and far walls. The dark area in the middle is called the lumen (see Figure 1(a)). The two boundaries at the far wall represent the lumen intima interface (LII) and media adventitia interface (MAI), and the LII and the MAI compose the intima media complex (IMC) (see Figure 1(b)). The IMT is defined as the distance between the LII and MAI. In clinical practice, the IMT can be manually measured by experienced doctors. However, there are many problems in the manual measurement of IMT, such as low efficiency and manual errors.⁸ To overcome the weaknesses of manual measurement, many efforts have been devoted to measuring the IMT based on semi-automatic or automatic measurement methods.^8–10

A semi-automatic method based on the Hough transform and a dual snake model for IMC segmentation was carried out by Xu et al.⁸ Nakagami modeling was used to estimate the IMT of the CCA by Destrempes et al.⁹ Furthermore, many other techniques have been used for IMT measurement, such as the active contour models,^10,11 completely automated layer extraction (CALEXia),¹² completely automated multi-resolution edge snapper (CAMES),¹³ the structured random forest,¹⁴ model-based approaches,¹⁵ Markov random field models,¹⁶ ant colony optimization,¹⁷ neural networks,¹⁸ and machine learning.¹⁹ The objective of most of the previous studies is to obtain accurate IMT estimates. However, there is significant speckle noise in carotid ultrasound images. Severe noise can reduce the accuracy of IMT measurement.²⁰ Therefore, to meet the requirements of clinical application, the accuracy of IMT measurement needs to be further improved.

The purpose of this study is to develop a more effective strategy for achieving satisfactory accuracy in IMT measurement.

In recent decades, thresholding has been applied as an important tool in the field of image segmentation. Bi-level thresholding uses only one threshold value, and the pixels in the image are separated into two classes based on this threshold value. Furthermore, when the number of threshold values is greater than one, the task is called “multi-level thresholding” (MT).²¹ To improve the performance of the MT technique, many works aim to obtain optimal multi-level threshold values based on the evolutionary approaches.^22–26 Wind-driven optimization (WDO)²⁷ is a new evolutionary approach, and adaptive WDO (AWDO) is a modification of WDO.²⁸ Otsu’s method is an important thresholding technique, owing to its high efficiency and good performance in image segmentation.²⁹ Some studies have shown that the Otsu’s method combined with the WDO/AWDO algorithm (Otsu-WDO/Otsu-AWDO) can obtain more accurate results for IMT measurement as compared with other similar methods.^27,28

However, Otsu-WDO and Otsu-AWDO are sensitive to speckle noise in carotid ultrasound images. Accordingly, this study proposes an improved Otsu-AWDO method for improving the robustness to speckle noise. First, a Nagare’s filter^30,31 is used for reducing the speckle noise in the carotid ultrasound images. Next, an IFC method³² is used for enhancing the blurred edges in the filtered images. Then, a new automatic method is used to extract the ROI from each carotid ultrasound image. Finally, the improved Otsu’s method, as combined with the AWDO algorithm, is used to segment the IMC for IMT measurement. The results of IMT measurements show the improved performance of the improved Otsu-AWDO as compared with other methods (see Section 3.2).

The layout of this paper is as follows. We describe the carotid ultrasound image acquisition protocol and explain the proposed method in Section 2. Section 2 also presents the performance evaluation methods and the statistical analysis methods. Section 3 reports the results of the proposed method and presents a comprehensive evaluation of the results obtained by our method and those from other methods. Section 4 provides the discussions. Finally, our conclusions are summarized in Section 5.

Materials and Methods

Materials

Image acquisition and recording

To verify the accuracy of the IMT measurements, six different datasets (dataset1, dataset2, dataset3, dataset4, dataset5, and dataset6) are used in this paper. Dataset1 consists of 12 B-mode longitudinal ultrasound images collected from the Yunnan province cancer center in Kunming, China. These images are acquired using the Esaote ultrasound machine. The size of the ultrasound images is $800 \times 608$ . The ultrasound images’ spatial resolution is 16.1 pixels/mm, and they have 256 gray levels. There are 41 B-mode longitudinal ultrasound images in dataset2, which are collected from the Tumor Hospital of Yunnan, Kunming, China. These images are acquired using a Toshiba Aplio500 ultrasound scanner. Their size is $960 \times 720$ , they have 256 gray levels, and the range of their spatial resolution is 14.2–24.8 pixels/mm. Dataset3 consists of 10 B-mode longitudinal ultrasound images collected from the Yan’an Hospital, Kunming, China. These images are acquired using the Philips ultrasound machine. The sizes of the ultrasound images are either $1024 \times 768$ or $800 \times 600$ . The range of their spatial resolution is 11.8–17.2 pixels/mm, and they have 256 gray levels. Dataset4 consists 32 B-mode longitudinal ultrasound images collected from the Tumor Hospital of Yunnan, Kunming, China. These images are acquired using the Hitachi-Aloka ultrasound machine. Their size is $1024 \times 768$ , they have 256 gray levels, and the range of their spatial resolution is 14.4–23.0 pixels/mm. There are 33 B-mode longitudinal ultrasound images in dataset5, which are collected from the Tumor Hospital of Yunnan, Kunming, China. These images are acquired using the LOGIQ E9 ultrasound machine. The sizes of the ultrasound images are either $800 \times 600$ or $960 \times 720$ . The range of their spatial resolution is 13.20–16.65 pixels/mm, and they have 256 gray levels. Dataset6 consists of 28 B-mode longitudinal ultrasound images collected from the Tumor Hospital of Yunnan, Kunming, China. These images are acquired using the Mindray Resona 7 machine. The size of the ultrasound images is $1260 \times 910$ . The range of their spatial resolution is 16.45–20.10 pixels/mm, and they have 256 gray levels. The textual markers of the collected images require removal. Thus, all images are automatically cropped to a size of $400 \times 400$ . In addition, the experiments for all methods in this study are conducted using MATLAB 2018a, and were tested on ASUS laptop Intel Core i7 machine with 16 GB of RAM.

Methodology

Figure 2 shows the schematic diagram of proposed method, and the details of each block are described as follows.

Image preprocessing

Speckle noise reduction

The primary cause of deterioration in the image quality of carotid ultrasound images is speckle noise.^14,27 Speckle reduction is an important step in the preprocessing of the ultrasound carotid images. In this study, the Nagare’s filter^30,31 is used for speckle noise reduction. This filter is a multi-directional perfect reconstruction filter bank designed with 2-D eigenfilter method, it can suppress the speckle noise via the effective utilization of the good frequency selectivity of the filters. However, almost all the despeckling filters are bound to produce distortion in the image edges.³³ Thus, this step can be omitted for ultrasound images with good image quality and low noise.

Image enhancement

To manage the blurred edges and complicated backgrounds in the filtered ultrasound carotid images, this study introduces an edge enhancement technique for the filtered images. According to the characteristics of the carotid ultrasound images, an improved fuzzy contrast (IFC) method³² can be used to enhance the region of the IMC in blurred carotid ultrasound images. Thus, a filtered image can be mapped to the fuzzy domain:

p_{i, j} = \frac{f_{i, j} - f_{\min}}{f_{\max} - f_{\min}}

(1)

where $f_{i, j}$ is the gray value of a pixel in the filtered image, $f_{\min}$ is the minimum gray value, and $f_{\max}$ is the maximum gray value. The improved fuzzy contrast³² is calculated as follows:

G = \frac{| p_{i, j} - r |}{| p_{i, j} + r |}

(2)

where $r$ is an adapted operator, and the range of $r$ is from 0 to 1. The value of $r$ is crucial for the enhancement of the carotid ultrasound images. In our research, the purpose of the enhancement is to enhance the region of the IMC, and to suppress the regions of the background with many speckles. A lower or higher value of $r$ can’t fulfill the purpose of the carotid ultrasound image enhancement. Based on the characteristics of the carotid ultrasound images, we use $r = 0.25$ for brighter images, and $r = 0.2$ for darker images. Then, we can apply a nonlinear transformation to $G : G^{'} = ψ (G)$ . The nonlinear enhancement function³² can be defined as:

ψ (t) = \frac{1 - e^{- k t}}{1 - e^{- k}}

(3)

where $k$ denotes an adjustment factor, and in this study, $k = 1.2$ . According to the IFC method, the adjusted membership function³² can be expressed as follows:

{p^{'}}_{i, j} = {\begin{matrix} p_{i, j} (1 - G^{'}) & p_{i, j} \leq r \\ 1 - (1 - p_{i, j}) (1 - G^{'}) & p_{i, j} \geq r \end{matrix}

(4)

Finally, the enhanced image can be obtained through inverse transformation.³² The inverse equation is defined as follows:

{f^{'}}_{i, j} = {p^{'}}_{i, j} (f_{\max} - f_{\min}) + f_{\min}

(5)

Region of interest (ROI) extraction

Automatically extracting the region of interest (ROI) from original carotid ultrasound images is very important for the IMT measurement and may affect the performance of subsequent algorithms. In clinical application, the far wall is selected for ROI extraction. Based on the statistics of the IMCs of the carotid ultrasound images, the IMC in the far wall is located below the lumen, and the median gray value of the lumen is 0–5. Furthermore, repeatability and reproducibility of the IMT measurement process are of great signiﬁcance to study the IMT.^19,34 Plaque tends to grow into irregular shapes that are difficult to model analytically, few studies have addressed this issue.¹⁷ Moreover, IMT without plaque remains a significant marker of an increased risk of vascular events and significantly predicts plaque occurrence.⁴ For these reasons, IMT should be measured preferably on the far wall of the CCA within a region free of plaque.^4,19 Assuming that ${IMT}_{p i x e l s}$ is measured in pixels and IMT has units of mm, then ${IMT}_{p i x e l s}$ can be calculated as follows:

I M T_{p i x e l s} = I M T * S R

(6)

Where $S R$ denotes the spatial resolution of the image; in this study, it ranges from 11.8–24.8 pixels/mm. The IMT without plaque is approximately 0.3–1.4 mm. The corresponding number of pixels is approximately 0.3SR–1.4SR. According to the structure characteristics of the IMCs of the carotid ultrasound images (see Figure 1) and the previous researches,³⁵ the gray level of the adventitia is far greater than that of both the intima and lumen, and the gray level of intima is far greater than that of the media. Thus, it can be assumed that the location of the LII in the far wall should meet one of the following two conditions: (a) the mean gray level of the pixels located at 1.4SR pixels under the LII is 1.3 times higher than that of the pixels of the LII; or (b) the mean gray level of the pixels of the LII is 1.3 times higher than that of the pixels located at 0.3SR pixels under the LII. Moreover, the average gray level of the LII is over 30, and the position of the LII in the far wall is below the center of the image. Based on above analysis, the position of the LII can be roughly determined. Then, a superior boundary for the ROI can be fixed to 30 pixels above the LII, and the bottom boundary of the ROI can be fixed to 40 pixels below the LII. Thus, the ROI can be automatically obtained based on the above process.

Manual segmentations

In this study, two vascular doctors performed the manual measurements for the IMT. Each expert (Ex1 and Ex2) made two manual measurements for every image from six datasets spaced at least 20 days apart, implying 624 measurements. Each expert’s result was obtained by averaging the two manual measurements calculated by the expert. A ground truth (GT) was obtained by computing the average of the two experts’ results.

Automatic segmentations

A fully automatic segmentation (AS) approach for IMT measurement using improved Otsu-AWDO is presented in this study. Additional details of the improved Otsu-AWDO are described as follows.

The Otsu’s method and the traditional 2D Otsu’ method

The Otsu’s method²⁹ shows good performance when the histogram of the processed image has two distinct peaks, one belonging to the foreground, and the other belonging to the background.³⁶ Scholars from different fields have been devoted to improving this method, and have proposed many algorithms.^37,38 However, when the images contain significant noise, these algorithms cannot obtain good segmentation results. To overcome the shortcomings of the 1D Otsu’s method, a 2D Otsu’s method has been proposed, with a 2D histogram.³⁹ As compared with the original Otsu’s method, the 2D Otsu’s method has a stronger robustness to noise. This method is introduced briefly as follows. The size of the source image $f (x, y)$ is assumed as $M \times N$ . This image has $L$ gray levels, the definition of its corresponding averaged image $g (x, y)$ is given in the following:

g (x, y) = \frac{1}{l^{2}} \sum_{m = - (l - 1) / 2}^{(l - 1) / 2} \sum_{n = - (l - 1) / 2}^{(l - 1) / 2} f (x + m, y + n)

(7)

The gray level of point $(x, y)$ in image $f (x, y)$ and $g (x, y)$ can be denoted as $i$ and $j$ respectively. Thus, we can obtain a gray level pair $(i, j)$ . Let $f_{i j}$ represents the frequency of the pair $(i, j)$ , and the definition of its joints probability is given in the following:

p_{i, j} = f_{i, j} / N

(8)

In above formula, $N$ represents the total number of pixels, and $\sum_{i = 0}^{L - 1} \sum_{j = 0}^{L - 1} p_{i j} = 1$ . We assumed that there are two classes $C_{1}$ and $C_{2}$ corresponding to the foreground area and background area, respectively, in two-dimensional histogram. As shown in Figure 3(a), the probability of pixels in regions 2 and 3 is negligible, at the same time, the pixels of region 1 are belonged to $C_{1}$ and the pixels of region 4 are belonged to $C_{2}$ . Thus, the probability of $C_{1}$ and $C_{2}$ can be obtained by:

P_{1} = \sum_{(i, j) \in C_{1}} p_{i j}

(9)

P_{2} = \sum_{(i, j) \in C_{2}} p_{i j}

(10)

P_{1} + P_{2} = 1

(11)

The class mean vectors are defined as:

m_{1} = {(m_{1 i}, m_{1 j})}^{T} = {(\sum_{(i, j) \in C_{1}} i p_{i j} / P_{1}, \sum_{(i, j) \in C_{1}} j p_{i j} / P_{1})}^{T}

(12)

m_{2} = {(m_{2 i}, m_{2 j})}^{T} = {(\sum_{(i, j) \in C_{2}} i p_{i j} / P_{2}, \sum_{(i, j) \in C_{2}} j p_{i j} / P_{2})}^{T}

(13)

The total mean vector is obtained by:

m_{T} = {(m_{T i}, m_{T j})}^{T} = {(\sum_{i = 0}^{L - 1} \sum_{j = 0}^{L - 1} i p_{i j}, \sum_{i = 0}^{L - 1} \sum_{j = 0}^{L - 1} j p_{i j})}^{T}

(14)

Based on Equations (9) to (14), Equation (14) is rewritten as:

m_{T} = P_{1} m_{1} + P_{2} m_{2}

(15)

The definition of between-class variance is given in the following:

σ_{b} = \sum_{k = 1}^{2} P_{k} [(m_{k} - m_{T}) {(m_{k} - m_{T})}^{T}]

(16)

The trace of $σ_{b}$ can be used to measure between-class variance, it is obtained by:

t r σ_{b} (s, t) = \sum_{k = 1}^{2} (P_{k} [{(m_{k i} - m_{T i})}^{2} + {(m_{k j} - m_{T j})}^{2}])

(17)

The optimal threshold vector $(s^{*}, t^{*})$ can be given as follows:

t r σ_{b} (s^{*}, t^{*}) = \max_{0 \leq s, t \leq L - 1} {t r σ_{b} (s, t)}

(18)

Improved Otsu’s method

In the traditional 2D Otsu’s method, the gray level of both the original image and the corresponding averaged image can be used to build the 2D histogram. Put another way, this method uses an average filtering algorithm to suppress noise. However, the ultrasound images contain residual speckle noise after the step of the speckle noise reduction. The average filtering algorithm shows good performance for suppressing Gaussian noise, but it shows poor performance for reducing speckle noise. Thus, a median filtering algorithm is used to reduce the speckle noise.⁴⁰ Mathematically, for an input image $I$ size of $m \times n$ , the gray value of an output image $M (x, y)$ at any pixel $(x, y)$ can be obtained by calculating the median of pixels within the $w \times w$ neighborhood in the image.⁴¹ Then, an average image $A (x, y)$ of the median image $M (x, y)$ is obtained by calculating the average of the pixels within the $l \times l$ neighborhood in the median image. The image $A (x, y)$ is called the “median-average image”.⁴¹ Then, the gray levels of both the original image and the corresponding median-average image are used to build the 2D histogram.

He et al.⁴² established a line intercept histogram based on a traditional 2D histogram. This method has good anti-noise properties and robust performance. Inspired by the He’s method, this study uses the gray levels of both the original image and the corresponding median-average image to build the 2D histogram, and a line intercept histogram is established based on the 2D histogram. The description of this method is as follows.

The images used in this study are 8-bit grayscale (256-level grayscale) images. Assuming the number of the gray levels of the original images is $L$ . Thus the value of $L$ is 256. In line intercept histogram, the gray level of a pixel $(x, y)$ in $I (x, y)$ and $A (x, y)$ can be denoted as $i$ and $j$ , respectively. Then, a pair $(i, j)$ for each pixel can be obtained, and $i + j = k$ represents a line perpendicular to the main diagonal, with an intercept of $k$ .⁴² The number of lines is $2 L$ . If $f_{k}$ represents the frequency of the pair $(i, j)$ , its joints probability can be obtained as follows:

p_{k} = \sum_{i + j = k} p_{i j} = \frac{f_{k}}{N}, k = 0, 1, \dots 2 L - 1

(19)

where $\sum_{k = 0}^{2 L - 1} p_{k} = 1$ . Thus, we can obtain the line intercept histogram based on the above procedure. Figure 3(b) shows a 2-D histogram divided into two regions by a threshold line $i + j = T$ $(0 < T < 2 L - 1)$ , and the corresponding regions are $C_{1} : 0 \leq i + j \leq T$ and $C_{2} : T < i + j \leq 2 L - 1$ , respectively.⁴² Therefore, in the line intercept histogram, the upper limit of the gray level is $2 L - 1$ (511). In this study, we extend the above improved Otsu’s method to MT segmentation and the between-class variance for $N$ classes is $σ_{B}^{2}$ . The improved Otsu’s function is given as follows:

σ_{B}^{2} = \sum_{n = 1}^{N} P_{n} {(m_{n} - m_{G})}^{2}

(20)

where $P_{n} = \sum_{k \in C_{n}} p_{k}$ , $m_{G} = \sum_{k = 0}^{2 L - 1} k p_{k}$ , and $m_{n} = \frac{1}{P_{n}} \sum_{k \in C_{n}} k p_{k}$ . Dividing the image into $N$ classes needs $N - 1$ thresholds. Thus, the best intercept threshold values can be obtained by maximizing the $σ_{B}^{2}$ , as follows:

(n_{1}^{*}, n_{2}^{*} \dots, n_{N - 1}^{*}) = \arg \max {σ_{B}^{2} (n_{1}, n_{2}, \dots n_{N - 1})}

(21)

The objective of IMC segmentation is to obtain the LII and MAI using an MT segmentation method. In this study, the pixels in the image need to be separated into four classes, based on three threshold values. Thus, the number of threshold levels is set as three.

Adaptive wind driven optimization (AWDO)

WDO is a new high efficiency evolutionary approach.⁴³ There are two main mathematical equations in the WDO algorithm. One is a velocity update equation, and the other is a position update equation. The velocity update equation is given as follows:

\begin{array}{l} u_{n e w} = (1 - α) u_{c u r} - g x_{c u r} + \\ [R T | \frac{1}{i} - 1 | (x_{o p t} - x_{c u r})] + (\frac{c u_{c u r}^{o t h e r \dim}}{i}) \end{array}

(22)

where $α$ is the coefficient of friction, $g$ is a gravity acceleration vector, $u_{c u r}$ represents the velocity of an air particle in the current iteration, $x_{c u r}$ denotes the current location, and $x_{o p t}$ represents the optimal position. All air particles are sorted in descending order according to air pressure, and $i$ represents the rank of an air parcel. $u_{c u r}^{o t h e r \dim}$ represents the air particle velocity in the current dimension, which can be affected by any other dimension. In addition, $c = - 2 | Ω | R T$ , where $T$ is the temperature, $Ω$ represents the angular velocity vector of the Earth’s rotation, and $R$ denotes the ideal gas constant. The position update equation can be denoted as follows:

x_{n e w} = x_{c u r} + (u_{n e w} Δ t)

(23)

where $x_{n e w}$ is the new position, ∆t represents the time interval, and ∆t = 1. According to Equation (24), the maximum velocity can be used to limit the updated velocity, to prevent an “out of bound” situation during the process of updating the velocity:

u_{n e w}^{*} = {\begin{matrix} u_{\max} & u_{n e w} > u_{\max} \\ - u_{\max} & u_{n e w} < - u_{\max} \end{matrix}}

(24)

where $u_{\max}$ represents the velocity boundary value. As shown in Equation (25), the new positions of the particles are updated by limiting $x_{n e w}$ between $x_{\max}$ and 0. Additional details of WDO are described in.⁴³

x_{n e w} = {\begin{matrix} x_{\max}, & x_{n e w} > x_{\max} \\ 0 & x_{n e w} < 0 \end{matrix}}

(25)

Using WDO for MT image segmentation can produce more effective results than many other methods.⁴⁴ However, the four parameters $α, g, R T$ and $c$ must be set manually. To reduce the complexity of the WDO and select the parameters automatically, a covariance matrix adaptation evaluation strategy (CMAES)^28,45 can be used for the WDO; this new approach is denoted as AWDO.⁴⁵ The CMAES is a population-based iterative global optimization algorithm for a continuous space, and enables automatic tuning of parameters. More descriptions of CMAES approach used for the WDO are available in Pardhu et al.²⁸ and Bayraktar and Komurcu.⁴⁶

Improved Otsu-AWDO for IMC segmentation

AWDO has proven to be more effective for MT problems than other similar methods.^28,45 In this study, the improved Otsu-AWDO is applied to obtain the LII and MAI. Figure 4 shows the step-by-step process of the improved Otsu-AWDO for IMC segmentation.

Remarks:

In step 4, the improved Otsu’s function is used as in Equation (20), that is, to obtain pressure function values for each air parcel. Based on the air pressure values, all air particles are sorted in descending order.

In step 7, to obtain a global optimal solution (global maximum pressure value), we compare each new solution with a corresponding previous solution. If the new solution is better than the previous solution, it is recorded; otherwise, the new solution is discarded, and the previous solution is preserved as it is.

In the penultimate step, after obtaining the three optimal values, the gray levels in the image can be divided into the four gray levels. Then, the LII and MAI can be determined from the demarcation lines of different gray levels. However, owing to the interference of noise in the carotid ultrasound image, the LII and MAI may be detected incorrectly. According to the characteristics of the IMC, the range of IMT without plaque is 0.3–1.4 mm. Based on Equation (6), the range of ${IMT}_{p i x e l s}$ without plaque is 0.3SR–1.4SR. In this step, if the distance between a pixel point in the LII and a corresponding pixel point in MAI is out of the range of ${IMT}_{p i x e l s}$ , the two pixel points are replaced by other adjacent pixel points on the two boundaries. Then, we can obtain the final boundaries (the LII and MAI).

Figure 5 shows the process of the IMC segmentation. Figure 5(a) shows an example of an original image. The corresponding filtered result, enhanced result, ROI image, and segmentation result are presented in Figure 5(b) to (e).

IMT measurement and performance evaluation methods

IMT measurement

In clinical application, the mean absolute distance (MAD) is the main measurement metric for the IMT.⁴⁷

With regard to the MAD, $d_{m e a n}$ can be defined as follows:

d_{m e a n} = \frac{1}{N} (\sum_{i = 1}^{N} Y_{i 1} - Y_{i 2})

(26)

where $N$ represents the number of columns in the LII or MAI (the number of columns in the LII is identical to that in the MAI), and $Y_{i 1}$ and $Y_{i 2}$ are the segmented IMC pixels in the columns. Thus, the $d_{m e a n}$ indicates the mean of IMT ( $I M T_{m e a n}$ ).¹⁴

Performance evaluation of automated segmentation methods

The performance evaluation metrics of the AS methods are calculated as follows.

The Pearson R-correlation coefficient¹⁶ and the absolute error¹⁸ of the AS measurements with GT data are calculated as follows:

R = \frac{\sum_{i = 1}^{L} (A S (i) - a s_{m e a n}) (G T (i) - g t_{m e a n})}{\sqrt{\sum_{i = 1}^{L} {(A S (i) - a s_{m e a n})}^{2}} \sqrt{\sum_{i = 1}^{L} {(G T (i) - g t_{m e a n})}^{2}}}

(27)

\begin{matrix} ε (i) = | A S (i) - G T (i) | & i = 1, \dots L \end{matrix}

(28)

where $A S (i)$ and $G T (i)$ are the values of IMT of the $A S$ and the $G T$ for the $i$ th case, respectively. Furthermore, $a s_{m e a n}$ and $g t_{m e a n}$ are the mean IMT values of the AS and GT, respectively. $L$ denotes the number of cases for the IMT measurement. A value of R closer to 1 indicates a higher quality of the IMT measurement for the automatic method. Moreover, a lower value of the absolute error indicates a better performance of the automatic IMT measurement. The coefficient of variation (CV%)¹⁴ can be obtained as follows:

C V = \frac{I O E}{I M T_{m e a n}} \times 100

(29)

where $I M T_{m e a n}$ is calculated using the MAD metric. The $I O E$ ¹⁴ is the inter-observer error, and is estimated as follows:

I O E = \frac{σ_{I M T}}{\sqrt{2}}

(30)

where $σ_{IMT}$ represents the standard deviation of the IMT measurements.

Statistical analysis

A Bland–Altman’s plot,⁴⁸ regression analysis plot,¹⁴ and boxplot^11,14 are used for the statistical analysis of the IMT measurements. Other statistical data, such as the average $I M T_{m e a n}$ values, mean execution time, and mean absolute error are required.

Results

Performance of manual segmentations

The two experts’ results (Ex1-Ex2) are shown in Table 1. The average $I M T_{m e a n}$ values of the two experts’ results are 528.0 ± 110.1 μm and 528.9 ± 110.3 μm, respectively. The average $I M T_{m e a n}$ of the GT is 528.4 ± 110.1 μm.

Table 1.

Average $I M T_{m e a n}$ Values (mean ± std in μm), Mean Bias, CV-coefficient Variation, R-Correlation Coefficient, Mean Execution Time and Absolute Error (mean ± std in μm) of Automatic Measurements and the Manual Measurements for 156 Carotid Ultrasound Images.

	Average $I M T_{m e a n}$ (μm)	Bias	CV%	R	Execution Time (s/image)	Absolute Error (μm)
Ex1	528.0 ± 110.1	_	14.745	_	_	_
Ex2	528.9 ± 110.3	_	14.746	_	_	_
GT	528.4 ± 110.1	_	14.734	_	_	_
Otsu-WDO	451.7 ± 138.7	−0.0768	21.713	0.8357	2.66	87.6 ± 63.7
Otsu-AWDO	463.3 ± 135.9	−0.0651	20.742	0.8469	2.61	75.9 ± 60.9
Improved Otsu-WDO	527.1 ± 110.7	−0.0014	14.850	0.9910	2.73	11.2 ± 9.8
Improved Otsu-AWDO	529.1 ± 111.5	0.0007	14.901	0.9922	2.71	10.1 ± 9.6

Performance of automatic segmentations

To reflect the superiority of the proposed method, performance tests for the proposed algorithm are implemented using 156 carotid ultrasound images. Furthermore, other algorithms such as Otsu-WDO,²⁷ Otsu-AWDO,²⁸ and the improved Otsu’s method proposed by this study as combined with WDO (improved Otsu-WDO) are compared with the proposed algorithm. All the steps of preprocessing (such as speckle noise reduction, image enhancement, and ROI extraction) are identical for these algorithms. According to the characteristics of the carotid ultrasound images in six datasets used in this study, the upper limit of the gray level in the line intercept histogram is $2 L - 1$ (511). Thus, the maximum position value in proposed approach is set as 511. Furthermore, the values of the maximum number of iterations, maximum allowed velocity, number of threshold levels, and population size in proposed approach are set as 70, 0.3, 3, 60, respectively. The performance of the proposed method with these parameters has been verified using IMT measurement experiments. In the Otsu-WDO approach, the four parameters $α, g, R T$ and $c$ for the velocity update equation can be set to 0.4, 0.2, 3, and 0.4, respectively.²⁷ Furthermore, the population size, maximum number of iterations, maximum position value, maximum allowed velocity and number of thresholds are set as 50, 100, 255, 70, and 3 respectively. The process of improved Otsu-WDO is similar to improved Otsu-AWDO. The maximum number of iterations, the population size and maximum position value in the improved Otsu-WDO are set as 200, 20, and 511, respectively. Other parameters about WDO in improved Otsu-WDO are the same as that in Otsu-WDO. The maximum position value in Otsu-AWDO is set as 255. Other parameters about AWDO in Otsu-AWDO are the same as that in improved Otsu-AWDO.

Figure 6 shows the segmentation results of different methods for a carotid ultrasound sample image. Figures 6(a) to (d) show the manual delineations performed by the two experts. The Otsu-WDO and Otsu-AWDO methods appeared to result in distorted edges (see Figures 6(e) and (f)). The improved Otsu-WDO method and proposed algorithm produced good edge detection (see Figures 6(g) and (h)). Moreover, Figure 7 shows some other examples of segmentation results.

Table 1 lists the average $I M T_{m e a n}$ values of the different segmentation methods as measured using the MAD metric. When comparing the average $I M T_{m e a n}$ values of Otsu-WDO (451.7 ± 138.7 μm), Otsu-AWDO (463.3 ± 135.9 μm), and improved Otsu-WDO (527.1 ± 110.7 μm), the improved Otsu-AWDO (529.1 ± 111.5 μm) is found to be closer to the GT (528.4 ± 110.1 μm).

For the purpose of validating the accuracy of the automatic measurement, we need to obtain the average LII/MAI tracings for each image, and to compute the bias between the automatically and manually measured $I M T_{m e a n}$ values. Figure 8 depicts Bland–Altman plots for comparing the Otsu-WDO, Otsu-AWDO, improved Otsu-WDO, and improved Otsu-AWDO approaches with the GT measurements. The mean bias of improved Otsu-WDO (–0.0014) is comparable to improved Otsu-AWDO (0.0007) and is significantly lower than that of the Otsu-WDO (–0.0768) and Otsu-AWDO (–0.0651). As compared with the CV values of the Otsu-WDO (21.713 %) and Otsu-AWDO (20.742 %), the improved Otsu-WDO (14.850 %) and improved Otsu-AWDO (14.901 %) are closer to the GT (14.734 %), as shown in Table 1. Figure 9 shows regression analysis plots depicting the $I M T_{m e a n}$ values of Otsu-WDO, Otsu-AWDO, improved Otsu-WDO, and improved Otsu-AWDO with respect to the GT. Among the four methods, the proposed method achieved the highest value of R (0.9922), as compared with the Otsu-WDO (0.8357), Otsu-AWDO (0.8469), and improved Otsu-WDO (0.9910) methods. Figure 10 reports the distribution of the calculated data using box plots. The interquartile range (IQR) value of improved Otsu-AWDO (0.1813 mm) is closer to that of the GT (0.1816 mm) than it is to that of Otsu-WDO (0.1942 mm), Otsu-AWDO (0.1898 mm), and improved Otsu-WDO (0.1804 mm). Moreover, when comparing the median values (MV) of Otsu-WDO (0.4437 mm), Otsu-AWDO (0.4553 mm), and the improved Otsu-WDO (0.5191 mm), the proposed method (0.5217 mm) is found to be closer to the GT (0.5254 mm).

To quantitatively evaluate the complexity of the four algorithms, we assumed that the four algorithms performed a complete procedure including four steps (speckle noise reduction, image enhancement, ROI extraction, IMC segmentation). Table 1 shows the average execution times for the four algorithms. The average execution times of improved Otsu-AWDO (2.71 s/image), improved Otsu-WDO (2.73 s/image), Otsu-AWDO (2.61 s/image), and Otsu-WDO (2.66 s/image) were roughly equivalent. Table 1 presents the absolute error for the IMT in the automatic measurements and manual measurements for the 156 carotid ultrasound images. It can be seen that the mean absolute error of improved Otsu-AWDO (10.1 ± 9.6 μm) is lower than that of Otsu-WDO (87.6 ± 63.7 μm), Otsu-AWDO (75.9 ± 60.9 μm), and improved Otsu-WDO (11.2 ± 9.8 μm).

Discussions

The objective of this study is to propose a fully automatic technique for IMT measurement in carotid ultrasound images. To reflect the superiority of the proposed approach, the proposed approach was compared with other similar existing approaches, such as Otsu-WDO and Otsu-AWDO. Furthermore, to further validate the superiority of improved Otsu-AWDO, an improved Otsu’s method combined with WDO (improved Otsu-WDO) was also used for comparison with the proposed approach. Figure 6 shows the segmentation results from the different methods. The results of Otsu-WDO and Otsu-AWDO include distorted edges (see Figures 6(e) and (f)), as they are sensitive to the speckle noise. In contrast, the results of improved Otsu-WDO and improved Otsu-AWDO show good performances (see Figure 6(g) and (h)), owing to their strong robustness to noise. The proposed approach can obtain good performance in different cases (see Figures 5(e), 6(h), and 7). This happens because the proposed method has strong robustness to the orientation and appearance of the CCA in the ultrasound images (i.e., slope and curvature).

To objectively evaluate the accuracy of the IMT measurement, several objective evaluation metrics are used to evaluate the different methods. Figure 8 shows the Bland–Altman plots⁴⁸ of the average versus the difference in the $I M T_{m e a n}$ values between the GT and automatic measurements. The mean biases of improved Otsu-WDO and improved Otsu-AWDO are evidently lower than those of Otsu-WDO and Otsu-AWDO (see Figure 8), indicating that the results of improved Otsu-WDO and improved Otsu-AWDO are closer to the GT data. Figure 9 reflects the correlations between the manual and automated $I M T_{m e a n}$ values for all methods. The proposed method achieved the highest R-correlation coefficient. In other words, the proposed method presents the highest correlation with the GT data. As seen in Figure 10, box plots are used to present the distributions of $I M T_{m e a n}$ values. The comparative results show that the IQR of improved Otsu-AWDO is closest to that of the GT, and the MV of the proposed method is closest to that of the GT. Table 1 presents the absolute errors between the automatic measurements and GT data. The proposed approach achieved the lowest absolute error value of all approaches. As can be seen in Table 1, the average $I M T_{m e a n}$ value of improved Otsu-AWDO is the closest to that of the GT as compared with those of Otsu-WDO, Otsu-AWDO, and improved Otsu-WDO. Furthermore, the CV values of the improved Otsu-AWDO and the improved Otsu-WDO are closer to the GT than the other two approaches. Thus, we can conclude that the IMT estimations of improved Otsu-AWDO are more accurate than those of the other similar methods.

Many studies regarding IMT measurements have been reported in recent years. An advanced method named as CALEXia was proposed by Molinari et al.¹² in 2010. In 2012, Xu et al.⁸ proposed a semi-automatic technique that used a Hough transform and a dual snake model to measure the IMT. In this work, a leak of weak edges could be avoided by using a robust initialization, and the sub-accuracy could be achieved with a search of the local minimum in a continuous space.⁸ An automatic method for segmenting the IMC in carotid ultrasound images using active contours was proposed by Petroudi et al.¹⁰ in the same year. Furthermore, an automatic approach named as CAMES was proposed by Filippo Molinari et al.¹³ in 2012. In 2014, Menchón-Lara et al.¹⁸ used a neural network method to estimate the IMT. In 2015, Bastida-Jumilla et al.¹¹ used an automated approach to measure the IMT based on a frequency-domain implementation of the active contours, providing higher efficiency than semi-automatic methods. In the same year, Lu Xiao et al.¹⁶ proposed an automatic method for finding the LII and MAI based on Markov random field models. Menchón‑Lara et al.¹⁹ proposed an automatic method in 2015 that used a machine learning technique and a statistical pattern recognition method to measure the IMT. In 2016, Li H et al.¹⁷ used a curvelet-guided ant colony optimization strategy for IMT measurement, and showed good robustness to noise. In 2018, a fast automatic IMC segmentation technique based on a structured random forest was proposed by Nagaraj et al.¹⁴

Table 2 summarizes the results from the proposed method and the previous methods. N in Table 2 represents the number of images used for IMT measurements. Although the R value of Li’s method (0.9920) is close to that of our method (0.9922) and the R values of this two methods are substantially higher than other methods, the IMT error of the proposed method (10.10 ± 9.60 μm) is significantly lower than that of Li’s method (41.00 ± 36.00 μm), and is the lowest of all of the methods.

Table 2.

The Comparison Results Between Previous Methods and Proposed Method (All data of Previous Methods Come From the Published Paper).

Method	N	Year	R	Error_IMT (μm)	Execution Time (s/image)	Automatic
Molinari et al.¹²	182	2010	_	54.00 ± 35.00	3.00	Yes
Xu et al.⁸	50	2012	0.9900	38.10 ± 16.40	0.46	No
Petroudi et al.¹⁰	100	2012	_	95.00 ± 61.50	21.00	Yes
Molinari et al.¹³	365	2012	0.9000	78.00 ± 112.00	<15.00	Yes
Menchón‑Lara et al.¹⁸	60	2014	0.9817	37.63 ± 25.18	3.44	Yes
Bastida-Jumill et al.¹¹	46	2015	0.9901	13.80 ± 31.90	12.20	Yes
Xiao et al.¹⁶	80	2015	0.9810	24.40 ± 22.70	1.70	Yes
Menchón‑Lara et al.¹⁹	55	2015	0.9332	49.90 ± 49.80	1.40	Yes
Li et al.¹⁷	224	2016	0.9920	41.00 ± 36.00	2.63	Yes
Nagaraj et al.¹⁴	70	2018	0.9295	_	0.47	Yes
Proposed method	156	2020	0.9922	10.10 ± 9.60	2.71	Yes

The proposed method still has limitations. First, the average execution time of the entire procedure (including speckle noise reduction, image enhancement, automatic ROI extraction, and IMC segmentation) was 2.71 s/image, which was longer than some of the previous automatic methods (see Table 2). The average time cost of the speckle noise reduction procedure (Nagare’s filter) was 1.98 s/image. Thus, we need to reduce the complexity of the algorithm, by finding a higher quality and more efficient despeckling filter. Moreover, in the step of IMC segmentation, a median filtering algorithm is used to overcome the sensitivity of the traditional 2D Otsu’s method to the speckle noise in ultrasound images. To further improve the performance of the IMC segmentation method without increasing the time complexity, future work will develop a new filter to replace the median filtering algorithm in the improved Otsu-AWDO. Moreover, in the IFC method, we use $r = 0.25$ for brighter images, and $r = 0.2$ for darker images. To further improve the adaptability of the algorithm, a new image enhancement algorithm based on adaptive parameter selection needs to be developed to replace the IFC method in the future. Furthermore, the proposed approach is used for extracting two nearly parallel boundaries (LII and MAI), for which reason its effectiveness for plaque may be limited. However, because plaque has irregular shapes that are difficult to model analytically, few studies have addressed this issue.¹⁷

Another possible limitation concerns the limited number of tested carotid ultrasound images in this work. Only six datasets of carotid ultrasound images were available for validating the performance of the proposed method. In future research, additional carotid ultrasound images from different ultrasound machines should be tested to further validate the clinical application value of the proposed method.

Conclusions

In the present study, an improved Otsu-AWDO method is proposed for estimating the IMT from carotid ultrasound images. In a step of preprocessing, a Nagare’s filter is used to address the noise in the carotid ultrasound images, and then the IFC method is used to enhance the blurred edges in the filtered images. According to the structural characteristics of the CCA in each ultrasound image, we use a new automatic method to extract the ROI from each carotid ultrasound image. The main stage of the proposed method is a segmentation stage. We propose an improved Otsu’s method for improving the robustness to speckle noise (to thereby improve the robustness of the Otsu-AWDO). First, we build a 2D histogram, based on an image and the corresponding median-average image. Then, we establish a line intercept histogram based on the 2D histogram. Finally, the best intercept threshold from the histogram is obtained based on the Otsu criterion. The improved Otsu’s method combined with the AWDO (improved Otsu-AWDO) is used to segment the IMC.

The proposed technique was tested using six datasets of 156 carotid ultrasound images. The IMT measurements using the proposed method were compared with values obtained from other similar methods. Quantitative metrics such as the absolute error, R-correlation coefficient, mean bias, and average $I M T_{m e a n}$ values prove the improved performance of the proposed approach. Thus, we conclude that the proposed approach is a potential alternative to the previous approaches for IMT measurement.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Grants (81771928 and 61761046) from the National Natural Science Foundation of China.

ORCID iDs

Kun Wang

Yuanyuan Pu

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