Automatic Left Ventricular Endocardium Detection in Echocardiograms Based on Ternary Thresholding Method Wataru Ohyama*, Tetsushi Wakabayashi*, Fumitaka Kimura*, Shinji Tsuruoka*, Kiyotsugu Sekioka** *Faculty of Engineering, Mie University, Tsu, Mie, 514-8507, Japan **School of Medicine, Mie University, Tsu Mie, 514-0001, Japan
[email protected] Abstract Methods for automatic detection of left ventricular endocardium in echocardiograms are required to quantitatively evaluate the functional performance of the left ventricle. This study proposes a new automatic detection method based on ternary thresholding method for echocardiograms. Two thresholds are determined by the discriminant analysis for the gray level histogram so that the input image is segmented into three regions, i.e. cardiac cavity (black region), near epicardium (white region) , and the rest (gray region). Then the input echocardiogram is binarized with the lower threshold (between black and gray) to detect the cardiac cavity. The binary images are contracted n times to remove small regions and to disconnect the region of cardiac cavity from the other false regions. Among the obtained regions which corresponds to the cardiac cavity is selected and dilated 2n times to create a mask which restricts the region of the second thresholding operation. The masked image of each frame is binarized with another threshold determined by the discriminant analysis in the restricted area. Results of the evaluation test showed that the accuracy of the extracted contours was favorably compared with the accuracy of manually traced contours.
1. Introduction The ultrasound systems are widely used for functional evaluation of heart because of the portability and the noninvasive real time visualization capability of internal structure. Several methods for automatic extraction of left ventricular endocardium in echocardiograms have been proposed, which are required to quantitatively evaluate the functional performance of the left ventricle[1, 2, 3, 4, 5, 8]. Although the ultrasound systems with real time endocardium detection function are commercially available [6], there is still a room for further improvement in
(1) automatic control of some parameters such as gain and threshold, (2) detection of the endocardium behind the inner wall structure such as papillary muscle, and (3) detection of endocardium as closed continuous curve. In principle, the simplest way for the endocardium detection is to binarize the echocardiograms to detect the cardiac cavity. However, considerable image processing techniques have to be preformed before and after the binarization to correctly detect the endocardiums because the SN ratio of echocardiograms are generally low [5]. The authors proposed a double thresholding method and experimentally showed the effectiveness [8]. The method consists of two thresholding operations, one for restricting the location of the cardiac cavity, and the other for final endocardium detection in the restricted region. This paper proposes a new double thresholding method which employs the discriminant analysis based ternary thresholding method to determine the first threshold.
2. Ternary Double Thresholding Method (TDTM) Fig.1 shows the flowchart of the automatic endocardium detection. The process consists of the three parts: (1) noise suppression by mean filtering across frames of ultrasound image sequence, (2) ternary thresholding and mask generation for restricting the location of cardiac cavity, and (3) binarization of the ultrasound image in the restricted region. Each part is described in the following subsection.
2.1. Noise suppression The echocardiograms contain considerable speckle noise, which is harmful for the endocardium detection. To suppress the noise, the mean of two adjacent frames is repeatedly taken four times:
fk( m ) (i,
1 ( m −1) j) = fk +1 (i, j ) + fk( m −1) (i, j ) 2
{
}
(1)
where k is the number of frame, m is the number of repetition, and fk( 0 ) (i, j ) is the value of (i,j) pixel of the input image. Hereafter the noise suppressed image is simply denoted by Fk = { fk (i, j )} omitting the superscript.
Fig.2 (a), (b) show an example of typical ultrasound image and its gray scale histogram, respectively. Fig. 3 and Fig.4 show the results of binary and ternary quantization based on the discriminant analysis for the gray scale histogram respectively [7]. Two thresholds t1 and t2 which maximize the betweenclass gray scale variance
where (-) denotes morphological contraction, and 1 1 1 H = 1 1 1 1 1 1
(5)
Echocardiograms Noise Suppression
First Thresholding (Ternary)
3
∑ ω j (µ j − µ T ) 2
(2)
j =1
are used for the ternary quantization, where ω j , µ j and µ T are a priori probability of class j, the average gray scale of class j, and the total average gray scale, respectively. Since the echocardiograms generally contain three regions, i.e. the cardiac cavity (black region), rear epicardium (white region), and the rest (gray region), the ternary quantization is more reasonable than binarization, and it generates a quantized image which reflects the physical structures of input image adequately. The result of ternary quantization can be utilized to detect a part of epicardium as well as the endocardium.
Mask Generation for Left Ventricular Detection Mask
Second Thresholding (Binary) Contour of Left Ventricular Endocardium Fig. 1 Flowchart of Extraction of Left Ventricular
2.4. Mask generation for region restriction Two thresholds t1 , t2 (t1 < t2 ) are determined so that the noise suppressed image Fk is segmented into three regions. To detect the region corresponding to the cardiac cavity the image is binarized by the lower threshold t1 . 0 bk (i, j ) = 1
( fk (i, j ) > t1 ) ( fk (i, j ) ≤ t1 )
(3)
Then the binary image Bk = {bk (i, j )} is contracted n times to remove small regions, and to disconnect the region of cardiac cavity from other false regions, i.e.
(4)
n times
is the structuring element.
2.3. Ternary thresholding for ultrasound image
σ 2B (t1 , t2 ) =
Bk- = (L (( Bk ( − ) H )( − ) H ) L ( − ) H ) 144444244444 3
(a) Ultrasound image
black
white
(b) Gray scale histogram of ultrasound image Fig.2 Example of typical ultrasound image and its gray scale histogram
Among the multiple regions in the Bk- the one which corresponds to the cardiac cavity is selected and dilated 2n times to create a mask Mk which restricts the region of the second thresholding operation. The size and the location of the cardiac cavity in the preceding frame are utilized to select the corresponding region. The sequence of masks is contracted and dilated in time domain to correct abrupt deformation of the masks due to inappropriate threshold selection. Fig.5 shows examples of the images imposed with the masks. The region of low contrast in each figure is the masked region.
Fig. 3 Binary image of Fig.2(a)
(a) first thresholding
Fig. 4 Ternary image of Fig.2(a)
(a)
(b)
(c) (d) Fig. 5 Left ventricular image imposed with mask
(b) second thresholding Fig. 6 By first and second thresholding extracted endocardial contour
The masked image of each frame is binarized again in the same way as in the first thresholding operation.
3. Evaluation test Total of 867 left ventricle short-axis echocardiographic images (for 15 cases) acquired with an ultrasound system (HitachiMedico EUB565A) were used to evaluate the accuracy of the automatic endocardium detection. The parameter n for contraction/dilation operations was set to 5 in the experiment. Fig.6(a) and (b) show the example of extracted endocardial borders by the first and the second thresholding operation, respectively. While the tangential contours to the ultrasound beam are not correctly extracted by the first thresholding operation due to the reduced signal amplitude, they are correctly extracted by the second thresholding operation in the restricted area. The automatically detected endocardium was compared with the manually traced one in the same echocardium to evaluate the accuracy of the proposed method. The correlation coefficients of two distances from the centroid of the cardiac cavity to each endocardium was used as the measure of the accuracy evaluation (Fig.7). The correlation coefficients for the cases: (1) manual trace by the same person A (2) manual trace by two person A, B (3) automatic detection and manual trace by person A (4) automatic detection and manual trace by person B were (1) 0.983( 0.011), (2) 0.967( 0.022), (3) 0.962(0.018), and (4) 0.942(0.028) . Fig.8 (a),(b) show the scatter diagrams of the case (1) and (3) respectively. This result shows that the accuracy of the automatic extraction is favorably compared with the accuracy of the manual trace. bi ai ||bi - c||
[pixel]
||ai - c|| c
(pixel) 120
120
100
100
80
80
60
60
r2 = 0.985
40
40
r2 = 0.964
20 2 0 4 0 6 0 8 0 100 120
20 2 0 4 0 6 0 8 0 100 120
(a) Intra observer
(b) Computer vs. observer
(pixel)
Fig.8 Scatter diagrams
4.Conclusion We proposed a new method of automatic endocardium detection by ternary double thresholding operation. The result of evaluation test showed that (1) the tangential contours to the ultrasound beam were correctly extracted by the double thresholding operation, and that (2) the accuracy of the automatic detection was favorably compared with the accuracy of the manually trace. The proposed method has characteristics such that (1) it is less dependent on the intensity and the contrast of the input images since it employs the threshold determination method based on the discriminant analysis of the gray scale histogram, (2) it is suitable to high speed parallel processing and hardware implementation since it is mainly composed of simple local operations for thresholding and contraction/dilation. Further studies on (1) performance evaluation using more images, (2) improvement of success rate of automatic extraction, (3) application to the quantitative evaluation of the left ventricle functional performance, and (4) application of the ternary thresholding to the epicardium detection are remaining as future research topics.
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References Contour A
Contour B
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Fig.7 Generation of the scatter diagram for two contours
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