An automatic method to determine mitral annular lines ...

Proceedings of the 22"d Annual EMBS International Conference, July 23-28, 2000, Chicago IL.

An Automatic Method to Determine Mitral Annular Lines From 2D + ID Precordial Echocardiogram Yu-Shen Liu, Yu-Tai Ching Department of Computer and Information Science National Chiao Tung University Shyh-Jye Chen Department of Radiology National Taiwan University Abstract We present a method to determine the sequence of mitral . annular lines in 2D + 1D precordial echocardiogram. We first use the optical flow technique a 2-means algorithm to determine a set of possible mitral annular points. A pair of mitral annular points could form the mitral annular line. The problem to determine the sequence of mitral annular lines in 2D + 1D echocardiogram is modeled as a problem to find the shortest path in a graph. The proposed method need very few user inputs. Experimental results show that we can find accurate mitral annular lines. Keywords: Precordial Echocardiography, Left Ventricle, mitral annular line, single-adaptive filter, optical flow, combinatorial optimization. I. INTRODUCTION

Since 3D + ID Echocardiogram is available, it is possible for us to calculate volumes of left ventricles so that we can evaluate the ejection fraction. There are two techniques to inquire echocardiogram, the Transesopharygeal Echocardiography and the Precordial Echocardiography. Precordial Echocardiography is a much easier technique in the imaging process to both the physicians and the patients. In this paper, we present a method which calculates the mitral annular line from a set of 2D + ID Precordial Echocardiogram with very few user inputs. This is a work toward designing an automatic method to calculate volume of the left ventricle from Precordial Echocardiogram. Image segmentation in an ultrasound image is a very difficult task. To extract the left ventricle from a Precordial Echocardiogram is even more difficult due to the following problem. Left Ventricle (LV) and Left Atrium (LA) become one chamber in the image when mitral valve totally opens. A physician can separate these two chambers by finding the mitral annular line using user interface manually. However, there are hundreds echocardiograms in a set of 3D t ID ultrasound images, user interface becomes infeasible. In this work, we present an automatic method to identify a sequence of mitral annular lines in a set of 2D + ID Precordiac Echocardiogram. Our approach uses optical flow 11-51 ,2-means algorithm and combinatorial optimization [8] techniques to determine a sequence of mitral annular line.

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We used the optical flow technique and 2-means algorithm to detect a set of points that could be on the mitral annulus. The mitral annular line connects a pair of such points. The problem to determine a sequence of mitral annular lines is modeled as a problem that finding the shortest path in a graph. The proposed method needs very few user inputs. We only needto input a point that shouldbe close to the center of the left ventricle. In the next section, we describe the proposed method. We shall present the results obtained using the proposed method in section 111. 11. METHODS

There are three steps in the proposed method. The first is the preprocessing step in which we use the single-adaptive filter to reduce the speckle noise. The optical flow technique is then applied to determine the correspondence between points in a pair of consecutive images. Since we are looking for the mitral annulus that generally has higher echogenecity, we use a two-means algorithm to identify those points. -Pair of such points determines the mitral annular line. To calculate the sequence of mitral annular lines is modeled as a combinatorial optimization problem, i.e., finding the shortest path in a graph. We describe each step in the following. (A) Preprocessing We use a single-adaptive filter [6] to reduce the speckle noise first. The single-adaptive filter, which does not like the Mean Filter to smooth all signals in the image, abates noise and strengths the signal of the area having similar intensity [7]. Suppose that the area is a window Wof size N x N around pixel (kJ) . The output of the filter denoted i(k,I) is obtained using the following equation, i(k,1) = h ( k ,I) + P ( k ,I)[x(k,I) - iM' (k,I)] .

In the above equation, x ( k , l ) is the intensity of pixel (k,I).

is the local estimation for the original signal (k,Z). And the value ofP(k,I) which is ranged over [0,1] is given by

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Proceedings of the 22"dAnnual EMBS International Conference, July 23-28,2000, Chicago IL.

If P ( k , l ) = 0 , the noise of this point will be altered by local observation

(B) Opticalflow Optical flow is a technique to match the point between pairs of consecutive images. If we take the time between two images as a unit, then optical flow is used to estimate the velocity. Assume that the image brightness are stationary with respect to time. For a point p in the original image, the optical flow technique is used to determined the corresponding pointp ' in the next image as the following. We first set up a (2n+l) by (2n+l) window Wp around the pointp and a (2N+1) by (2N+1) window Ws as the search area ofp. Ws must cover the location ofp'. We then estimated the s u m of square differences (SSD), denoted E, (U,V ) , for every point in Ws as the following equation. E, (U,v ) =

cC n

n

i=-n

j=-n

[ ~ ( x+ i, y

+ j,t ) -

~(x+ U + i, y

+ v + j , t + I)]'

. -N I u , v N ~. Then we get the probability mass function R, (U,v)= e-Ec(u,v) where k is a constant close to zero (0.001). Having defined the probability mass function. The expected velocity U,, = (U,,, v,) is estimated as the follow,

Because the velocities of pixels closer t o p are likely to have the same velocity as the pixels far away from p, we apply a weighting function, R,, to the velocity. Rn is inversely proportional to the distance top. The revised velocity

algorithm to identify such points. Furthermore, let 0 be a point in the center of left ventricle, mitral annular points can only below the point 0. Thus we can consider only the points below 0 and divide these points by a vertical line passing through 0 into two sets. The point sets to the left and to the right of the vertical line are denoted L and R respectively. The means of the velocities of these two sets are LV and RV. (C) Find the sequence of mitral annular lines Suppose that there are r images in a set of 2D + 1D echocardiogram. For each image, WI: calculated the two sets of points Li and Ri, i=l . .. r, and the rnean velocities Lvi and Rvi. Consider an image i. A point in Li and a point in Ri form a line that could be the mitral miular line. Let among these lines be the mitral annular line. Suppose p141 is the mitral annular lines in the next image.

3 2 should be similar to LM and R E , i.e.,

and The vector the length of v,

(3- (2-

v= LV)+ R V ) (1) should be small. We now present the way to model the problem as a graph. Given Lvi and Rvi, i=l ...n, we construct a graph G = (V,E) that 1. Let V = U V,, i=I ...I: Each vertex in V,corresponds to a line connecting a point in Li andl a point in Ri, i=l ... r. Every vertex in V,has a weighied edge to a vertex in 2. V,+I. The weight is given as the sum of the absolute values of x component and y component of v in eq. (1).

Given the graph G, we find the shortest path passing through vertices in VI to Vr, Since each vertex on the cycle corresponds to a line. The shortest cycle corresponds to the sequence of miral annular lines in a cardiac cycle.

:y VI

U = ( i l , ~is )

vz

.................................... 0

: v 3 -

Vr-I

Vr

Figure- 1 A graph G, each vertex in R has weighted edges to all the vertices in K+,. Vertices on the shortest path corresponds to the sequence of mitral annular lines.

The true velocity is obtained using an iterative method. The velocity of n+lst interation is given by the equation. un+l =1 s:; + S;l lS;;ucc+ S ; V where S, is the conservation error and Snis the neighborhood error in [ 5 ] . The algorithm iterates until difference between two successive velocities is smaller than a given threshold value. Since we already know that the mitral annular points are on the demarcation of fat and muscle. Fat and muscle generally have higher echogenecities. We use a 2-Means

J

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111. RESULT The proposed method has been tested on many set of 2D + 1D Precordial Echocardiogram. There are generally 25 to 30 images in a cardiac cycle. The only way to verify the correctness of the results obtained by the proposed scheme is perceptional judgment. In Figure 2, (a) and (b) are the original images and (a') and (b') are respectively the results after the mitral annular line were iden1:ified. Figure 3 shows the animation of one set of images containing the mitral annular lines. The Ws and Wp were respectively 21 and 3.

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Proceedings of the 22”‘ Annual EMBS International Conference, July 23-28,2000, Chicago IL.

All the user inputs is a single point 0 in the center of the left ventricle.

PI G.E.Mailloux, A. Bleau, M. Bertrand, and R. Petitclerc, “Computer Analysis of heart motion from two-dimensional Echocardiograms,” IEEE Tms. Bio. Engineering, pp. 356-364, vol. BME-34, May. 1987. [4] 1. Mikic, S. Krucinski, and J. D. Thomas, “Segmentation and tracking in Echocardiographic sequences: Active Contours guided by optical flow estimates,” IEEE Trans.Med. Jmag., pp. 274-284, vol. 17, 1998. [SI A. Sin& ”Optical flow Computation: A Unified perspective,” Los Alamitos, CA:IEEE Comput. Soc., 1991 [6] M. G. Strintzis, X. Magnisalis, C. Kotropoulos. 1. Pitas, and N. Maglamas, ”Maximum likelihood signal-adaptive filtering of speckle in ultrasound b-mode images,” in hoc. IEEE Engineering Medicine Biology Society Conf. (EMBS ’92), Paris, France, Nov. 1992.

[7] S.Malassiotis and M. G. Strintzis, “Tracking the left ventricle in Echocardiographic images by leaming heart dynamics,” IEEE Trans. Med. Imag. ,vol. 9, pp. 282-290, Mar. 1999. [8] T.Corman, C. Leiserson, R. Rivest, “Introduction to Algorithm‘’, M.I.T. press. 1989.

Fig2 (a) is the original segmentation of 18” Echo image of the sequence, and @) is the 23“. LA can be excluded as Fig 2 (a’) and @’) if segment with the result of this approach .

Fig3 the animation of one set of images containing the mitral annular line.

REFERENCES ..

[I] B. K P. Horn and B. G. Schunck, ‘Deter”g optical flow,” Artificial Intell., vol. 17, pp. 185-203, 1981. [Z] A. D. Bimbo, P. Nesi, and J. L. C. Sam, “Optical flow Computation using Extended Constraints,” IEEE Trans.Jmag. Roc.,pp. 720-739, vol. 5, May. 1996.

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