3D motion analysis of MR imaging using optical flow method

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1995 IEEE-EMBC and CMBEC Theme 2: Imaging

3D Motion Analysis

of MR

Imaging

Using Optical Flow Method

Siaw-Hwa Huang,

Shu-Tzu

Wang, Jyh-Horng Chen

.

Electrical Engineering, National Taiwan University, Taipei, Taiwan, R0.C.

Purpose

Optical flow is the velocity disbn’bution of each pixel in an image. In this paper, we extend 2D optical flow method to 3D optical flow analysis and also improve its performance around

boundary. Dynamic Analysis of heart and knee is under rotation and contraction.

investigation. Result Display To

Introduction distribution, we overlay

between the variation of the gray level gradient and the velocity of each pixel in the whole image[ 11.

E%$+Eyv+Et=o

,

while the gray level distriiution of the static background is: The motion we simulate includes,

The optical flow constraint equation

each pixel.

Cine

Study Short axis

view

of left ventricle is imaged using gated Cine sequence with GE 1.5 Signa MR imager. The

ROI

is 64x64. In the spatial domain, we use diffusion filter[3] to get In 1993, Amartur and Vess

derivative method t

median filter is and therefore ne s time in computation.

But

it uses

a

larger to

Trajectory Display

3x3 neighborhood and fit its gray scale with a polynomial and obtain the first, second order derivative

h m

this

polynomial. This method improves a lot in the calculated optical flow at boundary region and, moreover, get more accurate gradient values in general.

constraint equation as follows,

-

2 0 Confraction We compare

the

performance between previous method(Fig.2a) and our method(Fig.2b) to calculate the gradient. This is a 2D contracting heart simulation, where we

er boundary regions. To extend 2D optical flow algorithm to 3D, we derive the 3D

;t

_{E ,}

:;

_{E ,}

:]

_{E ,} x

[:I

v = -

[t]

E , E, E , E ,

Here, subscript means partial derivative,

u,v,w denotes the

velocity in the x,y,z direction respectively.

Material & Methods the

We use Sun sparc workstation and MATLAB to implement

m is simulated as the 3 0 Motion The phantom contracts a pixel toward the left ventricle myocardium(Fig. 1). The phantom’s resolution is

32x32 and the gray level distribution of this phantom is set to be,

center in the xy plane and translates a pixel in the z axis at the same time. Fig.3a shows the velocity in the xy plane and Fig.3b

Icx w

16 16 16

E(x,y,z) = 32+ 4(1 +cos(-). oos(~)*cos(-)) shows the velocity in the z

axis

direction

. n e results matches

well with the true motion field.

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Fig. 3 (a)

Fig.3 (b)

Fig4 (c)

Fig.4 (d)

or Mostvelo '

spatial domain or time

axis,

can also get more accurate gradient and obtain better results.

Conclusion

In this study, we improve the optical flow methods to have better algorithm in gradient calculations and extend 2D velocity field to 3D motion study. Results shows better performance at boundary and g e n d continuity of velocity field. To evaluate the clinical

data

results, we are comparing it with the MR

W&g study.

Joint analysis is also und m

185-203

2.A new approach to Stu

of Cine M R Images S

1993 3 . N o h

Medical Imaging, Vol. 11