978-1-4244-4547-9/09/$26.00 ©2009 IEEE TENCON 2009

Warped Anisotropic Diffusion of Ultrasound Image

Balza Achmad, Mohd. Marzuki Mustafa, Aini Hussain Department of Electrical, Electronic and Systems

Universiti Kebangsaan Malaysia Bangi, Malaysia

balzach@ugm.ac.id, marzuki@vlsi.eng.ukm.my, aini@vlsi.eng.ukm.my

Abstract— Ultrasound images contain speckle noise that creates granular pattern which degrades their quality. Typically, the granular noise has a circular pattern that circles the position of the ultrasound probe which acts as it center. As such, anisotropic diffusion filter cannot completely remove the granular noise. In this work, we propose a technique that pre-processes an ultrasound image using warping operation prior to the application of anisotropic diffusion as well as post-processes it via dewarping operation. Based on visual observation and power signal-to-noise ratio (PSNR) calculation of the test image, the proposed warped anisotropic diffusion (WAD) technique provides an improve result when compared with the original version of anisotropic diffusion (AD) technique.

Keywords-anisotropic diffusion; image warping; ultrasound image

I. INTRODUCTION Biomedical imaging plays important roles these days. Many

diagnostics made by medical doctors are based on the patient images provided by imaging instruments such as ultrasonography, x-ray machines, CT-scanners, and magnetic resonance imaging machines. Among those instruments, ultrasound imaging is considered as the cheapest and the most comfortable for the patients, hence this modality is very popular and most widely used throughout the world.

Ultrasound images, however, have a crucial disadvantage concerning with their quality. Fig. 1 shows an example of ultrasound image. Obviously, this image contains speckle noise that degrades the quality of the image. This degradation in some level creates difficulties for the doctors to make use of the image to support their diagnosis.

Many works have been done to reduce the presence of speckle noises in ultrasound images, for instance, speckle reduction imaging (SRI) method [1], homomorphic wavelet-based maximum a posterior (MAP) method [2], stochastic resonance (SR)-based wavelet method [3], undecimated double density wavelet transform based method (UDDWT) [4], morphological fuzzy filter [5], and anisotropic diffusion filter [6]. Anisotropic diffusion has drawn many attentions since its appearance on 1990 by Perona and Malik.

The speckle noise of ultrasound image is due to the

interference of many waves that cancel or reinforce each other creating random bright and dark patterns on the image. This noise forms granular patterns that follow certain direction, i.e. circular direction with center at the point where the ultrasound probe positioned. The above mentioned methods were normally applied using rectangular grid. For example, the diffusion process of the anisotropic diffusion method took into account the neighboring pixels located at the above, below, right and left of the calculated pixel. However, if we take a look on the pattern of the granules, it will be presumably better if the diffusion of the noise is computed with the use of circular grid. Fig. 2, which is a zoomed part of Fig. 1, shows the pixel grid of the usual anisotropic diffusion method, i.e. rectangular grid (Fig. 2a), and the proposed method, i.e. circular grid (Fig. 2b). Clearly, the granules follow the circular grid.

In this paper, we present the comparison between rectangular grid-based anisotropic diffusion (AD) and the circular grid based anisotropic diffusion. We call the latter warped anisotropic diffusion (WAD) for the reason discussed below.

This work was supported in part by the University Kebangsaan Malaysia under research grant contract number UKM-GUP-TKP-08-24-080

Figure 1. An example of ultrasound image

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The original AD equation is still applicable for this

purpose. However, the original image needs to be converted from its rectangular grid into circular grid using warping operation. AD technique can then be applied to the warped image. Finally, the diffused image has to be warped again from the circular grid to the original rectangular grid. Fig. 3 shows the schematic diagram of the proposed technique in contrast with the original AD technique.

The pixel coordinates in rectangular grid are denoted by (x, y), whereas for circular grid are denoted by (r, s). The variable s is derived from the angle θ in order to normalize the field of view of the ultrasound image (θL+θR) with respect to the width of the image. Fig. 4 illustrates how the rectangular grid is converted into circular grid. It can be seen that the top part of the image is expanded while the bottom part of the image is compressed.

The warping process uses the following equations to map the pixel coordinate in rectangular grid (x, y) into circular grid (r, s).

( )

LRL

ws θθθθ −

−+

=1

(1)

00

1)(

yh

yRadiusrR −

−+

= (2)

( )θsin0 Rxx += (3)

( )θcos0 Ryy += (4)

(x0, y0) is the coordinate of the probe, w and h are the width and height of original image, Radius is the distance between the probe and the outer pixel of the circular grid, θL and θR are the angles of the leftmost and rightmost pixels in the warped image, respectively.

For the dewarping process, the pixel coordinate in circular grid are remapped back into rectangular grid using the following equations.

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

= −

0

01tanyyxxθ (5)

)sin()( 0

θxx

R+

= (6)

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+−=

LR

Lwsθθ

θθ)1( (7)

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+−=

0

0)1(yRadius

yRhr (8)

The anisotropic diffusion process uses the original equations proposed by Perona and Malik [7],

( )),(),(),( txItxctxIt

T ∇∇=∂∂ (9)

Anisotropic Diffusion

Warping

Anisotropic Diffusion

Dewarping

Original image

Processed image

Processed image

(a) (b) Figure 3. The schematic diagram of the proposed technique.

(x0,y0)

θL θR

Radius

y x

s

r

Figure 4. Coordinate system of the grids.

(a) rectangular grid (b) circular grid

Figure 2. Pixel grid.

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where c(x, t) is the conductance function given by

α

κ

+

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∇+

= 1),(

1

1),(txI

txc (10)

II. RESULT AND DISCUSSION The comparison between the original anisotropic diffusion

and the proposed technique was shown by applying both methods on the same image. In order to be able to obtain quantitative assessment in term of signal-to-noise ratio, actual ultrasound image could not be used. Instead, a simulated ultrasound image was utilized. The image was an ultrasound image of kidney simulated using Field II simulation program developed by Department of Information Technology, Technical University of Denmark [8].

The input of Field II program was a scatterer map of patient’s kidney as shown in Fig. 5a. From this map, the simulator generated an ultrasound image that included speckle noise similar to an actual image gathered from an ultrasonography machine, which is given by Fig. 5b. This image was then processed directly using anisotropic diffusion equations, which gives an image shown in Fig. 5c. It can be seen that, the diffused image still contained some circular granules. This image would then be compared with the one that was pre-processed and post-processed through warping operations.

(c) anisotropic diffusion of the original image

(d) warped image

(e) anisotropic diffusion of the warped image

(f) dewarped image of (e)

(g) difference between (c) and (f)

Figure 5. Processed images

(a) scatterer model of a kidney

(b) ultrasound image

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Fig. 5d shows the image resulted from the warping process.

As mentioned before, the upper part of the image was expanded whilst the lower part was condensed as if the image was bent down. The effect of this bending was that the patterns of the granules were then all parallel horizontally. The arrangement of the speckle noise direction in turn enabled the application of usual anisotropic diffusion. The result of the anisotropic diffusion process is given in Fig. 5e.

Following the anisotropic diffusion process, the image was then warped back (or dewarped) to the original rectangular coordinate using (5) to (8). The result is given in Fig. 5f. Comparing this image to the direct application of anisotropic diffusion given by Fig. 5c, it can be seen that the warping-dewarping processes was able to eliminate the circular granules that stayed remain in the diffused image Fig. 5c. The difference between the two diffused images, given in Fig. 5g, shows the granules that were further eliminated by the proposed technique.

The quantitative figure of the comparison between the two AD techniques can be represented by the signal-to-noise ratio of the image. Table I shows the peak signal-to-noise ratio (PSNR) of the proposed method compared with those of the ultrasound and the AD images. It can be seen that both AD and WAD methods can increase the PSNR. However, WAD gives higher increase in PSNR than the original AD.

TABLE I. PSNR OF THE IMAGES

Image PSNR (dB) Ultrasound 12.48 Anisotropic Diffusion (AD) 12.97 Warped Anisotropic Diffusion (WAD) 13.15

Fig. 6, showing the grayscale profile of the three images at

row 105, provides us another proof. The WAD is capable in smoothing the homogenous area, for instance column 40 to 60, while preserving the edges, for examples column 35 and 155.

III. CONCLUSION The visual observation and quantitative evaluation of the

PSNR using simulated ultrasound image of a kidney demonstrate that the proposed WAD gives better result than the mere AD technique.

ACKNOWLEDGMENT The authors would like to thank the University Kebangsaan

Malaysia for the support of this research through research grant contract number UKM-GUP-TKP-08-24-080.

REFERENCES [1] N. Liasis, C. Klonaris, A. Katsargyris, S. Georgopoulos, N.

Labropoulos, C. Tsigris, A. Giannopoulos, E. Bastounis, “The Use of Speckle Reduction Imaging (SRI) Ultrasound, in the Characterization of Carotid Artery Plaques”, European Journal of Radiology, vol. 65, pp. 427-433, 2008.

[2] C. Guozhong, L. Xingzhao, “Cauchy PDF Modelling and Its Application to SAR Image Despeckling”, Journal of Systems Engineering and Electronics, vol. 19, issue 4, pp. 717-721, August 2008.

[3] V.P.S. Rallabandi, “Enhancement of Ultrasound Images using Stochastic Resonance-Based Wavelet Transform”, Computerized Medical Imaging and Graphics, vol. 32, pp. 316-320, 2008.

[4] D. Gnanadurai, V. Sadasivam, J. Paul Tiburtius Nishandh, L. Muthukumaran, C. Annamalai, “Undecimated Double Density Wavelet Transform Based Speckle Reduction in SAR Images”, Computers and Electrical Engineering, doi: 10.1016/j. compeleceng.2008.04.010

[5] E.d.S. Filho, M. Yoshizawa, T. Iwamoto, A. Tanaka, Y. Saijo, “Morphological Fuzzy Filter for Enhancement of Intravascular Ultrasound Images”, SICE Annual Conference in Sapporo, Hokkaido Institute of Technology, August 4-6, 2004.

[6] C. Munteanu, F.C. Morales, J.G. Fernández, A. Rosa, L.G. Déniz, “Enhancing Obstetric and Gynecology Ultrasound Images by Adaptation of the Speckle Reducing Anisotropic Diffusion Filter”, Artificial Intelligence in Medicine, vol. 43, pp. 223-242, 2008.

[7] P. Perona and J. Malik, “Scale-Space and Edge Detection Using Anisotropic Diffusion”, IEEE Transl. Pattern Analysis and Machine Intelligence. vol. 12, no. 7, pp. 629-639, July 1990

[8] J.A. Jensen and P. Munk, “Computer Phantoms for Simulating Ultrasound B-Mode and CFM Images”, Acoustical Imaging, vol. 23, pp. 75-80, Eds.: S Lees and L. A. Ferrari, Plenum Press, 1997.

020

406080

100120

140160

0 50 100 150 200position

gray

scal

e

UltrasoundADWAD

Figure 6. Grayscale profile at row 105.

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