Texture-Based Filtering and Front-Propagation ... - Semantic Scholar

Texture-Based Filtering and Front-Propagation Techniques for the Segmentation of Ultrasound Images ´ Miguel Alem´ an-Flores1 , Patricia Alem´ an-Flores2 , Luis Alvarez-Le´ on1 , 1 2 M. Bel´en Esteban-S´ anchez , Rafael Fuentes-Pav´ on , and Jos´e M. Santana-Montesdeoca2, 1

Departamento de Inform´ atica y Sistemas Universidad de Las Palmas de Gran Canaria, 35017, Las Palmas, Spain 2 Secci´ on de Ecograf´ıa, Servicio de Radiodiagn´ ostico Hospital Universitario Insular de Gran Canaria, 35016, Las Palmas, Spain [email protected]

Abstract. Ultrasound imaging segmentation is a common method used to help in the diagnosis in multiple medical disciplines. This medical image modality is particularly difficult to segment and analyze since the quality of the images is relatively low, because of the presence of speckle noise. In this paper we present a set of techniques, based on texture findings, to increase the quality of the images. We characterize the ultrasound image texture by a vector of responses to a set of Gabor filters. Also, we combine front-propagation and active contours segmentation methods to achieve a fast accurate segmentation with the minimal expert intervention.

1

Introduction

Ultrasound (US) imaging has become an important diagnostic tool in medicine [1]. Mainly, this medical image modality is known by its application in gynecology but US imaging is also important for diagnosis of abdominal organs or heart, fetal examination, etc. Its main advantages are that it is a cost effective, quick, painless and non-invasive technique. Among the disadvantages, we found that US imaging needs expert interpretation and the presence of a special kind of noise, called speckle. Ultrasound plays a crucial role in the diagnosis of breast cancer. Distinguishing benign and malignant nodules in breast US images is a useful way to avoid unnecessary biopsies. Most of the diagnostic criteria require an accurate segmentation of the nodule inside the image [2]. Manual segmentation performed by the radiologist is an expensive and time-consuming task that can be carried out with computer assisted methods. On the other hand, fully automatic techniques for ultrasound segmentation are not robust. We present a semi-automatic method 

Alphabetical order has been used in the author’s list.

R. Moreno-D´ıaz et al. (Eds.): EUROCAST 2007, LNCS 4739, pp. 960–967, 2007. c Springer-Verlag Berlin Heidelberg 2007 

Texture-Based Filtering and Front-Propagation Techniques

961

to extract nodule contours. It combines some segmentation methods with the minimal intervention of the radiologist, that selects a point inside the nodule. The presence of speckle noise in ultrasound images degrades the visibility of diagnostic criteria (nodule shape and contour). It is necessary to reduce it before processing the image. Many methods have been proposed, including the truncated median filter [3], anisotropic diffusion [4] and speckle-reducing anisotropic diffusion [5]. Most of them do not preserve key and useful details, such as edges. We propose to preprocess the image, applying a variation of the classical anisotropic diffusion scheme, guiding it by Gabor texture descriptors. The paper is structured as follows: Section 2 presents the texture-based filtering technique and focuses on Gabor filter as a texture feature extractor. Section 3 explains the use and combination of the front-propagation and active contours methods to segment regions of the ultrasound images. The work is concluded with an account of our main conclusions (Section 4).

2

Texture-Based Ultrasound Filtering

Before processing US images, it is necessary to reduce the presence of speckle noise. The aim is to remove it without blurring or distorting edges that could affect the diagnostic details. The speckle noise in ultrasound images is generally modelled as a multiplicative noise. Classical image filters, such as gaussian are focused on removal of additive noise, so they are not suitable for speckle filtering. Other common techniques include median filter and anisotropic diffusion filters. 2.1

Anisotropic Diffusion

A good result for US images is obtained by applying the anisotropic diffusion, introduced by Perona and Malik [4]. This method filters the image, smoothing inside the different regions in preference to smooth across the boundaries: ⎧ δI ⎨ δt = div(g(∇I)∇I) (1) ⎩ I(t = 0) = Io where Io is the original noisy image. The gradient magnitude ∇I is used to detect the edges, that stop the diffusion through the function g(.) g(x) = e−αx

2

(2)

α is a contrast noise estimator, computed from the gradient magnitude histogram [6]. Gradient magnitude is not a good border detector in US, because of the presence of speckle. The texture contains information about the different areas or tissues in the image. Consequently, to improve the Perona-Malik scheme, we propose to include the texture information as a guide for the diffusion process.

962

2.2

M. Alem´ an-Flores et al.

Texture Extraction Through a Gabor Filter Bank

Texture is defined as a statistical pattern of the grey levels in the image. It is not specified by the intensity in a single point, it is always based on some neighbourhood. We extract texture features from the grey value texture pattern in the ultrasound images. The texture is characterized by a vector of scalar descriptors ri , computed as the responses of an image I to different filters R = {r1 , ..., rn }

(3)

Bidimensional Gabor filters [7] are commonly used for image texture extraction [8] [9] [10] [11] and segmentation of US images [12] [13]. They represent a generalization of the functions proposed by Gabor [14], and model the response of some mammalian visual cortex cells [15]. They are the product of a gaussian by a complex sinusoidal wave x2

g(x, y) = e where



y2

ω (−π( σω 2 + σ2 )) (i(2πλ(x cos ω+y sin ω))) x y

e

xω = (x − x0 ) cos ω + (y − y0 ) sin ω yω = −(x − x0 ) sin ω + (y − y0 ) cos ω

(4) (5)

σx e σy are the gaussian standard deviations. (x0 , y0 ) and (λ, ω) set the gaussian position in the spatial and frequency domain respectively. This function is a bandpass filter, associated to a specific range of frequencies (or filter band). It responds to signals oriented in a specific orientation (or filter direction). The real asymmetrical part acts as a smooth filter, while the imaginary symmetrical part acts as a border detector. Figure 1 shows the real and imaginary part of a Gabor filter in the spatial domain. To compute the texture vector, we filter the image with a set of Gabor filters, called Gabor filter bank. The filters have different values for the parameters σx , σy , λ ,ω. A typical design strategy consist in avoiding the overlap of the halfmagnitude filter responses in the frequency domain, while covering the whole domain. All the filters have the same half-magnitude frequency bandwidth in octaves. Figure 2 shows a Gabor filter bank with 6 bands and 2 orientations. Using a filter bank of N different bands and M different orientations, we obtain a NxM responses Fnm , with 1 ≤ m ≤ M and 1 ≤ N ≤ N , that are the components of the texture vector R. The responses contain information about orientation and frequencies of the intensity patterns in the neighbourhood of each point. 2.3

Texture Guided Anisotropic Diffusion

We have modified the anisotropic diffusion scheme by changing the intensity gradient term by the gradient of the texture vector δI = div(g(∇R)∇I) δt

(6)

Texture-Based Filtering and Front-Propagation Techniques

(a)

963

(b)

(c)

(d)

Fig. 1. A Gabor filter in the spatial domain σx = 10, σy = 20, λ = 0.20, θ = π/3, x0 = y0 = 0, γ = 0. a) Real part. b) Imaginary part. c) Real part magnitude. d) Imaginary part magnitude.

The numerical implementation of this equation is as follows. We compute the gradient magnitude of the texture vector for a pair of pixels p,q of the image as ∇R(p, q) =

 



(Fnm (p) − Fnm (q))

(7)

1≤m≤M 1≤n≤N

At each iteration of the diffusion, the new pixel value Ipt+Δt is computed as Ipt+Δt = Ipt +

Δt  t g(∇R(p, q))∇Ip,q η q∈η

(8)

where η represents the neighbourhood of pixel p. Figure 3 shows a breast ultrasound image and the smoothed version obtained by the truncated median filter, the classical anisotropic diffusion and the texturebased anisotropic diffusion.

3

Front-Propagation Segmentation of Ultrasound Images

Some accurate segmentation techniques, such as active contours methods [16], need the initialization of the curve. This time-consuming task is not always available. Some other methods, such as region-growing [17] can obtain a rough draft of the nodule contour setting only one point. However, this implementation needs a proper threshold to distinguish the inner region of the nodule. We propose to combine front-propagation segmentation [18] and active contours to obtain a segmentation of the nodule.

964

M. Alem´ an-Flores et al.

3

2

1

0

−1

−2

−3 −3

−2

−1

0

1

2

3

(a)

(b)

Fig. 2. Gabor filter bank of 6 bands and 2 orientations. a) Half peak magnitudes of the filters. b) Real part magnitudes in the spatial domain.

3.1

Front-Propagation Pre-segmentation

The radiologist can easily select a point inside the nodule. This initial point is expanded outside with the front propagation technique, until the gradient magnitude is high enough to stop the process (near the edges) ⎧ δu ⎨ δt = −g(∇Is )∇Is (9) ⎩ u(t = 0) = u0 where u represents the level set, Is is the filtered image and u0 the initial point. The presence of an edge stops the process through the function g(.) 1 g(Is ) =  1 + α∇Is 2

(10)

With this method, we obtain a rough segmentation of the nodule, that is improved by the active contours, also called snakes. 3.2

Active Contours Segmentation

This method consists in forth deforming an initial contour of the object to find the object boundaries, following a set of internal and external forces. We use the following scheme ⎧ δv ∇v ⎨ δt = g(Is )∇vdiv( ∇v ) + λ∇v∇g(Is ) ⎩

(11)

v(t = 0) = ut = n

where v represents the snake and vt=0 is the front-propagation segmentation. λ is a parameter that regulates the attraction force. Figure 4 shows a comparison between manual delimitation of the nodule in image in 3, and region-growing and front-propagation semi-automatic segmentations.

Texture-Based Filtering and Front-Propagation Techniques

(a)

(b)

(c)

(d)

965

Fig. 3. Breast ultrasound image filtered with different smoothing methods. a) Original US image. b) Truncated Median Filter. c) Anisotropic Diffusion. e) Texture-based Anisotropic Diffusion.

3.3

Numerical Results

To test the method, we use two different measures. We have two segmentations: the manual one performed by the radiologist (A) and the semiautomatic one (B). The first measure is the coincidence percentage: it is defined as the area of the intersection of the two segmentations divided by the area of the union and multiplied by 100. When two segmentations are identical, this coincidence percentage is 100. |A B|

.100 (12) CP (A, B) = |A B| The second measure is the proportional distance. We extract the contour of both segmentations: C1 and C2 . We compute the distance from each point of the first contour to the other and vice-versa. The sum of these quantities is divided by the square root of the area of the manual segmentation and corrected by a scale factor. When two segmentations are identical, this proportional distance is close to 0.



d(xi ,C2 ) |C1 |

xi ∈C1

P D(A, B) =



d(xi ,C1 )

2 + xi ∈C|C 2|  2 |S|

√ . π.100

(13)

We have tested the method in a set of 30 breast US images. The performance of our approach is presented in table 1. The best results are obtained with the combination of front propagation and active contours.

966

M. Alem´ an-Flores et al.

(a)

(b)

(c)

Fig. 4. Comparison of different segmentation methods in a breast US image: a) Regiongrowing segmentation. b) Front-propagation segmentation. b) Combination of frontpropagation and active contours segmentation. Table 1. Numerical results for different segmentation methods in a set of 30 US breast images

Segmentation Method Region-growing Front-propagation Front-propagation + Active Contours

4

PD 9.70 8.01 5.84

CP 76.68 81.74 86.94

Conclusions

We introduce a method that uses the image texture information to filter the speckle noise present in the US images. The modification of the Anisotropic diffusion scheme, adding the texture information, increases the results of this method in the US images. The texture is computed through the Gabor filter bank responses. We propose the combination of front-propagation and active contour (snakes) methods to obtain the shape of the nodule. This method allows obtaining a widely precise contour of an object inside an image. We use a rough pre-segmentation as initial snake. This pre-segmentation is obtained by a front propagation procedure. The initial seed of the algorithm is set by the radiologist, who selects an internal point of the nodule. Our methods offer higher accuracy, compared with other approaches.

References 1. Erikson, K.R., Fry, F.J., Jones, J.P.: Ultrasound in medicine-a review. IEEE Transactions on Sonics and Ultrasonics 21(3), 144–170 (1974) 2. Stavros, A.T., Thickman, D., Rapp, C.L., Dennis, M.A., Parker, S.H., Sisney, G.A.: Solid breast nodules: use of sonography to distinguish between benign and malignant lesions. Radiology 196, 123–134 (1995)

Texture-Based Filtering and Front-Propagation Techniques

967

3. Davies, E.R.: On the noise suppression and image enhancement characteristics of the median, truncated median and mode filters. Pattern Recogn. Lett. 7(2), 87–97 (1988) 4. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990) 5. Yu, Y., Acton, S.T.: Speckle reducing anisotropic diffusion. IEEE Transactions on Image Processing 11(11), 1260–1270 (2002) 6. Voci, F., Eiho, S., Sugimoto, N., Sekibuchi, H.: Estimating the gradient in the perona-malik equation. IEEE Signal Processing Magazine 21(3), 39–65 (2004) 7. Daugman, J.G.: Complete discrete 2-d gabor transforms by neural networks for image analysis and compression. IEEE Transactions on Acoustics, Speech and Signal Processing 36(7), 1169–1179 (1988) 8. Bovik, A.C., Clark, M., Geisler, W.S.: Multichannel texture analysis using localized spatial filters. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(1), 55–73 (1990) 9. Weldon, T.P., Higgins, W.E.: Design of Multiple Gabor Filters for Texture Segmentation. In: vol. 4, pp. 2243–2246 (1996) 10. Dunn, D., Higgings, W.E.: Optimal gabor filters for texture segmentation. IEEE Transactions on Image Processing 4(7), 947–964 (1995) 11. Anil, K., Jain, A.K., Farrokhnia, F.: Unsupervised texture segmentation using gabor filters. Pattern Recogn. 24(12), 1167–1186 (1990) 12. Mohamed, S.S., Abdel-galil, T.K., Salama, M.M.A., Fenster, A., Rizkalla, K., Downey, D.B.: Prostate cancer diagnosis based on gabor filter texture segmentation of ultrasound image. In: CCECE 2003, vol. 3, pp. 1485–1488 (2003) 13. Xie, J., Jiang, Y., Hung-Tat, T.: Segmentation of kidney from ultrasound images based on texture and shape priors. IEEE transactions on medical imaging 24, 45–57 (2005) 14. Gabor, D.: Theory of communication. Journ. of Inst. Electrical Engineers 93(26), 429–457 (1946) 15. De Valois, R.L., De Valois, K.K.: Spatial Vision. Oxford University Press, Oxford (1988) 16. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: ICCV, pp. 694– 699 (1995) 17. Sato, M., Lakare, S., Wan, M., Kaufman, A., Nakajima, M.: A gradient magnitude based region growing algorithm for accurate segmentation. In: Proceedings of the International Conference on Image Processing, vol. 3, pp. 448–451 (2000) 18. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)