Shape and Pixel-Property Based Automatic Affine Registration ...

Shape and Pixel-Property Based Automatic Affine Registration Between Ultrasound Images of Different Fetal Head Feng Cen, Yifeng Jiang, Zhijun Zhang, and H.T. Tsui Electronic Engineering Department The Chinese University of Hong Kong Shatin, NT, Hong Kong SAR {fcen, yfjiang, zjzhang, httsui}@ee.cuhk.edu.hk

Abstract. The difficulties in the automatic registration of the ultrasound images of different fetal heads are mainly caused by the poor image quality, view dependent imaging property and the difference of brain tissues. To overcome these difficulties, a novel Gabor filter based preprocessing and a novel shape and pixel-property based registration method are proposed. The proposed preprocessing can effectively reduce the influence of the speckles on the registration and extract the intensity variation for the shape information. A reference head shape model is generated by fusing a prior skull shape model and the shape information from the reference image. Then, the reference head shape model is integrated into the conventional pixel-property based affine registration framework by a novel shape similarity measure. The optimization procedure is robustly performed by a novel mean-shift based method. Experiments using real data demonstrate the effectiveness of the proposed method. Keywords: ultrasound image registration, shape similarity, gabor filter, mean shift.

1

Introduction

Ultrasound imaging has become the most important medical imaging tool in obstetric examination. It is considered to be a safe, non-invasive, real-time and cost-effective way to examine the fetus. Imaging and measuring the head of the fetus is a key routine examination to monitor the growth of the fetus. The registration of different fetal heads is very useful for comparing the growth of different fetuses and constructing the normalized model of the fetal head for the diagnosis of fetal head malformation. However, the registration of ultrasound images is more difficult than that of other medical imaging modalities due to the poor image quality of ultrasound images caused by the speckle noise. The methods of medical image registration is typically divided into two categories: feature based methods [1] [2] and pixel-property based methods. As the automatic extraction of the anatomical G.-Z. Yang and T. Jiang (Eds.): MIAR 2004, LNCS 3150, pp. 261–269, 2004. c Springer-Verlag Berlin Heidelberg 2004


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structure features is quite difficult in ultrasound images, many researches tend to use the pixel-property based methods for the automatic registration of ultrasound images. For example, Meyer et al [3] used the mutual information measure to affine and elastic registration, Shekharet al [4] investigated using the preprocessing by median filter and intensity quantization to improve the robustness of the registration and Gee et al [5] proposed to use the constraint of the mechanics of freehand scanning process to reduce the computational load in non-rigid registration. The Biparietal Diameter (BPD) is the maximum diameter of a transverse section of the fetal skull at the level of the parietal eminences. The BPD plane contains the most valuable information for the obstetric doctor to investigate the fetal head and monitor the growth of the fetus. So, in this paper, we shall focus on the automatic registration between the ultrasound images of different fetal heads in the BPD plane. Actually, the ultrasound image is view dependent, i.e., the structures closely parallel to the ultrasound beam direction will not show up clearly. So, the parts of a skull in the ultrasound beam direction are often invisible in the ultrasound images. Furthermore, in most situation, the difference of the brain tissue between different fetuses is large. Therefore, the conventional pixel-property based methods will fail in our study. In this paper, we propose a novel shape and pixel-property based method to register the ultrasound images of the BPD plane between different fetuses. In the proposed method, a prior shape model, obtained by hand measurement of a group of fetal head ultrasound images, is used to represent the prior shape information about the skull in the BPD plane. Then, the prior shape model is updated with the reference image to generate a reference shape model. The benefit of combining of the prior shape model and the shape information in the reference image is the more accurate representation of the skull shape even in the case that the skull structure is partly invisible in the ultrasound image. A novel shape similarity measure is proposed to assess the similarity between the shape model and the ultrasound image. Finally, the registration is performed with a linear combination of the shape similarity measure and conventional pixel-property based similarity measure of correlation ratio (CR)[6]. A robust optimization is performed by a novel mean-shift based method. In addition, a Gabor filter based preprocessing is proposed to reduce the influence of the speckles and extract the intensity variation for shape information.

2

Preprocessing

The speckle noises in ultrasound images are able to be viewed as in an irregular and complex texture pattern[7]. This fact inspires us to employ the Gabor filters for the preprocessing of the ultrasound images to reduce the negative impact of the speckle on the performance of registration. The preprocess is illustrated in Fig. 1 (a). First, a wavelet-like Gabor filter bank is constructed to decompose the ultrasound image in spatial frequency space into multiscale and multiorientation. A 2-D complex Gabor filter represented as a 2-D impulse response is given by[9]

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u

v

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Fig. 1. (a)The preprocessing procedure diagram. (b)The responses of Gabor filter bank in spatial frequency domain. Only the portion larger than the halfpeak magnitude is shown for each filter. 
 1 1 x2 y 2 h(x, y) = exp − + 2 exp(j2πF x ), 2πσx
σy
2 σx2
σy


(1)

where (x , y  ) = (x cos θ + y sin θ, −x sin θ + y cos θ) are rotated coordinates, F is the radial center frequency and σx and σy are the space constants of the Gaussian envelope along the x and y axes, respectively. Let BF and Bθ denote the frequency bandwidth and the angular bandwidth, respectively. The Gabor filter bank, covering the spatial frequency domain, can be generated by varying four free parameters (F, θ, BF , Bθ ). After Gabor filter decomposition, a Gaussian smoothing is processed for the output amplitude of each channel. The smoothing filter, gk,s (γx, γy), is set to have the same shape as the Gabor filter of the corresponding channel but greater spatial extents. The subscripts s = (0, ..., S − 1) and k = (0, ..., K − 1) denote the scale and orientation of the outputs, respectively, and the parameter γ controls the spatial extent of the smoothing filter. In our implementation, we use the parameter set suggested by [8], since the Gabor filters generated with this parameter set have the optimal texture separability. The response of Gabor filter bank in spatial frequency domain is shown in Fig. 1(b). Finally, compounding the real parts and imaginary parts of the outputs of smoothing filters, respectively, we get        r r i i  (2) Hk,s (x, y), G (x, y) =  Hk,s (x, y) − µH i  , G (x, y) =   k,s k,s r i where Hk,s (x, y) and Hk,s (x, y) are the real part and imaginary part of the  i output of gk,s (γx, γy), respectively, and µH i is the mean value of k,s Hk,s (x, y) r i over the entire image. Since the G (x, y) and G (x, y) can be considered as the representation of the amplitude of the texture pattern and the variation

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of the image intensity, respectively, we call Gr (x, y) the texture intensity map and Gi (x, y) the intensity variation map. To be easily adopted into the pixel similarity measure Eq. 7, the double-valued Gr (x, y) is quantized to 256 levels.

3

Registration

The registration procedure of the proposed method is illustrated in Fig. 2. It consists of two major parts, i.e., the generation of reference shape model and the shape and pixel-property based registration of the ultrasound images.

Fig. 2. Diagram of the proposed registration procedure.

3.1

Reference Shape Model Generation

The purpose of this procedure is to build a shape model that can more accurately represent the shape information of the interest organ in the reference image. The shape model, M (x, y), used in this paper is a binary bit map having the same size as the reference image. The regions of value 1 in the shape model is a shape depiction of the object of interest. The intensity variation map of the reference image and a prior shape model are used to generate the reference shape model. Two steps are involved into this procedure. First, the prior shape model is aligned with the intensity variation map of the reference image by maximize the shape similarity measure with respect to the affine transformation of the prior shape model; then, the shape information extracted from the intensity variation map and the prior shape model are fused to produce the reference shape model.

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Here, we propose to use the normalized sum of intensity variation within the region defined by the shape model to assess the similar degree between the object shape in the image and the shape model. The proposed shape similarity measure can be written as ηS (M, Gi ) =

 Gi (x, y)M (x, y) x,y

Gimax

,

(3)

where Gimax is the max value of Gi (x, y) over the entire intensity variation map. The range of ηS (M, Gi ) is from 0 to 1. Assuming that the prior shape model transformed by a given affine transformation TM is MpTM (x, y) = Mp (x, y) ◦ TM , here, Mp (x, y) is the initial prior shape model, the alignment between the prior shape model and the reference ∗ that maximize the shape similarity measure, i.e., image is to seek the TM ∗ = arg max{ηS (MpTM , Gir )}, TM TM

(4)

where Gir is the intensity variation map of the reference image. In our study, the prior shape model of the fetal head in BPD plane only takes into account the skull, because it is the most prominent structure in the ultrasound images of the fetal head. The shape of the skull can be modeled as an elliptic strip. The prior shape model, as shown in Fig. 6(a), is acquired by hand measurement of a group of ultrasound images of the BPD plane, After alignment, the shape information of the reference image is extracted by  1 if Gir (x, y) > ασHri , (5) Ms (x, y) = 0 if Gir (x, y) ≤ ασHri  i where σHri is the standard deviation of k,s Hk,s (x, y) over the entire reference image and α the parameter controlling the extraction of the shape information. In our experiment, the α is set to 1. Then, the reference shape model, an example is shown in Fig. 6 (b), is obtained by Mr (x, y) = MpTM (x, y) ⊕ Ms (x, y). 3.2

(6)

Shape and Pixel-Property Based Registration

The similarity measure in the proposed registration method involves two major parts: the shape similarity measure and the pixel-property based similarity measure. The shape similarity measure is the same as Eq. 3. According to our preliminary study, the CR similarity measure have larger extent of the attraction basin than other pixel-property based similarity measure. Moreover, the value of CR measure is comparable to that of the shape similarity measure. Thus, the CR is adopted as the pixel-property based similarity measure in our method. Suppose that the texture intensity maps of the reference image and floating image are Grr and Grf , respectively, and the floating image is tansformed by a given affine transformation T . The CR measure is given by[6]

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ηP (Grr , Grf ◦ T ) =

V ar[E(Grf ◦ T |Grr )] . V ar(Grf ◦ T )

(7)

Then, the shape similarity measure and pixel-property similarity measure are linearly combined to give the cost function for the registration, i.e., η(Ir , If ◦ T ) = ηP (Grr , Grf ◦ T ) + βηS (Mr , Gif ◦ T ).

(8)

where β is a weighting constant, Ir the reference image, If the floating image. 3.3

Maximization of Similarity Measure

Generally, the desired solution in image registration is related to a strong local maximum of the similarity measure close to the start position, but not necessarily the global maximum. Here, ”strong” not only refers to the magnitude of the local maximum, but also means the large extent of the attraction basin. Therefore, we propose to use the Powell’s direction set method[10] to provide the direction of each sub-line maximization and the mean-shift algorithm[11] to perform the sub-line maximization. This method can robustly searching for the strong local maximum. Assuming Ω is a local window around the current location x on the cost function surface with a window radius λ, one dimensional mean-shift based maximizing procedure is iteratively moving the current location by s−x

 s∈Ω K λ η(s)s s−x − x, (9) m(x) =  η(s) s∈Ω K λ where K is a suitable kernel function. This iteratively moving procedure is equivalent to hill climbing on the convolution surface given by  s − x H η(s), (10) C(x) = λ s where H is the shadow kernel of K. For simplicity and effectiveness, we choose the kernel K as a flat kernel, and the corresponding shadow kernel is the Epanechnikov kernel [11], which is a smoothing kernel and can effectively smooth the local fluctuation on the surface of similarity function. Moreover, by varying the kernel scale λ from large scale to small scale progressively, the optimization can be run robustly and accurately in a coarse-to-fine strategy. An example of the mean-shift maximization in one dimension is shown in Fig. 3.

4

Experiments and Results

Two ultrasound images, as shown in Fig. 5(a), obtained from two different women with around 20-week pregnancy were used in our experiments. The image size is 256 × 256.

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Fig. 3. Searching for maximum with mean-shift method in one dimension. The start position is marked with a solid square, the intermediate steps are shown by hollow circles and the final result is represented by a solid diamond.

The smoothing effect of the Gabor filter based preprocessing on the pixel similarity function is given in Fig. 4. From Fig. 4(b), we can observe that the undesired local maxima in large scale have been effectively smoothed and removed when using the texture intensity maps for the pixel similarity measure. The preprocessing outputs of the reference and floating ultrasound images are shown in Fig. 5 (b) and (c). Note that the texture intensity map after requantization, Fig. 5 (b), can also be view as a despeckled and contrast enhanced ultrasound image. In Fig. 6, we show the shape model and the final registration result, Fig. 6 (d). In the shape models, the value of white regions is 1. Although there are some small noticeable registration errors, the accuracy of the result is acceptable for the affine registration between two different subjects.

(a)

(b)

Fig. 4. Correlation Ratio as a function of misalignment caused by translation in y axis and scaling in x axis for (a) the original image pair and (b) the texture intensity maps of the image pair.

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(a)

(b)

(c)

Fig. 5. Results of Gabor filter preprocessing for the reference image (top row) and the floating image (bottom row).(a) Original ultrasound images. (b) Texture intensity maps of the images. (c) Intensity variation maps of the images . For display convenience, it is also quantized to 256 levels.

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Fig. 6. (a)the prior shape model. (b) the reference shape model. (c)the floating image when registered.(d)the final registration result shown in the reference image. The white curves superimposed on (c) and (d) are the edges detected by Canny edge detector in the corresponding texture intensity map of the floating image.

5

Conclusions

In this paper, we have proposed a novel method for affine registration of the ultrasound images. This method consists of a Gabor filter based preprocessing of the ultrasound images, a shape and pixel-property based similarity measure and a robust searching of strong local maximum based on the mean-shift algorithm. We demonstrate the effectiveness of this method with the experiment

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on the registration of the ultrasound images between different fetal heads. The proposed method can be easily extended to the registration of other organs, if the prior shape model of fetal skull is replaced by that of other organs. In our future work, we shall study to apply the proposed method for the registration of other ultrasound images and extend the proposed method to the registration of ultrasound volumes.

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