Optimal Search Guided by Partial Active Shape Model for Prostate Segmentation in TRUS Images Pingkun Yan*a and Sheng Xua , Baris Turkbeyb , Jochen Krueckera a Philips
Research North America, 345 Scarborough Road, Briarcliff Manor, NY 10510; Institutes of Health, National Cancer Institute, Molecular Imaging Program, Bethesda, MD 20892
b National
ABSTRACT Automatic prostate segmentation in transrectal ultrasound (TRUS) can be used to register TRUS with magnetic resonance (MR) images for TRUS/MR-guided prostate interventions. However, robust and automated prostate segmentation is challenging due to not only the low signal to noise ratio in TRUS but also the missing boundaries in shadow areas caused by calcifications or hyper-dense prostate tissue. Lack of image information in those areas is a barrier for most existing segmentation methods, which normally leads to user interaction for manual correction. This paper presents a novel method to utilize prior shapes estimated from partial contours to guide an optimal search for prostate segmentation. The proposed method is able to automatically extract prostate boundary from 2D TRUS images without user interaction for correcting shapes in shadow areas. In our approach, the point distribution model was first used to learn shape priors of prostate from manual segmentation results. During segmentation, the missing boundaries in shadow areas are estimated by using a new partial active shape model, which uses partial contour as input but returns complete estimated shape. Prostate boundary is then obtained by using a discrete deformable model with optimal search, which is implemented efficiently by using dynamic programming to produce robust segmentation results. The segmentation of each frame is performed in multi-scale for robustness and computational efficiency. In our experiments of segmenting 162 images grabbed from ultrasound video sequences of 10 patients, the average mean absolute distance was 1.79mm±0.95mm. The proposed method was implemented in C++ based on ITK and took about 0.3 seconds to segment the prostate from a 640x480 image on a Core2 1.86 GHz PC. Keywords: Transrectal ultrasound, prostate, image guided intervention, image segmentation, partial active shape model, deformable model, dynamic programming.
1. INTRODUCTION Prostate cancer is the most common type of cancer found in American men, other than skin cancer. It is the second leading cause of cancer death in men in the United States.1 Transrectal ultrasound (TRUS) guided needle biopsy is the most frequently used method for diagnosing prostate cancer due to its real-time nature, low cost, and simplicity.2 However, due to the relatively poor image quality and low sensitivity and specificity of ultrasound (US) for prostate cancers, it is difficult to use US only for targeted biopsy guidance because most cancers are not visible sonographically. On the other hand, magnetic resonance (MR) imaging is superior for visualizing the prostate anatomy and focal lesions suspicious for prostate cancer. However, MR imaging is costly and the magnetic environment makes interventional procedures too complicated thus making MR imaging unsuitable as an intra-procedural modality for routine biopsy guidance. Therefore, it is desirable to fuse these two complimentary modalities to take advantage of the superior visualization of MR images in TRUS guided biopsy.3, 4 Sample corresponding TRUS and MRI views of the prostate in a patient undergoing TRUS/MRI fusion-targeted biopsy are shown in Figure 1. Realtime fusion of TRUS with MR imaging for image-guided prostate interventions requires accurate and near-realtime registration of the two image modalities.5 Prostate contours segmented from TRUS images can improve TRUS/MRI registration accuracy. In addition, accurate segmentation of prostate can play a key role
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Figure 1. Corresponding TRUS (left) and MRI (right) views of the prostate in a patient undergoing TRUS/MRI fusiontargeted biopsy. The red spot indicates the current MRI-based biopsy target, the blue spots indicate additional suspicious lesions. The prostate was manually pre-segmented in 3D MRI. The green contour is the intersection of this segmentation with the current ultrasound plane and corresponding MRI multi-planar reconstruction.
Figure 2. Major challenges for segmentation of prostate boundaries from TRUS images. A: low signal-to-noise ratio; B: large intensity variation inside of prostate and similarity between prostate and non-prostate tissues; C: shadow artifact where no boundary is available.
in the following interventional procedures, such as biopsy needle placement6 and prostate motion monitoring.4, 5 However, segmentation of prostate boundaries from TRUS images is a challenging task. For a prostate segmentation method to succeed, the following challenges presented in TRUS images have to be properly addressed. Firstly, compared to CT or MR images, the signal-to-noise ratio of TRUS images is much lower, which causes algorithms relying on the intensities of single pixels to fail. Secondly, pixel intensity distributions are quite inhomogeneous in both inside and outside of prostate. Regions with similar appearances can be observed in both prostate and non-prostate areas. It is also very common that the appearances vary significantly inside each tissue. Therefore, there is no global characterization of prostate and non-prostate areas, which makes it hard to directly differentiate prostate from surrounding tissues based on pixel intensities and region appearances. Finally, shadow artifacts often appearing at the anterior side of the prostate make the segmentation very difficult because of lack of image information in those areas. The challenges are also visually indicated in Figure 2.
A number of methods have been reported in the past decade. However, fully automatic segmentation methods have only obtained limited success. A major portion of the existing methods still require expert interaction during the segmentation process for either initializing contours or adjusting segmentation results.7, 8 Among all the reported methods, deformable model and statistical shape model based algorithms demonstrated the most promising segmentation results. Badiei et al.9 presented a semi-automatic segmentation method by warping ellipses, which were fit to the detected edges in TRUS images. The method took advantage of the similarity between prostate shape and warped ellipse. Although the method is simple and efficient, its application is limited to images in mid-gland region with regular shapes. In addition, it needs six initialization points to be selected from specific locations. A 2D semi-automatic discrete dynamic contour (DDC) model for prostate boundary segmentation was presented by Ladak et al.10 The DDC deforms in the prostate image to extract boundary starting from an initial contour defined by four manually picked points. Wang et al.11 extended the method to 3D segmentation but it requires manually editing the segmentation results to get required accuracy. Shen et al.12, 13 presented automatic segmentation methods for extracting prostate contour/surface from 2D and 3D US images. Spatially adaptive Gabor support vector machine (G-SVM) was developed to classify texture patterns extracted by rotation invariant Gabor filter bank. Statistical shape model was then fit to the output image of GSVM to get prostate boundary in the image. However, due to the use of G-SVM, the method is computationally intensive and may not be appropriate for use in TRUS guided prostate interventions. In addition, similar to other automatic segmentation algorithms,14, 15 good performance was demonstrated only on images without significant shadow artifacts. In this paper, we propose a new automatic segmentation method for extracting prostate boundaries from 2D TRUS images by using a novel partial active shape model (PASM) to guide the optimal search of a discrete deformable model (DDM) to address the above challenges. In our approach, the point distribution model was first used to learn shape priors of prostate from manual segmentation results. Initialization contour is obtained automatically by fitting the mean shape to the boundaries in the image. For computational efficiency, a coarseto-fine multi-resolution strategy is used in both initialization and contour deformation. At each resolution level, DDM searches for the global minimum in the defined range under shape prior guidance. The problem of heavy computation for global search was overcome by employing the dynamic programming algorithm, which can be computed very efficiently and fast. The a priori shape is estimated by using PASM. As opposed to approximating the whole prostate boundary in traditional methods like,11, 12, 16 which may contain misleading information, only parts of prostate contour with salient boundary features are used for producing shape estimate. The proposed PASM can help to get more accurate segmentation by selecting the more reliable contour parts. By integrating all these components together, the proposed method is able to extract complete prostate boundary even when part of the boundary is missing due to imaging shadows, which was previously manually corrected by user interaction as in other works.11, 16 Furthermore, the proposed method is much more computationally efficient compared to other methods with similar performance. The rest of the paper is organized as follows. We present the proposed PASM and DDM in Section 2. The selection of prostate boundary features, automatic initialization of shape model, and the integrated multi-resolution segmentation method are also discussed. In Section 3, the TRUS images used in our work are presented. Next in Section 4, we demonstrate the segmentation results using the proposed method with quantitative evaluation. We finally conclude the work in Section 5.
2. METHODS The proposed segmentation method consists of two major components, the estimation of prostate shape prior using PASM and the hierarchical deformable segmentation using DDM. Since prostate boundary feature plays a key role in both components, feature extraction is first presented. Detailed descriptions of the two components are provided after that. In the end, the integrated multi-resolution segmentation scheme is presented.
2.1 Prostate Boundary Feature Extraction In TRUS images, the most easily observable boundary feature is the dark-to-bright transition. In order to extract this feature, similar to the work of Hodge et al.,16 the normal vector profile (NVP) is used. In our work, the shape model is represented by a set of sequential points, called model points. NVP is a vector f = [f1 , f2 , · · · , f2m ]T
Figure 3. Illustration of prostate shape estimation from salient partial contour. Due to the shadow artifacts, which are commonly observed in TRUS images, the given initial contour may be far from the desired contour. A misleading shape can be estimated by using the whole initial contour. While using only the salient partial contours, a more reasonable shape prior can be obtained.
with dimension of 2m centered at each model point. The ith element fi is the intensity of the pixel, which is i − m distance away from the center point along the normal direction of the shape model at that point. To detect the dark-to-bright transition, the contrast of NVP f is computed as c = pT · f , where p is also a 2m vector with the first m elements to be 1 and the other half to be −1. That is p = [1, · · · , 1, −1, · · · , −1]T . The saliency of each contour point is then decided by the contrast value c of NVP. A model point is considered to be salient if the contrast c is smaller than a threshold. Due to the TRUS characterizations that we pointed out in the challenges, especially because of the shadow artifacts, not all the contour points are salient. In our work, contour parts containing the consecutive salient contour points are detected by using Algorithm 1. Algorithm 1 Partial Salient Contour Detection - Estimate the intensity distribution of prostate according to the shape initialization. - Get the salient contour points whose NVP contrast c is smaller than −2m. - Compute the average intensity value around each point. If the value is smaller than the lower boundary of the prostate’s intensity range, remove the point from the salient point set, since this is likely to be in shadow area. - Apply 1D median filter to the point list and remove isolated points, which are often caused by noise.
2.2 Partial Active Shape Model Shape priors can be very helpful in guiding image segmentation, especially when the boundaries of structures are not clear because of low signal-to-noise ratio, limited image resolution, or missing boundary information.17 During segmentation, the shape prior of an image can be estimated from shape statistics according to a given contour. The shape statistics of the prostate can be calculated from a set of training samples, which are manually outlined from the corresponding TRUS images, by using point distribution model (PDM). The estimated shape is then used as either an initial contour or shape guidance for further segmentation. However, if the given contour is far away from the desired segmentation result due to the commonly observed shadow artifacts in TRUS images, an incorrect shape prior may be estimated as shown in Figure 3. It will be hard to obtain a reasonable segmentation in the following steps given this misleading shape prior. Some example segmentation results due to the misleading shape priors are shown in Figure 4. In order to solve the problem, a new partial active shape model (PASM) is proposed. The idea is to use only those contour points with salient features for shape estimation. A complete prostate shape can be estimated by fitting the PDM to these salient
Figure 4. Example segmentation results of prostate from ultrasound images without PASM. Shape priors are estimated by using the whole contour during the segmentation process. Yellow contours show the automatic segmentation results and the ground truth is shown in magenta.
Figure 5. Build the point distribution model (PDM) from contour points on a set of manual segmentation results. Each planar shape xi is represented by n points along the contour.
points, which may provide better result than using the whole contour. The computation of shape statistics using PDM and shape estimation using PASM are presented in detail as follows. 2.2.1 Computing Prostate Shape Statistics Point distribution model (PDM) has been successful in modeling shape statistics since it was introduced by Cootes et al.18 PDM is a statistical approach and able to extract a compact representation from a set of given training instances. Besides approximating the training shapes, PDM can also generate new shapes which may not exist in the training set. In PDM, each planar shape is represented by n points as the vector: x = [x1 , x2 , . . . , xn ; y1 , y2 , . . . , yn ]T .
(1)
Thus, each shape is an observation in the 2n dimensional space. Figure 5 shows a set of training images with prostate contour manually outlined. In our work, the contour points are equally spaced (Euclidean distance based spacing) sampled from the shapes. After normalization,12 principal component analysis (PCA) is used for dealing with redundancy in the m ¯ and a matrix input data after alignment. The resulting shape model consists of a function of the mean shape x Φ which includes the most significant t eigenvectors of the covariance matrix of the input data. The modes are
ordered according to the percentage of variation that they explain. In our work, we set the percentage threshold as 95%. In the original PDM,18 a new shape x can be decomposed using the mean shape and eigen-shapes and represented by a parameter vector b as ¯ ). b = ΦT (x − x (2) The approximation of the shape is then given by linearly combining the eigenvectors as ˆ=x ¯ + Φb. x
(3)
2.2.2 Estimating Shape Prior from Salient Partial Contour If the whole contour is used for shape estimation, a shape prior can be obtained by using (2) and (3). However, in order to deal with the shadow artifacts, only the partial salient contour will be used for shape estimation. Therefore, a new estimation method is developed in our method. ¯ s , and Φs denote the subset of the contour points with dark-to-bright transition image features, Let xs , x ¯ , and corresponding sub-matrix of eigen-shapes Φ, respectively. The corresponding points from the mean shape x partial contour can be represented as ¯ s + Φs bs + , xs = x (4) where is the approximation error. The parameter vector bs can be computed by minimizing the mean square of the error E = kk2 , which yields ¯ s − Φs bs k2 . arg min E = arg min kxs − x bs
bs
(5)
Differentiating both sides of (5) with respect to bs results in ∂E ¯ s ). = 2ΦTs Φs bs − 2ΦTs (xs − x ∂bs
(6)
The mean square error E is minimized when the left side of (6) equals to 0. Therefore, the coefficients bs can be computed by using Moore-Penrose inverse as bs = ΦTs Φs
−1
¯s) . ΦTs (xs − x
(7)
The estimated shape from PASM is generated by replacing the coefficients b in (3) with bs as ˆ=x ¯ + Φbs . x
(8)
ˆ estimated from (8) has two desired properties. Firstly, the estimated shape is an approximation The shape x to the partial salient contour xs by fitting the corresponding parts of the shape statistics to it in regard to minimizing the mean square error E. Secondly, the estimated shape is an interpolation of the shape statistics with weights bs for the components in the rest of the contour. Instead of trying to approximate the potentially misleading contour in that part, the estimated shape just follows the shape statistics to make a reasonable estimation.
2.3 Segmentation using Discrete Deformable Model Under the guidance of shape prior obtained by using PASM, deformable model is employed to segment TRUS images for extracting boundaries. However, it is computationally inhibitive to compute the NVP features at every pixel location with all the possible orientations, which are required by the traditional deformable model.19 Thus, a discrete deformable model (DDM) is proposed to solve the problem. The definition of energy function associated with DDM is given below. In order to efficiently deform the shape model towards the minimum of the energy function, an optimal search is performed by using dynamic programming, which greatly reduces the computational complexity and guarantees global minimum inside the search range. The details are given as follows.
2.3.1 Discrete Deformable Model The discrete deformable model consists of a shape model represented by a set of sequential points, with an associated energy function. The prostate is segmented from TRUS images by deforming the DDM through moving the model points to minimize the associated energy function. In our work, for each model point, the energy function consists of three terms, external image feature term, internal contour continuity and curvature term, and PASM shape guidance term E(vi ) = Eext (vi ) + Eint (vi ) + EP ASM (vi ).
(9)
The external energy Eext (vi ) is defined by the contrast of NVP features and attracts the contour towards the prostate boundary defined by dark-to-bright transition Eext (vi ) = pT · f,
(10)
as defined in Section 2.1. The internal energy Eint (vi ) is defined by the model continuity and curvature, and used to preserve the geometric shape of the model during deformation. In our work, we consider the case when Eint (vi ) includes the second order term, i.e. the computation of Eint (vi ) involves the model points vi−1 and vi+1 . Let d denote the average distance between the model points. The internal energy term can be computed as Eint (vi ) = α(kvi − vi−1 k + kvi+1 − vi k − 2d) + βk(vi − vi−1 ) − (vi+1 − vi )k,
(11)
where α and β are the weights of the continuity and curvature, respectively, and d is the average distance between neighboring contour points. The first term at the right side of (11) tends to keep the contour points from either too close or too far. The second term wants to make the model smooth by penalizing sharp angles. The PASM term is defined by the distance between point vi from the model and the corresponding point vi0 on the estimated shape using PASM EP ASM (vi ) = γkvi − vi0 k, (12) where γ is a positive weighting parameter. The PASM term plays a key role in segmentation with two major contributions. Firstly, it guides the deformable model to get smoother contour and to overcome noise influence. More importantly, it drives the deformable model towards the estimated shape prior in shadow areas, where the prostate boundary is missing as shown in Figure 2. By adding the energy function of each model point together, the total energy function that DDM seeks to minimize is defined as Etotal (v1 , v2 , · · · , vn ) = E2 (v1 , v2 , v3 ) + E3 (v2 , v3 , v4 ) + · · · + En−1 (vn−2 , vn−1 , vn ).
(13)
2.3.2 Optimal Search Using Dynamic Programming One way to find the minimum of the energy function (13) is to do an exhaustive enumeration and pick up the instance with minimum energy. It will provide the global minimum inside the search range, however, will also be extremely slow. For a model defined by n model points with m candidate search locations for each point, the computational complexity is O(mn ). Therefore, a more efficient way is required. Inspired by the work of Bergtholdt and Schn¨ orr,20 dynamic programming is employed by DDM to perform an optimal search for the minimum of the associated energy function. The dynamic programming solution involves generating a sequence of functions of one variable {Si }n−1 i=1 (the optimal energy function), where for obtaining each of them a minimization is performed over a single dimension. A global minimum is obtained by backward collecting the single minimum solutions. In order to apply dynamic programming to solving our problem, we let vi correspond to the state variable in the ith decision stage in our implementation.21 Since the energy function is second order, a two element vector of state variables, (vi+1 , vi ), is used. Now the optimal value function is a function of two adjacent points on the model and the minimization of (13) can be obtained by computing min
v1 ,··· ,vn−2
E(v1 , v2 , · · · , vn ) = min {Sn−2 (vn−2 , vn−1 ) + En−1 (vn−2 , vn−1 , vn )} , vn−2
(14)
where the optimal value function Si is computed as Si (vi , vi+1 ) = min Si−1 (vi−1 , vi ) + Ei (vi−1 , vi , vi+1 ) . vi−1
(15)
In addition to the energy matrix corresponding to the optimal value function {Si }, a position matrix is also needed to record the location of the optimal value at each state. Each entry of the position matrix at stage i stores the value of vi that minimizes (15). In order to find the model position with minimum energy using the backward method of solution for discrete dynamic programming problems, minvn Sn−1 (vn−1 , vn ) is found, which is in fact the energy of the optimal contour. Tracing back in the position matrix, the optimal position of DDM is found. This procedure constitutes a single iteration. The search algorithm of DDM guarantees to get the global minimum inside the search range. Dynamic programming will give the same result as the global search. However, the computational complexity is only O(nm3 ) and storage space requirement is O(nm2 ). Compared to the global search, the computational complexity has been greatly reduced. Furthermore, dynamic programming based optimal boundary search improves the segmentation performance of DDM. Unlike the traditional deformable model,19 it is not moving the model points one by one but searching over the whole specified space. It helps DDM to avoid being trapped by local minimum. Therefore, DDM is able to catch the prostate boundary even if the initialized contour is not close to the boundary.
2.4 Initialization Initialization is a very important step in automatic deformable segmentation. For the algorithm to be able to extract the prostate boundary, the deformable model must initially be placed close to the boundary of interest. Initialization should also be fast and robust. The initialization process proposed in this paper is guided by the normal vector profile features in TRUS images and the PDM to exploit both the dark-to-bright transition and shape statistics. Unlike most other model based techniques, which require a manual initialization to start the model fitting, we use an automatic initialization method where the average shape of training models is first used as a seed model. A coarse-to-fine pyramid approach is used to increase the capture range and efficiency of the initialization process. At each resolution level, contour points of the seed model move along the normal direction to find the darkto-bright transition. After all the points have moved, partial salient contour is then identified as described in Section 2.1. A similarity transformation Ts between the partial salient contour and the corresponding part of the ¯ is computed. The transformed shape Ts x ¯ is then used at the initialization result at the current mean shape x level. The shape obtained at the finest level is used as the final initialization result.
2.5 Integrated Multi-scale Segmentation Method The overall description of the proposed multi-scale segmentation method consisting of the above components is provided here. In order to suppress noise, median filtering is applied as a preprocessing step. After experimenting with different window sizes, the 5×5 window size was chosen in our work, which gave the best results in our experiments. The overall steps of the integrated segmentation method are described in Algorithm 2. Algorithm 2 Multi-resolution TRUS image segmentation - Compute the prostate shape statistics using PDM (see Section 2.2.1) - Preprocess the target image using median filtering. - Decompose the image into a multi-resolution pyramid.22 - Initialize a model automatically as in Section 2.4. for coarse-to-fine levels in the image pyramid do ˆ using the PASM model as in Section 2.2. - Estimate shape prior x ˆ as in Section 2.3. - Segment the prostate boundary using DDM with shape prior x end for - Return with the segmentation result from DDM at the finest level. It is worth noting that in each resolution level, DMM deformation is just performed once to get the global minimum inside the search range. Unlike in other traditional deformable model based approaches,19, 23 there is no need to have multiple iterations. Therefore, the process is efficient and fast.
Figure 6. Example segmentation results of prostate from ultrasound images with shadow areas on top of the prostate. Yellow contours show the automatic segmentation results and the ground truth is shown in magenta.
3. MATERIALS Ultrasound images used in the experiments were obtained by using an iU22 scanner (Philips Healthcare, Andover, MA). Ultrasound video frames were grabbed by using a video card. Each image has a size of 640×480 pixels. The pixel sizes of the frame-grabbed images are 0.1493mm, 0.1798mm, and 0.2098mm for 4cm, 5cm, and 6cm depth settings, respectively. In our experiments, 1687 images were grabbed in total from video sequences of 10 patients undergoing TRUS/MRI-fusion guided prostate biopsies (see Figure 1). Table 1. Numbers of total images and segmented images for patients.
Patient # images # Manual Seg
P1 141 19
P2 127 19
P3 183 16
P4 219 21
P5 133 13
P6 150 14
P7 103 12
P8 211 16
P9 202 17
P10 218 15
Manual ultrasound segmentations obtained by a radiologist were considered as the ground truth for evaluation. Since the images were continuously grabbed from videos with a frame rate of 30 Hz, the change between neighboring images was small. Thus, the radiologist only manually segmented 162 images, the numbers of total images and segmented ones for each patient are shown in Table 1. All the images were segmented retrospectively.
4. RESULTS Some example segmentation results are shown in Figure 6. Note that the proposed method is able to extract the complete prostate contour even though the boundary information is missing in the shadows. It is also robust to the noise and the intensity variations inside and outside of the prostate. In our work, the mean absolute distance (MAD) error metric was used to quantitatively evaluate the performance of the automatic segmentation method. Let vi and vi0 denote the ith contour point from the segmented contour and the ground truth, respectively, after equally spaced sampling. The MAD is defined as n
M AD =
1X kvi − vi0 k, n i=1
(16)
Figure 7. Mean absolute distance (MAD) error and standard deviation of the distance between manually and automatically segmented prostate contours. Left: segmentation errors without PASM; Right: segmentation errors with PASM used.
where n is the number of sample points of each contour. In our experiments, n was set to be 64. The standard deviation of the distance was also computed to see how much variation exists in the segmentation results. The evaluation results are shown in Figure 7. Compared to the segmentation results shown in Figure 4, the performance of segmentation has been significantly improved after PASM was applied. To get an overall quantitative evaluation of the segmentation results over all the patients, the average mean absolute distance was computed by taking the average of the segmentation errors. The average mean absolute distance of the segmentation results using PASM is 1.79mm±0.95mm, while the distance is 3.29mm±3.4mm for the segmentation results without using PASM. The proposed method was implemented in C++ based on ITK24 and took 0.3 seconds to segment prostate from a 640x480 image on a Core2 1.86 GHz PC.
5. CONCLUSIONS AND DISCUSSION In this work, we demonstrated that missing boundary information in prostate TRUS image can be well estimated from the available partial salient contours. By using the estimated complete shape prior together with a robust DDM model, the prostate can be automatically segmented from TRUS images with very promising results. The work in this paper also features an efficient segmentation algorithm. By using the proposed DDM method, computational complexity has been significantly reduced. The time required for segmenting each image is much shorter than other existing methods. While the algorithm is very effective for prostate mid-gland segmentation, its accuracy in the base and apex of the prostate is limited mostly due to the irregular shape of prostate in those areas and hardly distinguished structure boundaries. This problem will be addressed in the future work. In addition, hardware acceleration will be explored in the hope to run the algorithm in real-time interventional procedures.
ACKNOWLEDGMENTS The authors would like to thank Mr. Martin Bergtholdt from Philips Research Hamburg, Germany for the inspiring discussions.
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