Free-Form Deformations Using Adaptive Control Point Status for

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Keywords: Whole heart segmentation, free-form deformations, atlas propagation .... where, Φj is the coordinate of the control point φj, Cs is the boundary of the.
Free-Form Deformations Using Adaptive Control Point Status for Whole Heart MR Segmentation Xiahai Zhuang1 , Kawal Rhode2 , Reza Razavi2, David J. Hawkes1 , and Sebastien Ourselin1 1

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Centre for Medical Image Computing, Medical Physics Department, University College London, WC1E 6BT, UK [email protected] Division of Imaging Science, King’s College London, SE1 7EH, UK

Abstract. Whole heart segmentation from cardiac MRI is useful in clinics but challenging due to the large shape variation of the heart and many indistinct boundaries commonly presented in the MR images, especially in pathological cases. Image registration for whole heart MR images has been developed and applied to atlas propagation based segmentation [1]. In this paper, we base on this segmentation framework and propose a new non rigid registration, a free-form deformations (FFDs) registration using adaptive control point status, for the segmentation refinement. This method activates and optimises control points according to the combined information of the deformation field and the heart surface from the atlas to improve the registration performance. The segmentation framework using this registration demonstrates a RMS accuracy of 1.8 ± 0.2 mm in 10 pathological data. Keywords: Whole heart segmentation, free-form deformations, atlas propagation, registration.

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Introduction

Whole heart segmentation [1,2] is an important technical development, providing delineations of a set of local regions of the heart on diagnostic images, especially based on magnetic resonance imaging (MRI). The segmentation of these local regions, mainly the anatomical substructures of the heart such as the atria and the ventricles, are crucial for specific functional analysis. In addition, whole heart functional analysis requires an accurate whole heart segmentation to enable the detection of subtle functional changes of the organ. Such analysis can lead to earlier diagnosis of cardiac diseases and better management of treatments. However, the segmentation from magnetic resonance (MR) images are still challenging due to the indistinct boundaries among local regions and the large shape variation of the heart. Atlas propagation using image registration for segmentation has shown good robustness and potential of being applicable to a wide range of pathological cases [1]. Unlike the segmentation using a statistical shape model, which needs a training phase from a large dataset [2], this propagation framework does not N. Ayache, H. Delingette, and M. Sermesant (Eds.): FIMH 2009, LNCS 5528, pp. 303–311, 2009. c Springer-Verlag Berlin Heidelberg 2009 

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require such training for different pathologies to perform the segmentation of an unseen case. Instead, it only requires the manual segmentation of one cardiac MR image as a template to perform the segmentation propagation. This propagation employs three image registration steps [1]. Firstly, a global affine registration is performed to obtain an automatic localisation of the global heart structure. Then, a locally affine registration is applied to ensure a good local correspondence of the anatomical substructures of the heart, such as the four chambers and major vessels. Finally, a non rigid registration based on the fluid algorithm [9] is performed to refine the segmentation propagation. However, the fluid registration used in [1] can be challenged for many pathological cases where the local shape of the heart is more variable and the images are more likely to be corrupted by noise and artefacts. To deal with such cases, we propose a new adaptive free-form deformations (FFDs) registration, extending and generalising the non-uniform FFDs proposed by Schnabel et al. [4]. The control points in the FFDs are associated with a status, active or passive. Active control points are then optimised, allowed to move (e.g. be active) during some specific step(s) of the registration process, while passive control points will not be optimised (e.g. remain fixed). This active-passive selection is based on the a priori information coming from a cardiac MR atlas. We demonstrate that this adaptive control points scheme performs well in the ten pathological data and improves the registration performance compared to the traditional standard FFDs. This paper is organised as follow. Section 2 presents the methodology of the FFDs registration with adaptive control point status. Section 3 describes the proposed segmentation framework. Section 4 presents the segmentation results on ten pathological cases using both the proposed adaptive FFDs and standard FFDs. Section 5 draws the conclusion and highlights the potential future work.

2 2.1

Adaptive Control Point Status Related Work

FFDs registration employs a or a series of B-splines mesh(es) to estimate the deformation field from the target image to the source image [3,6]. Schnabel et al. associated a status, active or passive, to each control point of the FFDs to simulate Non-Uniform Rational B-splines (NURBS) [4]. Such status is priorly computed before optimising the FFDs of each level, using either the reference image measures such as local entropy, or the joint image pair measures such as the gradient of the associated cost function [4]. Also, the status stays constant during the registration process at each level. This method, embedded into a multi-resolution registration scheme, improved the performance and significantly reduced the run-time compared to a standard FFDs scheme [4]. However, there are two potential challenges in terms of applying this framework to cardiac MR image registration. Firstly, in the context of cardiac MR image segmentation, the adjacent tissues of the heart such as the lung and the liver, should be considered as background information. In other words, they should not influence the registration

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Fig. 1. Left: the target image; middle: the FFDs mesh in the target space with unnecessary active control points (white dots); right: the source image

process. However, using the status setting in [4], these areas will be taken into account, because they present relevant information for the status determination measures. For example, Fig. 1 demonstrates such situation, the control points located around the liver or papillary muscle (white dots) will also be considered as active. Hence, during the registration, the liver in the target image is likely to register to the myocardium in the source image due to their similar intensity value, while the papillary muscle in the source image is also likely to register to the myocardium in the target image. As a result, the deformation in these regions will bias the segmentation propagation of the endocardial and epicardial surfaces and generate erroneous outcomes. Secondly, if the status is pre-set and remains constant, some control points could be inactivated, leading to diminishing the modelling ability of the FFDs meshes. For example, as shown in Fig. 2, the control points (white dots in middle row of (a)) around the contour of the ellipse will not be activated by using proposed measures in [4]. This is because the local supports of these control points are linked to the uniform regions in the source image, where the intensity gradient is low. Such low gradient results in the low value of the local entropy of the uniform region or the derivative of the intensity-based cost functions, and thus inactivates the associated control points. Instead, only the control points mapped to the boundary of the circle in the source image will be activated, as the black dots shown in the top row of Fig. 2 (b). If the status is not adaptively updated but remains constant, then the ellipse in the target image will not be able to deform appropriately to match the circle in the source image. 2.2

Adaptively Updated Status of Control Points

Due to the two challenges, we propose to set the status of control points adaptively for each registration iteration. As shown in Fig. 2 (c), after each registration iteration, the resultant deformation Ti inversely transforms or resamples

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(a)

(b)

(c)

(d)

Fig. 2. Registration of an ellipse, the target image, and a circle, the source image, using adaptive FFDs where the control point status is adaptively updated for each registration iteration. The white dots in (a) are special control points explained in the text. (b) shows the FFDs meshes, the contour of the ellipse, and the contour of the inverse-transformed source image. The black dots are activated control points and the arrows demonstrate the registration driving forces. (c) gives the source image inversely transformed into the target space at different registration steps. (d) demonstrates the deformed FFDs meshes at different registration steps whose concatenation gives the resultant transformation field.

the source image Is into the coordinate of the target image space (referred as target space) to get Isi . Hence, the status of the control points should be updated based on the updated information from Isi given the shape of the source image is priorly known, as shown in Fig. 2 (b). Based on this idea, we can extend the two measures in [4] as follows. For the joint image pair measures such as the gradient of associated cost function, the status can be updated based on the updated derivative of the cost function with respect to each control point at each iteration. However, this is inefficient because the computation of the derivative of a passive control point is expensive and unnecessary. For the reference image measures such as the local entropy or local intensity variance, the status can be updated based on computing the measures using the updated information from the inversely transformed source image Isi at each

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iteration. However, this scheme is still not suitable for the registration task in the context of cardiac MR image segmentation where the control points linked to the liver are supposed to be passive, though it should work well for images with uniform background. Therefore, we extend this idea to embed the shape of the source image into the status-setting process. As Fig. 2 (b) demonstrates, given the contour of the circle is priorly known, we only activate the control points within a certain distance to the updated circle contour at each registration step. Such update is achieved by inversely transforming the source image into the target space:  active, if ||Φj − Ti−1 (Cs )|| ≤ l , (1) Status(φj ) = passive, if ||Φj − Ti−1 (Cs )|| > l where, Φj is the coordinate of the control point φj , Cs is the boundary of the source image and l is the distance threshold, which is related to the local support of the control points. Since the segmentation of the atlas is priorly known indeed in the whole heart segmentation framework, this status-setting is suitable for the non rigid registration step in the refinement. Practically, we choose 5 to 15 mm for l, depending on the spacing of the FFDs mesh, to simulate irregular shaped Bspline meshes around the endocardial and epicardial surfaces. This not only avoids unnecessary computation of the derivative of a large number of passive control points, but also avoids activating control points in the adjacent tissues. 2.3

Directional Optimisation

Since intensity non-uniformity and artefacts are commonly presented in cardiac MR images, we further propose to constrain the active control points to move within the perpendicular direction of the inverse-transformed atlas surface. This constraint can help avoid optimising the control points along the biased gradient of the cost function due to intensity non-uniformity or artefacts. Similar to the perpendicular adaptation of vertices in active contour model [5], this directional optimisation can improve the robustness of the segmentation propagation. Given the boundary surface Cs of the atlas from the source image space, let v sY be a vector perpendicular to surface Cs at coordinate Y , v tX be the corresponding vector in the target space at coordinate X, T be the transformation and Y = T (X). v sY can be priorly computed from the normalised gradient of Cs : v sY = Normalise ∇C(Y ) .

(2)

Therefore, the direction v tX for moving control point φj in target space can be computed from the inverse-transformed atlas surface at coordinate X = Φj : v tX = Normalise ∇(T −1 (Cs )(X)) = Normalise ∇(Cs (T (X)) = Normalise ∇Cs (Y ) · ∇T (X) , because T −1 (Cs )(X) = Cs (Y ), where Y = T (X).

(3)

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Segmentation Framework

The segmentation framework in [1], which propagates the segmentation in the source image (atlas) to the target image (unseen image), has four steps: – A cardiac MR atlas with all regions of interest segmented; – A global affine registration to localise the heart in the atlas to that in the unseen cardiac MR image; – A locally affine registration to further initialise the substructures such as four chambers and major vessels between the atlas and the unseen image; – A non rigid registration to refine the propagation. Registration. In this paper, we use the same initialisation registrations, including the global affine registration and the locally affine registration as in [1]. For the refinement registration, we employ the proposed adaptive FFDs registration to fine-tune the segmentation. Furthermore, we use both the multi-level FFDs in [4] and the maximal displacement constraint of FFDs and concatenation in [6] to guarantee a diffeomorphic registration, because the diffeomorphism preserves the topology of the heart and is desired in this segmentation framework. For the similarity measure, we use the normalised mutual information [7]. Atlas. The atlas we used in the experiment was constructed from ten healthy volunteer MR images using the same acquisition sequence, of resolution 2 × 2 × 2 mm. Firstly of all, we resampled all the MR images into 1 × 1 × 1 mm and normalised the intensity to the same scale. Then, we manually segmented the four chambers and major vessels of the MR images to construct the corresponding label images, as the image in Fig. 3 (right). Finally, we registerred all the label images to a common space using the global affine registration, the locally affine registration, and the fluid registration [9]. The resultant transformations were used to deform the corresponding MR images into the common space to achieve an intensity mean image. The common space is not a mean shape, but a manually constructed label image with enlarged distances between the superior regions and ventricles, as shown in Fig. 3. These enhanced features help avoid overlapping of local regions and hence can improve the registration robustness [8]. Fig. 3 shows the resultant images.

Fig. 3. The heart atlas: the intensity image (left) and the label image (right). In the label image, different chambers are assigned with different label values.

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Results

Finally, we evaluate the segmentation framework using 10 pathological MR cases, which displayed a variety of heart abnormalities such as ventricular hypertropy and other anatomical abnormalities from Tetralogy of Fallot and myocardial ischemia diseases. They were acquired at St. Thomas’ Hosptial, London, using the balanced SSFP sequence for whole heart imaging with acquisition resolution 2 × 2 × 2 mm at the end-diastolic phase. The images were reconstructed or resampled into 1 × 1 × 1 mm voxel size. The manual segmentations, regarded as gold standard, have been done by a technician with cardiac anatomy knowledge slice by slice using Analyze 8.1. The segmentation error is computed from the root mean squared (RMS) surface distance between the segmented surface and the gold standard. Table 1 presents the RMS error for each anatomical sub-structures, including epicardial surface of left ventricle (EpiLV), endocardial surface of left and right ventricles (EndoLV and EndoRV), endocardial surface of left and right atria (EndoLA and EndoRA) and all these local surfaces as a whole measure (Whole), using both the proposed adaptive FFDs and the standard FFDs for segmentation refinement. The adaptive FFDs almost outperforms the standard FFDs in all categories, except for EndoRV. Especially at EpiLV, the adaptvie FFDs achieves a significantly improved accuracy, 2.3±0.7 mm RMS error, which compares with 3.1 ± 1.1 mm by the standard FFDs. This is because aligning the adjacent liver, lung tissues, and papillary muscles can bias the registration of the myocardium in the standard FFDs. Such bias makes the registraiton more likely to step into local minima and produce unrealistic deformations, as the examples shown in Fig. 4. Table 1. The segmentation error, RMS surface distance, and the percentage (%) of the error distribution: < 2 mm, 2 ∼ 5 mm, and > 5 mm RMS (mm)

< 2mm (%)

2 ∼ 5mm (%)

> 5mm (%)

19.9 ± 4.2 14.9 ± 7.3 14.5 ± 4.0 24.0 ± 9.0 16.9 ± 5.0 16.7 ± 3.9

4.8 ± 3.7 1.3 ± 0.9 3.3 ± 3.2 4.5 ± 5.3 2.5 ± 2.7 2.2 ± 1.2

20.2 ± 4.2 16.7 ± 7.1 16.7 ± 5.8 25.0 ± 6.3 21.5 ± 5.7 20.3 ± 4.0

7.4 ± 5.2 2.1 ± 2.7 3.2 ± 3.1 6.8 ± 7.3 4.3 ± 4.0 2.7 ± 1.5

Segmentation using adaptive FFDs EpiLV EndoLV EndoRV EndoLA EndoRA Whole

2.3 ± 0.7 1.6 ± 0.3 1.9 ± 0.6 2.3 ± 0.6 1.8 ± 0.4 1.8 ± 0.2

75.3 ± 6.2 83.8 ± 7.8 82.2 ± 5.7 71.5 ± 10.4 80.6 ± 6.7 81.1 ± 4.0

Segmentation using standard FFDs EpiLV EndoLV EndoRV EndoLA EndoRA Whole

3.1 ± 1.1 1.8 ± 0.7 1.9 ± 0.6 2.5 ± 1.0 2.2 ± 0.7 2.0 ± 0.3

72.5 ± 5.9 81.2 ± 8.4 80.0 ± 7.9 68.2 ± 9.9 74.2 ± 7.1 77.0 ± 4.2

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Fig. 4. Four random examples of using the adaptive FFDs registration (left) and the standard FFDs registration (right) for segmentation refinement

Table 1 also gives the error distribution for each category. The proposed FFDs achieves 1.8 ± 0.2 RMS error for the whole heart surface (Whole), and over 80% error is within 2 mm and more than 97% is within 5mm. The segmentation of EpiLV and EndoLA have demonstrated bigger errors than other categories. The major error source for EpiLV comes from the region between the left ventricle and liver tissue where boundary is not always clear from cardiac MR images; while for EndoLA, it is due to the inconsistent definition of the boundary between the left atrium and the pulmonary veins and left auricula.

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Conclusion

We have presented a new FFDs registration for the refinement in the atlas propagation based whole heart segmentation. This registration adaptively activates the control points within the a priori selective regions and restricts their moving directions to constrain the deformation of the FFDs mesh, and improves

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the optimisation efficiency. We applied this method to the segmentation framework and evaluated its performance on 10 pathological cases. The results have demonstrated a RMS accuracy of 1.8 ± 0.2 mm and an improved performance compared to the registration using standard FFDs. For the future work, we will validate our segmentation framework using a wider range of pathological data; and consider alternative similarity measures such as the phase registration [10] to extend it for echocardiography.

Acknowledgement The work was funded by EPSRC grant GR/T11395/01. The authors would like to thank colleagues Yipeng Hu and Marc Modat for their valuable discussion.

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