Segmentation of the Bones in MRIs of the Knee Using Phase, Magnitude, and Shape Information

Rationale and Objectives

The segmentation of textured anatomy from magnetic resonance images (MRI) is a difficult problem. We present an approach that uses features extracted from the magnitude and phase of the MRI signal to segment the bones in the knee. Moreover, we show that by incorporating shape information, more accurate and anatomically valid segmentations are obtained.

Materials and Methods

Eighteen volunteers were scanned in a whole-body 3T clinical scanner using a transmit-receive quadrature extremity coil. A gradient-echo sequence was used to acquire three-dimensional (3D) volumes of raw complex image data consisting of phase and magnitude information. These images were manually segmented and features were extracted using a bank of Gabor filters. The extracted features were then used to train a support vector machine (SVM) classifier. Each image was then automatically segmented using both the SVM classifier and a 3D active shape model (ASM) driven by the classifier.

Results

The use of phase and magnitude information from both echoes obtained the most accurate classifier results with an average dice similarity coefficient of 0.907. The use of 3D ASMs further improved the robustness, accuracy and anatomic validity of the segmentations with an overall DSC of 0.922 and an average point to surface error along the bone-cartilage interface of 0.73 mm.

Conclusions

Our results demonstrate that the incorporation of phase and multiple echoes improve the results obtained by the classifier. Moreover, we show that 3D ASMs provide a robust and accurate way of using the classifier to obtain anatomically valid segmentation results.

Magnetic resonance imaging (MRI) is a widely available and well accepted non invasive imaging technique. MRI acquisition is performed in k-space where a complex signal is acquired and reconstructed to produce a complex image, with phase and magnitude components as shown Fig 1 . The development of algorithms to allow the automatic and semiautomatic segmentation of MRIs has been the focus of much research. However, most of this research only uses the magnitude of the acquired complex MR signal, discarding the phase information.

Open full size image

Figure 1

Example sagittal slice (Case 11) showing the ( left ) phase and ( right ) magnitude at top T E1 = 4.9 milliseconds and bottom T E2 = 8.6 milliseconds.

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Materials and methods

MRI Acquisition

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Feature Extraction

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Iφ(x,y,z)=I(x,y,z)A(x,y,z)=ejφ(x,y,z). I

(

)

(

)

(

)

(

)

where A(x,y,z) A

(

) is the magnitude of the complex image. As a result, both the magnitude image A(x,y,z) A

(

) and the complex phase image Iφ(x,y,z) I

(

) can be Fourier transformed and filtered with the same bank of Gabor filters, producing 2 different sets of features.

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Classification

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3D ASM

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A 3D statistical shape model of the bones is used to represent the variability in shape of the bones. The approach used to automatically obtain the corresponding landmarks required, to build the SSM, was previously described elsewhere ( ) and follows the minimum description length optimization framework ( ). The number of training shapes in this model was increased using a bootstrap approach where the model was used to accurately segment the manual segmentations of the dual echo images (using an ASM and then a deformable model based relaxation). All the extracted surfaces were used in the model to create a combined SSM (consisting of the patella, tibia, and femur bones) that incorporated 42 different knees, each consisting of p j ; j = 1, 2, … , M (= 23,046) points.

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Segmentation System

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Validation Methodology

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Results

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Table 1

Mean (Standard Deviation) of the Dice Similarity Coefficient on the Bone Segmentation over the 14 Testing Datasets Segmented Three Times with Three Different Training Datasets ( CV 1 to CV 4 )

T E 1 T E 2 T E 1 T E 2 Support vector machine classifier Phase 0.68 (0.07) 0.73 (0.04) 0.83 (0.05) Magnitude 0.78 (0.05) 0.81 (0.04) 0.88 (0.03) Mag-phase 0.85 (0.03) 0.85 (0.02) 0.907 (0.021) ASM three-dimensional Mag-phase — — 0.918 (0.022) Relaxed Mag-phase — — 0.922 (0.021)

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Table 2

Mean (Standard Deviation) of the DSC on the Bone Segmentation over the Datasets

Patella Tibia Femur Affine_T E_ 2 0.60 (0.19) 0.82 (0.07) 0.83 (0.08) Three-dimensional active shape model Mag-phase_T E_ 1 T E 2 0.856 (0.028) 0.918 (0.030) 0.924 (0.028) Relaxed Mag-phase_T E_ 1 T E 2 0.870 (0.029) 0.920 (0.030) 0.929 (0.026)

Each segmented 51 times (three different training datasets [from CV 1 to CV 4 ] using 17 different atlas image initializations) except cases 17 and 18, which were segmented 68 times.

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Discussion

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Acknowledgment

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References

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Segmentation of the Bones in MRIs of the Knee Using Phase, Magnitude, and Shape Information

Rationale and Objectives

Materials and Methods

Results

Conclusions

Materials and methods

MRI Acquisition

Feature Extraction

Classification

3D ASM

Segmentation System

Validation Methodology

Results

Discussion

Acknowledgment

References

Further Reading

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