Experimental setup:
1. Dataset: T1-weighted MRI images using eight public datasets (OASIS, ABIDE, ADHD200, MCIC, PPMI, HABS, Harvard GSP,
FreeSurfer Buckner40), all images are resampled to 256×256×256 size, And the unit voxel is 1mm isotropic (I understand it is a cube voxel with a side length of 1mm), and then the affine space is standardized, and the size is modified to 160×192×224. All MRI images are anatomically segmented using FreeSurfer software , and using a visual inspection of the total error of segmentation versus affine transformation, we end up with 30 anatomical structures containing at least 100 voxels. Use the obtained segmentation results to test the designed network structure.
The training set: validation set: test set are 3231:250:250 respectively.
2. Evaluation index: The Dice coefficient compares the correctness of the structure prediction, and the Jacobian determinant obtains the local characteristics of the deformation field.
3. Baseline Methods (Baseline Methods): Use symmetric normalization (SyN) in the ANTs package (advanced normalization tool) as the first baseline, so that SyN has a cross-correlated similarity measure, obtained by scanning across datasets Improved parameters to replace ANTs default parameters. The SyN step size is 0.25, the Gaussian parameter is (9, 0.2), and the three dimensions are iterated up to 201 times. NiftyReg is additionally added as a baseline method.
Atlas-based Registration Atlas-based registration
The atlas dataset is constructed by jointly and iteratively calibrating MRI image datasets and averaging them together, and the fixed image is a single image.
Comparison of the results of different methods
The results show that for voxels whose Jacobian is not positive, all methods will produce small islands in the deformation field, but the deformation of most voxels is diffeomorphic. VoxelMorph has no explicit constraints on diffeomorphism, and is a consequence of smoothing losses that produce smooth deformation fields that perform well. Although the other two methods require diffeomorphism (enforce or strongly encourage), the results are not as good as expected and even have negative effects. Comparing the Dice coefficient, it is found that VoexlMorph reaches or even exceeds the other two methods. The calculation time is greatly shortened, especially the time on the CPU.
Dice coefficient of different methods and different parts
Regularization Analysis (Hyperparameter Sensitivity Analysis)
Experiments with different regularization parameter λ
As shown in the figure, the average Dice coefficient of the validation set for different values of the smoothing regularization parameter λ is shown. It changes smoothly in a large range of λ values, which shows that VoexlMorph has better robustness to the choice of λ. Even setting λ=0 without forcing regularization on the registration results in better results than affine registration (0.586). The author analyzes that it may be because the network needs to register each pair of images as much as possible during training, so that the transformation function generates an implicit regularization for the data set.
Training set size and special case optimization
Using the MSE method, calculate the Dice coefficient on the training set with different data sizes, the reserved test set and the test set optimized for special cases.
It can be seen from the result graph that when the amount of data is small, there is no significant improvement. When the amount of data increases, the Dice coefficient increases significantly until it is comparable to the most advanced technology, but further increasing the amount of data will not increase the Dice coefficient.
Manual anatomical description (manually segmented labels)
The atlas-based training network was used to test 39 images in the Buckner40 dataset, and a special case optimization operation was also set.
The Dice coefficient optimized through special cases is significantly improved.
MRI image registration of different subjects
To overcome variability in registration, double the number of features in the network layer and test on 250 randomly selected registration pairs.
×2 indicates double statistical features (the number of features is doubled), and the cross-correlation CC is more stable than the mean square error MSE.
Registration using auxiliary data
Use the MSE parameter λ=0.02 and evaluate in two practical situations:
1. Use anatomical segmentation sub-labels when training;
2. Use coarse labels when training;
experiment as follows:
a. Use a subset of anatomical labels for training
γ Indicates the regularization parameter. When the abscissa is negative infinity, it means that it is completely unsupervised learning without labels; when the abscissa is positive infinity, it means that the auxiliary label value is used for training. obs can be understood as a labeled structure, and unobs is an unlabeled structure
. The first two columns show that the Dice coefficient of the unlabeled sub-label has improved, and the third column shows that when the label is labeled, there is a better result when γ is larger. At this time, the registration accuracy of the unlabeled structure decreases in the range of log γ ∈ [−3, −2], which can explain the model overfitting, and the improved Dice coefficient hurts the registration accuracy of other unlabeled structures.
b. Coarse label training
eg: label all white tissues as an anatomical structure. In this case, the relationship between coarse labels and more accurate auxiliary data can be evaluated. The fourth column (top) of the above figure shows the experimental results. When log γ =-2, the result is 3 Dice points more than the Dice coefficient without auxiliary information. Improvement
c. Regularity of transformation
The regularity of the deformation field is evaluated by the non-positive voxels of the Jacobian determinant. The table shows all the quantitative regularity measures of γ. The VoexlMorph deformation law decreases slowly with the increase of γ (in the logarithmic γ level) when γ is 0.1 When , about 0.2% of the voxels exhibit folding (distortion of the deformation field, normally a box), up to 2.3%. When γ=∞, there will be 10-13% folded voxels. Considering the Dice coefficient and the folding situation, when γ=0.01, the effect is better, and the deformation of the deformation field is not so disordered, and it is roughly within the box.
d. Manually labeled data set test
Tested on the Buckner40 data set, the results are shown in the fourth column (below) of experiment a, and the Dice coefficient has a small increase, which may be due to the high baseline Dice coefficient of the Buckner40 data.
Summarize
VoxelMorph uses unsupervised loss performance to reach a high level in terms of Dice coefficients, and greatly reduces training time. It can use auxiliary information and rough label information to improve network performance; use amortized optimization (global optimization) to get better results on smaller training sets. Effect; special case optimization has small enhancements to experimental results; experiments on γ demonstrate that performance gain varies according to quality and number of anatomical segmentations available, using only a single structure label does not affect the registration of other structures, half/all or even It is the coarse label that will improve the registration accuracy of other structures, and other auxiliary methods can also be used for enhancement. eg: different modalities or anatomical points.
VoxelMorph is universal and not limited to one kind of problem, and uses different loss functions to deal with different specific problems. Multimodal registration can be performed using MI.