GroupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method
Yunlu Zhang, Xue Wu, H. Michael Gach, Harold Li, Deshan Yang
GGroupRegNet: A Groupwise One-shot DeepLearning-based 4D Image Registration Method Yunlu Zhang, Xue Wu,
H. Michael Gach,
Harold Li,
Deshan Yang
Departments of Radiation Oncology, Biomedical Engineering, and Radiology,Washington University in Saint Louis, St. Louis, MO, USAE-mail: [email protected]
September 2020
Abstract.
Accurate deformable 4-dimensional (4D) (3-dimensional in space andtime) medical images registration is essential in a variety of medical applications.Deep learning-based methods have recently gained popularity in this area for thesignificant lower inference time. However, they suffer from drawbacks of non-optimalaccuracy and the requirement of a large amount of training data. A new methodnamed GroupRegNet is proposed to address both limitations. The deformationfields to warp all images in the group into a common template is obtained throughone-shot learning. The use of the implicit template reduces bias and accumulatederror associated with the specified reference image. The one-shot learning strategyis similar to the conventional iterative optimization method but the motion modeland parameters are replaced with a convolutional neural network (CNN) and theweights of the network. GroupRegNet also features a simpler network design anda more straightforward registration process, which eliminates the need to break upthe input image into patches. The proposed method was quantitatively evaluated ontwo public respiratory-binned 4D-CT datasets. The results suggest that GroupRegNetoutperforms the latest published deep learning-based methods and is comparable tothe top conventional method pTVreg. To facilitate future research, the source code isavailable at https://github.com/vincentme/GroupRegNet . Submitted to:
Physics in Medicine & Biology
1. Introduction a r X i v : . [ ee ss . I V ] S e p roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method
2. Methods
Let I N denotes a group of gray scale images I N = { I n | n = 1 , . . . , N } . I n : Ω → R , Ω ⊂ R d represents each image in the group. The proposed method applies for I n as 2Dor 3D images, but throughout the rest of the paper, we assume they are 3D imagesrepresenting one phase in time in a 4D-CT dataset. The objective of GroupRegNet isto find a set of dense transformations that map the same anatomical locations betweenany two individual images in the group.The optimization problem to be solved by GroupRegNet is formulated as:argmin T N tem ( L simi ( T N tem ◦ I N , I tem ) + λ L smo ( T N tem )) + λ L cyc ( T N tem )) , (1)where L simi , L smo , and L cyc are the similarity, smoothness, and cyclic regularizationlosses, T N tem is a set of transformations { T n tem | n = 1 , . . . , N } that maps anatomicallocations in the template to the corresponding locations in the input images, T n tem ◦ I n and T N tem ◦ I N represent the warped n th input image and all warped input images, respectively, I tem = N (cid:80) n ( T n tem ◦ I n ) is the implicit template by averaging warped input images [12], λ and λ are the weights for smoothness and cyclic regularization, respectively. Thecyclic regularization term will only be present if the relative motion in the image group isperiodic or symmetric. The objective of the iterative optimization then becomes findingthe optimal transformation T n tem that aligns every image in the group to a templateimage while keeping the deformation field smooth and cyclically consistent. The inversetransformation T tem n that maps the same anatomical locations in the input image tothe implicit template is determined from a fixed-point method [3]. The transformationmapping between the n th and m th image T nm can be calculated using the compositionof the deformation field: T nm ( x ) = T n tem ( T tem m ( x )).Figure 1: Flowchart of GroupRegNet. The expression (n, D, H, W) represents thenumber of images in the group and the spatial dimensions of the image. roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method D n tem instead ofthe transformation field T n tem x , which are related through T n tem ( x ) = D n tem ( x ) + x . Thedetails of the components in this flowchart are further elaborated in the next subsections. Figure 2: Detailed structure of the CNN sub-network. The overall design is similar toU-Net with modifications. The rectangle blocks represent the feature maps with denotednumber of channels (top) and image scale (bottom).The CNN model consists of convolution, downscale/upscale, and skip connection.The detailed structure of this CNN is shown in figure 2. The overall structure is thesame as U-net, which is used by most medical image registration networks. However,several changes have been made to meet the need of the one-shot groupwise registration.(i) In the original U-net, the downscale and upscale layers are implemented by max-pooling and transposed convolution. They are replaced by a more straightforward roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method D n tem is then upscaled to the original resolution to warp theinput images. The scale used in this work is 0 . The local normalized cross-correlation (NCC) coefficient is adopted to measure thesimilarity loss L simi between the template and warped input images for its robustnessagainst noise and intensity shift. Let ¯ f ( x ) = (cid:80) x i f ( x i ) /n and ˆ f ( x ) = (cid:80) x i ( f ( x i ) − ¯ f ( x )) denote the local mean and variance images, respectively, where x i loops overa cubic volume with a size n around the voxel x , with n = 5 in the currentimplementation. The NCC coefficient between the two images is calculated using N CC ( f, g ) = 1 | Ω | (cid:88) x ∈ Ω (cid:80) x i ( f ( x i ) − ¯ f ( x ))( g ( x i ) − ¯ g ( x )) (cid:113) ˆ f ( x )ˆ g ( x ) . (2)Accordingly, the similarity loss L simi is the average negative NCC coefficient between anindividual warped input image and the template image L simi ( T N tem ◦ I N , I tem ) = − N (cid:88) n N CC ( T n tem ◦ I n , I tem ) . (3) L simi is in the range of [ − ,
1] for which a lower value indicates a higher similarity.The smoothness regularization loss L smo encourages a smooth and realistictransformation, which accounts the displacement field gradient and the gradient of theimage [9]: L smo ( D N tem , I tem ) = 13 N | Ω | (cid:88) n,x ∈ Ω ,i ∈ X,Y,Z ( (cid:107)∇ i D n tem ( x ) (cid:107) exp( −|∇ i I tem ( x ) | )) . (4)Here ∇ i D n tem ( x ) is the partial derivative of the displacement field with respect to axis i ,which is approximated by a forward difference.An optional cyclic consistent regularization loss is used if deformation fields in thegroup are periodic or symmetric, such as those present in a respiratory-binned 4D-CT. roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method L cyc ( T N tem ) = (cid:115) | Ω | (cid:88) x ∈ Ω ,i ∈ X,Y,Z ( (cid:88) n T n tem ,i ( x )) . (5) The one-shot learning strategy is used in GroupRegNet to eliminate the requirementof abundant training data. The input images in the group are stacked in the channeldimension, then it is fed into the neural network to derive the current total loss andto update the weights iteratively through backpropagation. The weights in CNN areindependently initialized at the beginning of each iterative registration process. In thissense, the one-shot strategy is similar to the iterative optimization in the variationalregistration.After each iteration, a set of convergence criteria is evaluated to determine whetherthe iterative process should be terminated. The main criterion is the standard deviationof the recent similarity losses. A list of N stop latest similarity losses is maintained. Alower standard deviation of this list indicates that a more stable solution has beenreached. More specifically, the optimization will stop if(i) The standard deviation σ of N stop latest similarity losses is less than the threshold σ stop .(ii) Current similarity loss is not smaller than the previous minimum similarity loss andnot larger than the previous minimum plus σ stop / N iter .The parameter N stop , σ stop , and N iter are empirically determined to be 100, 0 . D N tem is the output from CNN of the last iteration. For all evaluated cases, thisset of criteria and parameters have proved to be able to overcome the local minimumwhile avoiding prolonged computation. One example of the similarity loss vs. numberof iteration is shown in figure 3. The proposed algorithm is implemented in PyTorch. Adam optimizer with the learningrate of 0.01 is used for optimization. The number of downscales in CNN is set to 3 andthe initial number of channels is 32. The default Kaiming initialization method is usedfor all convolutional layers. The regularization terms λ and λ are empirically set to1 × − and 1 × − , respectively. Computations are conducted on an 8-core CPUAMD Ryzen 3700X with a Nvidia 2080Ti GPU. To facilitate future research, the sourcecode is available at https://github.com/vincentme/GroupRegNet . roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method L simi vs. number of iterationfor case 10 of the DIR-Lab dataset.
3. Experimental
To quantitatively evaluate the accuracy of GroupRegNet, the publicly available 4D-CT dataset DIR-Lab [2] was used. This dataset provides 10 thorax 4D-CT scans,each consisting of 10 respiratory-binned phases. Three hundred pairs of correspondinglandmarks in the lung were manually delineated by an expert at phases of End-Inhalation (EI) and End-Exhalation (EE). Two additional observers annotated partof the landmarks with the reported inter-observer variance ranged from 0 . ± .
99 mmto 1 . ± .
19 mm. In addition, 75 sets of landmarks were delineated in all expiratoryphase images, i.e. T00, T10, to T50.The registration accuracy was evaluated by comparing the Euclidean distance, i.e.,target registration error (TRE), between the deformed landmarks using the determineddeformation fields and annotated landmarks. Note that the 300 pairs of landmarksprovided by DIR-Lab suffer from two limitations. First, the number and density oflandmarks are limited. Second, the accuracy of landmarks is only at the voxel level.Fu et al. [6] recently proposed an automatic method that can generate a large amountof matching landmarks (1886 pairs on average) evenly distributed in the lung regionwith subvoxel-level accuracy (average TRE of 0 . ± .
45 mm). Therefore, these densematching landmarks were also used in this study. The landmarks provided by DIR-Laband by Fu et al. [6] are denoted by Landmark300 and LandmarkDense, respectively.Another dataset, the point-validated pixel-based breathing thorax (POPI) from [12]was also used to quantitatively evaluate the registration algorithm. This dataset consistsof six respiratory phase-binned 4D-CT. About 100 pairs of corresponding landmarks percase at EI and EE phases were created by a semi-automatic approach. roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method To reduce computation time and improve convergence, the input images were croppedto the bounding box that encompassed the landmarks in all phases plus an 8-voxelmargin in all directions. The CT image intensity was approximately normalized to therange of [-1,1] after dividing by 1000. The input images were not spatially resampled,segmented, or vessel enhanced before feeding into GroupRegNet.
4. Results
Table 1: Comparison of TREs (mean ± std in mm): GroupRegNet vs. other learning-based and conventional DIR methods using the DIR-Lab dataset evaluated by (a)Landmark300 and (b) LandmarkDense. case before reg. GroupRegNet LungRegNet[7] Fechter[4] MJ-CNN[8] GDL-FIRE[11] Fu[5] Bartlomiej[10] pTVreg[13]1 3 . ± .
78 1 . ± .
51 0 . ± .
54 1 . ± .
88 1 . ± .
63 1 . ± .
60 1 . ± .
50 0 . ± . . ± .
892 4 . ± .
90 1 . ± .
49 0 . ± .
52 1 . ± .
65 1 . ± .
56 1 . ± .
63 1 . ± .
57 0 . ± . . ± .
903 6 . ± .
05 1 . ± .
71 1 . ± .
64 1 . ± .
82 1 . ± .
70 1 . ± .
90 1 . ± .
00 1 . ± . . ± .
074 9 . ± .
86 1 . ± .
97 1 . ± .
99 1 . ± .
76 1 . ± .
96 2 . ± .
01 1 . ± .
55 2 . ± . . ± .
275 7 . ± .
51 1 . ± .
22 1 . ± .
31 1 . ± .
60 1 . ± .
28 2 . ± .
56 1 . ± .
63 1 . ± . . ± .
426 10 . ± .
96 1 . ± .
72 2 . ± .
93 2 . ± .
78 2 . ± .
70 2 . ± .
70 2 . ± .
61 1 . ± . . ± .
927 11 . ± .
42 1 . ± .
65 1 . ± .
16 1 . ± .
65 1 . ± .
03 3 . ± .
99 1 . ± .
98 1 . ± . . ± .
918 14 . ± .
00 1 . ± .
08 3 . ± .
77 3 . ± .
00 2 . ± .
78 5 . ± .
52 3 . ± .
70 1 . ± . . ± .
299 7 . ± .
97 1 . ± .
69 1 . ± .
94 1 . ± .
85 1 . ± .
94 2 . ± .
46 2 . ± .
88 1 . ± . . ± . . ± .
34 1 . ± .
63 1 . ± .
06 1 . ± .
24 1 . ± .
61 2 . ± .
88 1 . ± .
97 1 . ± . . ± . . ± .
48 1 . ± .
77 1 . ± .
58 1 . ± .
35 1 . ± .
44 2 . ± .
16 1 . ± .
83 1 . ± . . ± . .
08 1 .
48 2 .
24 2 .
98 2 .
20 2 .
76 2 .
55 2 . . (a) Landmark300 case before reg. GroupRegNet pTVreg[13]1 3 . ± .
86 0 . ± .
33 0 . ± .
172 4 . ± .
23 0 . ± .
36 0 . ± .
223 5 . ± .
08 0 . ± .
37 0 . ± .
234 7 . ± .
11 0 . ± .
35 0 . ± .
555 4 . ± .
84 0 . ± .
36 0 . ± .
306 9 . ± .
46 0 . ± .
57 0 . ± .
637 8 . ± .
73 0 . ± .
40 0 . ± .
258 8 . ± .
71 0 . ± .
43 0 . ± .
689 5 . ± .
77 0 . ± .
45 0 . ± . . ± .
31 0 . ± .
43 0 . ± . . ± .
11 0 . ± .
41 0 . ± . .
20 0 .
85 0 . (b) LandmarkDense The accuracy of GroupRegNet was compared with seven recently publishedmethods on the DIR-Lab dataset, as shown in table 1. The landmarks in EI phase(phase T00) were deformed to EE phase (phase T50) according to the calculated DVFs,and then compared to the annotated landmarks in EE phase to derive the TREs.GroupRegNet and pTVreg were evaluated on both LandmarkDense and Landmark300,while other methods only reported results on Landmark300. roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method . ± .
77 mm, evaluated on Landmark300,which was lower than most of the surveyed methods, and comparable to pTVreg [13],which is the top method listed on the DIR-Lab website. The average root meansquare error (RMSE) of GroupRegNet and pTVreg were at least 30% smaller than othermethods. GroupRegNet performed particularly better for cases with large deformations(e.g., cases 6, 7 and 8). It should also be noted that the variance of the TREs usingGroupRegNet was even less or at least equal to the inter-observer variance, suggestingthat its accuracy was superior to that of manual annotations in most regions.When evaluated using LandmarkDense, the average TRE and RMSE ofGroupRegNet were 0 . ± .
41 mm and 0 .
85 mm, respectively, demonstrating a sub-millimeter accuracy. The average RMSEs were similar comparing GroupRegNet vs.pTVreg while the former usually yielded smaller standard deviations but slightly largeraverage TREs. Note that the standard deviations of pTVreg in cases 6 and 8 wereexceptionally large, which was not observed in GroupRegNet. (a) (b)
Figure 4: Accuracy of GroupRegNet evaluated on LandmarkDense in case 7 of DIR-Lab.(a) histogram of TREs, (b) the location of the worst point determined by GroupRegNetin phases EI and EE.The TRE histogram for GroupRegNet in case 7 is shown in figure 4(a) wherethe percentage of the TREs below 1 mm, 1 . . . ± .
77 mm to 1 . ± .
64 mm. Comparing to the results from roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method ± std in mm) between GroupRegNet and otherlearning-based or conventional methods on POPI dataset. case dimensions before reg. GroupRegNet Fechter[4] GDL-FIRE[11]1 512x512x141 5 . ± .
73 1 . ± .
59 1 . ± .
68 1 . ± .
742 512x512x169 14 . ± .
20 1 . ± .
93 2 . ± .
28 2 . ± .
383 512x512x170 7 . ± .
05 0 . ± .
51 1 . ± .
54 1 . ± .
014 512x512x187 7 . ± .
89 0 . ± .
47 1 . ± .
83 1 . ± .
625 512x512x139 7 . ± .
08 1 . ± .
81 1 . ± .
97 1 . ± .
096 512x512x161 6 . ± .
68 0 . ± .
51 1 . ± .
95 1 . ± . . ± .
77 1 . ± .
64 1 . ± .
54 1 . ± . .
42 1 .
21 2 .
14 2 . Fechter and Baltas [4] and GDL-FIRE [11], the average RMSE was reduced by 44%.All previous evaluations were carried out between phases EI and EE. The 75landmarks annotated on the expiratory phases of the DIR-Lab dataset were utilizedto test whether there are large variations among different phases. The landmarks inphase T00 were deformed to other phases and then compared to manual annotations, asshown in table 3. The TREs of phases T10 and T50 were usually smaller than those ofother phases, which could be attributed to the former having smaller deformations andthe latter being more stable than the intermediate phases. In addition, the intensity roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method ± std in mm) of GroupRegNet on different targetphase images from the DIR-Lab dataset using 75 landmarks. The result of pTVreg onphase T50 is included for reference. case T10 T20 T30 T40 T50 pTVreg T501 0 . ± .
29 0 . ± .
65 1 . ± .
60 1 . ± .
64 1 . ± .
57 0 . ± .
492 0 . ± .
77 0 . ± .
58 0 . ± .
56 0 . ± .
52 1 . ± .
53 0 . ± .
493 1 . ± .
79 1 . ± .
58 1 . ± .
59 1 . ± .
61 1 . ± .
62 1 . ± .
504 1 . ± .
60 1 . ± .
80 1 . ± .
83 1 . ± .
24 1 . ± .
98 1 . ± .
915 1 . ± .
08 1 . ± .
57 1 . ± .
91 1 . ± .
62 1 . ± .
86 1 . ± .
786 1 . ± .
89 1 . ± .
78 1 . ± .
70 1 . ± .
36 1 . ± .
83 1 . ± .
767 0 . ± .
79 1 . ± .
16 1 . ± .
07 1 . ± .
81 1 . ± .
65 0 . ± .
498 1 . ± .
52 1 . ± .
22 1 . ± .
09 1 . ± .
13 1 . ± .
78 1 . ± .
749 1 . ± .
62 1 . ± .
70 1 . ± .
67 1 . ± .
70 1 . ± .
77 1 . ± . . ± .
93 1 . ± .
18 1 . ± .
36 1 . ± .
63 1 . ± .
56 0 . ± . difference maps between each phase and the warped template image via the reverseDVF T tem n are shown in figure 6. There was not a single intensity-difference map thatwas obviously better or worse than its counterpart, suggesting similar GroupRegNetperformance regardless of phases.Figure 6: Intensity-difference map between each phase and warped template in coronalview of DIR-Lab case 10. Due to the stochastic nature of weights initialization in the neural network, concernsmay arise with regard to optimization convergence and variance among multiple runs.In addition, the computation speed is important in practical applications. Two caseswith relatively small and large motions from both datasets were repeatedly registeredfive times using GroupRegNet. The variance of the registration accuracy, numberof iteration, and computation time are summarized in table 4. The variance of the roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method repeatability error mean of TREs std of TREs cropped dimensions num. of iter. computation time time per iter.mean ± std in mm sDIR-Lab case 1 0 . ± .
12 0 . ± .
02 0 . ± .
03 240 × ×
83 317 ±
24 265 ±
18 0 . . ± .
21 0 . ± .
03 0 . ± .
03 294 × ×
97 764 ±
55 973 ±
255 1 . . ± .
23 1 . ± .
02 0 . ± .
02 271 × ×
116 1073 ±
151 1792 ±
250 1 . . ± .
17 1 . ± .
01 0 . ± .
02 169 × ×
99 712 ±
78 412 ±
44 0 . registration accuracy was evaluated in terms of repeatability errors and statistics ofTREs. The former was calculated as the distance between the displaced landmarksand their average locations over five runs. Then the average and standard deviationof the repeatability error were computed over all landmarks and runs. The determinedrepeatability errors ranged from 0 . . .
03 mm, indicating similar accuracies of repeated runs. Furthermore, all registrationswere completed without convergence issues.Computation time per iteration ranged from 0 . .
5. Discussion
A new DIR method GroupRegNet is presented to register 4D medical images and todetermine all pairs of dense DVFs. The results on two respiratory 4D-CT datasetssuggest that it is able to achieve state-of-the-art performance. This study is uniquein that it has successfully combined and implemented implicit template groupwiseregistration and one-shot unsupervised learning approach. Although many componentshave been introduced in the literature, they are organically and strategically integrated,and the method outperforms many other complex and dedicated methods. For instance,figure 5(c) shows the DVF transition around the chest wall where the sliding motion wassuccessfully revealed without additional dedicated steps such as segmentation or DVFdecomposition[5]. The implicit template shown in figure 5(f) was successfully revealed byaveraging the warped input images, which showed less noise compared to original images.This is also an advantage of the implicit template groupwise registration method overthe pairwise registration method; for the latter both the reference and moving imagesare inevitably corrupted by noise.From a broader perspective, GroupRegNet can be viewed as a mixture ofconventional and learning-based methods. It follows the same iterative optimizationprocess of the conventional approach and only uses the images to be registered as input.Furthermore, segmentation images, annotated landmarks, or deformation fields do not roupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method
6. Conclusion
In this paper, a groupwise one-shot learning neural network for 4D image registrationwas presented. The implicit template strategy was first integrated with the learning-based approach. The utilization of one-shot learning strategy eliminated the needfor abundant training data. The simple network structure made the registrationat the original resolution without breaking up the input images into patches. Theaccuracy of GroupRegNet in terms of average RMSE was better than that of thelatest learning-based methods and comparable to the top conventional method. Theperformance of GroupRegNet is expected to be further improved with the additionof more complex networks and strategies, such as generative adversarial network andattention mechanism.
EFERENCES Acknowledgments
This research was partially supported by the Agency for Healthcare Research andQuality (AHRQ) grant number R01-HS022888, National Institute of Biomedical Imagingand Bioengineering (NIBIB) grant R03-EB028427 and National Heart, Lung, and BloodInstitute (NHLBI) grant R01-HL148210.
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