FluidRegNet: Longitudinal registration of retinal OCT images with new pathological fluids

Authors: julia  andresen
jan  ehrhardt
claus  von der burchard
johann  roider
heinz  handels
hristina  uzunova
Venue: MIDL_io_2024_Conference
Published: 2024-01-31 12:28:30

Abstract: Eye diseases such as the chronic central serous chorioretinopathy are characterized by fluid deposits that alter the retina and impair vision. These fluids occur at irregular intervals and may dissolve spontaneously or thanks to treatment. Accurately capturing this behavior within an image registration framework is challenging due to the resulting prominent tissue deformations and missing image correspondences between visits. This paper presents FluidRegNet, a convolutional neural network for the registration of successive optical coherence tomography images of the retina. The correspondence between time points is established by predicting the position of the origin of the fluids by creating a fluid seed in the form of sparse intensity offsets in the moving image and registering the fluid seed to the affected area in the follow-up image. We show that this leads to deformation fields that more accurately reflect the actual dynamics of retinal fluid growth compared to other image registration methods. In addition, the network outputs are used for unsupervised fluid segmentation.

Main paper: 
 introduction: 
 The eye disease central serous chorioretinopathy (CSCR) is characterized by the formation of fluid deposits below and sometimes within the retina, which severely impair the patient's vision. Although these fluids are clearly visible on optical coherence tomography (OCT) images, the underlying pathomechanisms are still poorly understood (Pfau et al., 2021) . However, it is known that the fluid distribution can change considerably within short time, which means that OCT images from successive examinations can have a very different shape and appearance. Nevertheless, the correct quantification of fluid development is a crucial step in understanding disease development and progression. A longitudinal image registration framework establishing spatial correspondence between images from different time points is, therefore, a key for the computer-aided assessment of retinal OCT timeseries, and can be used for e.g. volume change tracking, progress control or automatic segmentation by only requiring the ground truth annotation of the first time point.Yet, the nature of fluids in the retina can be extremely varying, showing different biophysical properties. For example, intraretinal fluids (IRF) cause local displacements of the normal retinal tissue, while subretinal fluids (SRF) lift the entire overlying retina. Additionally, different treatments are able to reduce or even completely dissolve the fluid deposits, that, however, can repeatedly emerge in the further course of image acquisition. This dynamic of emerging and dissolving fluids does not allow for conventional longitudinal registration approaches, due to the missing correspondences between time points, requiring for a specialized approach that can capture the dynamics of retinal fluid growth in CSCR.The longitudinal registration of OCT images has been studied in the literature primarily for non-pathological images, e.g. (Niemeijer et al., 2009; Lang et al., 2016; Lee et al., 2017; Gong et al., 2019) . For images with pathologies, existing image registration methods (Wei et al., 2017; Pan et al., 2019 Pan et al., , 2020;; Andresen et al., 2022a) can successfully be used to model size changes of existing fluids, yet, they usually fail to accurately capture the nature of the displacements caused by newly emerging fluid deposits. Often a smearing of the normal retinal tissue over the fluid area is observed (Andresen et al., 2022a) . Furthermore, most methods require given segmentations of retinal layers (Wei et al., 2017; Pan et al., 2019 Pan et al., , 2020)) , which need to be acquired through laborious and time-consuming manual work.A common approach to tackle the problem of missing correspondences is to model the causing structures (here: new lesions) directly and integrate them into the registration process as prior knowledge, as in (Shin et al., 2018; Uzunova et al., 2019; Andresen et al., 2022b) . However, such modeling approaches often do not account for the healthy tissue displacement caused by the pathology, which, in the case of retinal OCTs, might be severe. An attempt to implicitly model these fluid-induced deformations is given by (Uzunova et al., 2022) , however, this method does not explicitly model the pathological displacement, and, furthermore, requires ground truth fluid segmentations.Another concept to model emerging pathological structures during image registration is to account for their differing appearance by using metamorphosis models. They can jointly estimate appearance and shape differences between images and have been shown to be suitable for the registration of pathological images. To the best of our knowledge, these methods either consider appearance differences for the entire imaged tissue (Meng et al., 2022) or require exact ground truth pathology segmentations to model only the appearance differences in the pathology regions (Niethammer et al., 2011; Maillard et al., 2022; François et al., 2022; Joshi and Hong, 2023; Wang et al., 2023) .Inspired by metamorphosis methods, in this work, we present a deep learning-based approach for the longitudinal registration of OCT images that is capable of capturing the dynamics of retinal fluid growth in a fully unsupervised manner. The proposed fluid registration network, FluidRegNet, is not only able to model existing growing and shrinking lesions by predicting spatial deformations, but also newly emerging fluids can be represented using a novel sparse appearance seed approach. This leads to more realistic displacements of the healthy and pathological tissue compared to conventional registration approaches. Furthermore, the proposed method does not require any ground truth pathology labels for training and can also be used for an unsupervised segmentation of retinal fluids.  
methods: 
 The goal of our registration method is to geometrically align OCT images from different time points featuring realistic, fluid-induced deformations. While growing and shrinking lesions can be captured by the resulting deformation field, newly emerging or dissolving lesions cannot be solely modeled by spatial deformations, as there are no corresponding lesion pixels in the reference image. In this work, we propose to explicitly and sophisticatedly tackle the clinically relevant problem of newly emerged pathological fluids as a major clinical biomarker. We present FluidRegNet, a registration framework that addresses the issues arising from the frequently changing clinical manifestations of fluids in CSCR. The intuition behind the presented approach is to mimic the onset of fluid formation in the moving image by inserting so-called lesion appearance seeds: minimal regions of changed intensities which can be then stretched to the fluid region by a suitable deformation field (Fig. 1 ). Since we assume that the deformations inside and outside fluid deposits are different, a masked regularizer loss is used, that also implicitly tackles the problem of dissolving fluids.Inspired by metamorphic approaches, our method assumes that a follow-up image F can be reconstructed from a baseline moving image M by applying an appearance offset map A and a deformation field φ, such that F ≈ (M +A)•φ. Since our scenario considers follow-up images of the same patient, the appearance offset would typically be small, however, here we model A such that it represents the seed of an emerging retinal lesion, thus, A needs to be sparse. These assumptions yield the following objective:EQUATIONwhere L Dist is the normalized cross correlation image distance loss that has successfully been applied for OCT image registration before (Pan and Chen, 2023) , L Reg serves to regularize the deformation field and L Sparse enforces sparsity of the appearance offsets.The regularization of the deformation field is crucial in the presented method, thus, the following multi-component regularization loss is used:L Reg (φ) = L Dice S retina F , S retina M • φ + γL Jac (φ) + δL Diff (φ) .(2)Here, L Dice is the Dice loss between the retina segmentation of the follow-up image S retina F and the warped retina segmentation of the moving image S retina M , giving weak guidance to the registration task and ensuring good overlap of the entire imaged tissue. Since the fluid volume can change very strongly and to different degrees for each image pair, we use a masked diffusion loss L Diff that ensures smooth displacement fields for the normal retinal tissue but allows arbitrary deformations in fluid regions. For this purpose, rough lesion segmentations are generated by binary thresholding of moving and fixed images. The resulting masks are dilated and combined to form a pseudo-lesion mask Λ. The diffusion loss is then given byL Diff (φ) = 1 |Ω\Λ| x∈Ω\Λ 2 i=1 ∥∇φ i (x)∥ 2 2 ,where Ω is the set of all image pixels. Still, foldings are avoided both inside and outside fluids by penalizing negative values of the Jacobian determinant of the deformation field J φ usingL Jac = max (0, -|J φ |) 2 .The final part of Eq. 1 is the appearance sparsity loss:L Sparse (A) = x∈Ω |A(x)| + η max (0, A(x)) 2 (3)that favors small and, due to the second term, negative values of A, which effectively leads to sparse appearance maps reflecting the low intensities of fluids in OCT images.The architecture of FluidRegNet builds on U-Net with two separate output heads for deformation field and appearance offset map. On each level, two convolutional layers with kernel size 3 followed by batch normalization and leaky ReLU activation are used. Two inputs are given to the network: a two-channel image consisting of the moving and fixed images; and a one channel difference image M -F . The inputs are first processed by two separate input blocks and then combined by concatenation. For exact architecture, see appendix (Fig. 4 ).As observed in previous work (Andresen et al., 2022a) , training from scratch with a multicomponent loss function, such as Eq. ( 1), can degrade the network's performance due to the complicated entanglement of shape and appearance. We, therefore, follow a threestep training scheme. First, the network is pre-trained for 200 epochs only considering the deformation output of the CNN. Second, a warm-up step is used throughout the next 50 epochs, in which only the layers generating the sparse appearance map are trained while the remaining layer weights are frozen. Finally, the entire network is fine-tuned for 450 more epochs. Network training is performed with a batch size of 10 on a single NVIDIA Tesla V100 GPU with 32 GBs of RAM using Adam optimization, an initial learning rate of 1e -4 and a learning rate decay of 0.8 after every tenth of the epochs. The weight parameters α, β, γ, δ and η are set to 1, 3e -4 , 1000, 1 and 210, accordingly. 
data: 
 We develop our model on 369 OCT images from 61 eyes of 33 CSCR patients acquired longitudinally with a Spectralis OCT device. Manual annotations of the retina, IRF, SRF and pigment epithelial detachment (PED) have been generated by medical experts for 19 patients. This results in 163 manually annotated image volumes, 105 of which contain fluids.For the remaining patients, only retina segmentations are given. The follow-up period ranges from two months to eleven years, with two to 17 images per eye (see appendix, Table 3 for details). All images are sized 496×512×25 voxels with a field of view of 2×6×6 mm 3 . The pre-processing of the images features flattening at the Bruch's membrane, denoising using a guided filter with radius 1 (He and Sun, 2015) and normalization to the intensity range [0, 1]. All experiments are carried out on 2D B-scans with five-fold cross-validation using 80% of patients for training and 20% for testing. Results are averaged over all test images.To evaluate registration accuracy, each image is aligned to its subsequent follow-up and results are compared against image registration benchmarks ANTs SyN (Avants et al., 2008) and VoxelMorph (Balakrishnan et al., 2019) . For fair comparison, FluidRegNet is also trained as a "classical" registration framework, using the diffusion regularizer on the entire image domain and omitting the appearance offset branch. VoxelMorph and the classical FluidRegNet are trained for 700 epochs and with the same loss function. ANTs SyN is performed with cross correlation image similarity metric, four resolution levels, no initial affine transformation and the default settings for all other parameters.Results are reported in Table 1 for the manually annotated images, showing absolute symmetric surface distance (ASSD) and 95% Hausdorff distance (HD) of the inner limiting membrane (ILM). Deformation field regularity is assessed by the average number of pixels with |J φ | < 0. Additionally, we show that our region-based regularizer in combination with sparse appearance offsets leads to more realistic deformations by evaluating the volume change |1-|J φ || separately in normal tissue and fluid regions. It is expected that the volume changes in the fluid regions will be larger than in the retinal tissue because the tissue is displaced by the fluid changes. Results show that FluidRegNet outperforms VoxelMorph in terms of registration accuracy. While the regularity of the deformation fields of VoxelMorph is best, it impairs its ability to capture large deformations (Fig. 2 ). Compared to SyN, FluidRegNet produces more regular deformation fields, while SyN aligns the ILM more accurately. The deformations resulting from SyN however are unrealistic for image registration pairs with newly forming fluids (Fig. 2 ). In contrast, FluidRegNet provides plausible deformations that are mainly large in the area of the pathologies, while the healthy tissue is displaced accordingly. Despite the different behavior inside and outside fluids, the resulting deformation fields contain very few inversions, assessed by an average of 54.17 negative Jacobian determinant pixels, corresponding to only 0.02% of all pixels.In this experiment, two assumptions are made to achieve an unsupervised segmentation of newly emerged retinal fluids: New fluids correspond to image regions with, firstly, a strong increase in volume and, secondly, large appearance offsets. Thus, the set of segmented new lesion pixels is given by S = {x ∈ Ω|φ(A(x)) < τ A ∨ |J φ (x)| > τ φ }. The thresholds τ A and τ φ are found using grid search and set to -0.017 and 4.7 respectively in order to achieve the highest segmentation accuracy while providing good detection results. For comparison, two unsupervised anomaly segmentation approaches are applied: Natural synthetic anomalies (NSA, (Schlüter et al., 2022) ), which uses Poisson image inpainting to generate synthetic Table 1 : Registration results for FluidRegNet (FRN) compared to VoxelMorph (VXM, (Balakrishnan et al., 2019) ) and symmetric image normalization (SyN, (Avants et al., 2008) ). Used metrics: absolute symmetric surface distance (ASSD) and 95% Hausdorff distance (HD) to the inner limiting membrane (ILM) in micrometers; and various evaluations of the displacement field Jacobian J φ . anomalies, a core component of the Medical Out-of-Distribution Analysis Challenge1 winner approach (Baugh et al., 2023) ; and f-AnoGAN (Schlegl et al., 2019) , a GAN-based approach developed specifically for OCT images and trained on healthy images only (here, an internal dataset of 50 healthy subjects).F M M • φ VXM |J VXM φ | M • φ SyN |J SyN φ | M • φ FRN (M + A) • φ FRN |J FRN φ | F M M • φ VXM |J VXM φ | M • φ SyN |J SyN φ | M • φ FRN (M + A) • φ FRN |J FRN φ | |Jφ| |Jφ|The results for unsupervised detection and segmentation of new fluids are shown in Table 2 . To evaluate the segmentations, the mean Dice Score (DSC) between the predicted and the ground truth segmentations of new lesions is reported. Also, the detection rate of new lesion cases is reported, classifying each image with DSC > 0 as correctly detected. Since the generated segmentations do not distinguish between IRF, SRF and PED, we first present results for all pathologies combined in one binary segmentation. DSCs per pathology type are then reported by calculating the average DSC between the ground truth per lesion type and each predicted new lesion overlapping with the ground truth.The results show that FluidRegNet reliably detects newly formed IRF (94.44%) and SRF (86.22%). Newly developed PED, however, is detected in only 27.59% of cases (examples in the appendix, Fig. 5 ). It can be noted that new PEDs are indeed the most challenging for all methods, since they are majorly underrepresented in the dataset (only 58 B-scans overall) and generally lie in the same area as SRFs. Compared to our CNN, NSA performs a better detection for all lesion types. In terms of segmentation accuracy, however, FluidRegNet achieves significantly better results and also outperforms f-AnoGAN in all metrics.Assuming that the patients' initial visits are segmented manually, we use FluidRegNet to chronologically segment fluids for the successive visits. Each longitudinal patient image I i , with i ∈ [0, t-1] and t the last acquisition time point, is registered to its subsequent I i+1 using the deformation field φ i . Starting from the segmented initial examination S 0 , the subsequent segmentations are generated for each patient as S i+1 = S i • φ. Fluids that reappear or are newly emerging in the course of treatment are modeled as described in the previous section and added to the segmentation of the previous time point. Similarly, segmentations of dissolving pathologies are removed if |J φ i | < 0.3 for at least 90% of the lesion pixels or the maximum thickness of the remaining fluid is less than five pixels. For comparison, NSA and f-AnoGAN are applied for the segmentation of each time point individually. Fig. 3 shows quantitative and qualitative results for the chronological fluid segmentation. For images with fluids in the manual ground truth, the DSC is calculated, whereas for images with no ground truth fluids, the average number of false positive pixels is reported. Requiring only one segmented start time point, FluidRegNet provides the best segmentation accuracy and the smallest amount of false positives compared to fully unsupervised anomaly detection methods. FluidRegNet can, thus, be used to accurately estimate fluid distribution and volume in time series data in an unsupervised manner. 
discussion: 
 In this paper, we presented FluidRegNet, an unsupervised registration framework for longitudinal OCT images containing pathological fluids. The presented approach overcomes the problem of missing correspondences for the registration of images with newly emerging fluids, by introducing a sparse appearance seed as an attempt to model the onset of pathological structures before applying the deformation field. Combined with a sophisticated regularization scheme, FluidRegNet provides more realistic, fluid-aware deformations and is able to handle severe appearance and shape differences between images. Our experiments show, that next to an improved registration accuracy, the presented method can also be reliably applied for unsupervised anomaly detection, and shows improved or on-par performance to state-of-the-art methods in both tasks. Even though a substantial improvement is achieved in this area, like most learning-based image registration methods, FluidRegNet has difficulties in capturing very large deformations, which we plan to address in future research. We also plan to explicitly address the problem of dissolving fluids and capture them in our framework in an improved manner. For clinical use, further tests need to be carried out on the performance of FluidRegNet in diseases with more complicated fluid patterns such as age-related macular degeneration. In addition, cases in which different fluid types occur in the same image regions should be investigated in more detail. The choice of multiple weighting parameters in the loss function is another drawback of our method. We suggest beginning with a classical registration optimizing hyperparameters for image distance and spatial regularization only before introducing appearance offsets.FluidRegNet provides a valuable tool for longitudinal registration of OCT images that captures the actual dynamics of retinal fluid growth better than other methods. Its application for unsupervised segmentation of time-series images could significantly reduce the cost of their tedious manual annotation. Finally, the realistic nature of our deformation fields enables detailed visualization of regressive and progressive areas in the eye.http://medicalood.dkfz.de/web/ 
 
 Appendix:  


Decision: All reviewers agreed that addressing the problem of longitudinal registration of retinal OCT images is an important and challenging task in medical image analysis. The proposed approach, which involves jointly estimating appearance and geometric deformations in time-series OCT images, is interesting and under-explored in the literature. Given the consistent positive recommendations from all reviewers, the meta reviewer is pleased to recommend acceptance of the paper. However, the authors are strongly encouraged to thoroughly address all comments raised by the reviewers in their final revisions.

Reviews: review: paper_summary: paper_summary: The paper addresses the challenge of capturing the dynamics of retinal fluid growth in conditions like chronic central serous chorioretinopathy (CSCR), where fluid deposits alter the retina and impair vision. Previous methods often require segmentation and prior knowledge of lesions, which can be limiting. The proposed approach utilizes a novel sparse appearance seed method to model emerging fluids and lesion growth/shrinkage without the need for ground truth labels in pathological regions during training.
main_review: main_review: Based on the authors response my points were properly addressed and some confusing sentences in the paper were rephrased. I don't have any further comments. I think it is a good paper, so I don't have any reason to change my rating.
strength_weakness: strength_weakness: - Training involves three steps: initially focusing on deformation output, then generating sparse appearance while keeping deformation frozen, and finally fine-tuning the entire network. What about the computational cost vs the other methods?
questions: questions: - In the last part, it is discussed the potential of the method to estimate the unsupervised fluid segmentation in subsequent time-points if an initial segmentation is provided. Nevertheless, given the way the segmentation are discarded and that the fluid is 'already there', not appearing, I feel like this could be applied also with classical approaches, like SyN, why is it a 'strength' of the model then?
paper_summary: paper_summary: This paper discusses the problem of missing correspondences for the registration of images with newly emerging fluids in the retina, which can severely impair a patient's vision. The paper proposes a registration framework called FluidRegNet that addresses this issue by mimicking the onset of fluid formation in the moving image by inserting minimal regions of changed intensities called lesion appearance seeds. The framework assumes that the deformations inside and outside of fluid deposits are different and uses a masked loss function to train the network. The correct quantification of fluid development is crucial in understanding disease development and progression.
main_review: main_review: This paper discusses the problem of missing correspondences for the registration of images with newly emerging fluids in the retina, which can severely impair a patient's vision. The paper proposes a registration framework called FluidRegNet that addresses this issue by mimicking the onset of fluid formation in the moving image by inserting minimal regions of changed intensities called lesion appearance seeds. The framework assumes that the deformations inside and outside of fluid deposits are different and uses a masked loss function to train the network. The correct quantification of fluid development is crucial in understanding disease development and progression.

By adding more description on the network architecture and the limitations of the method, I believe that this draft became more solid candidate for a possible accepted paper. I will sustain my initial evaluation, which was '4: Weak accept.'
strength_weakness: strength_weakness: One weakness of the paper is that it does not provide a good novelty in the architecture of the proposed method. While the paper mentions that the method is fully convolutional and uses a U-Net-like architecture, it does not provide a detailed description of the network's layers or parameters. Thus, their outperformance may be from the design of a new loss function.

Another weakness of the paper is that it does not provide a detailed analysis of the limitations of the proposed method.
questions: questions: Detailed information on the model architecture with the number of layers or nodes will supplement this paper. Also, more details in designing loss functions will strengthen the paper.
paper_summary: paper_summary: This work presents a method for OCT registration that attempts to address the presence of spontaneously occurring or disappearing fluid deposits. This is achieved by detecting fluid deposits in the images, and injecting a small fake fluid deposit in the paired image at the corresponding spot. By registering the adapted pairs, the small fake fluid deposits can be blown up to match the dark image intensities in the true deposits, which prevents large errors in the deformations fields caused by registration methods looking for "a compromise" of dark image intensities to fill the fluid deposits. This approach additionally enables unsupervised fluid segmentation.
main_review: main_review: My justification remains the same as for my preliminary rating: the paper presents a sensible, well executed method with a relevant methodological contribution. The concerns I expressed have been properly addressed, and I have no further objections to accepting the paper.
strength_weakness: strength_weakness: Most of the figures are too small to see. This makes it unpleasant to read the printed version of the paper.

The authors state that they trained the network using OCT scans from 61 eyes, but there is no information on what images were used for evaluation.
questions: questions: The information on what images were used for evaluation is missing. This should be added.

Comments: title: Sustain my initial evaluation
comment: By adding more description on the network architecture and the limitations of the method, I believe that this draft became more solid candidate for a possible accepted paper. I will sustain my initial evaluation, which was '4: Weak accept.'
Thank you very much for reviewing our paper and your valuable feedback. 

Regarding your point about the computational cost of our method, it is true that FluidRegNet requires more storage than Voxelmorph and takes longer for training due to the larger number of parameters. Still, with a memory consumption of less than 5 GBs of GPU RAM during training (when using a batch size of 10), FluidRegNet does not require more storage than other U-Net-based CNNs and can be trained on a single GPU. With the significant performance gain compared to Voxelmorph, we consider the difference in storage requirements (and training times) justifiable. Additionally, we would like to mention that we used 700 training epochs for all image registration networks, thus the number of training steps is the same for all methods compared. In the paper, we have extended the description of network training both for FluidRegNet and the competitive methods.

Yes, in Table 1 results are reported for registering each image to its subsequent follow-up image. We added this to the paper and revised Table 1 to show the standard deviations of the considered metrics. 

Upon your remark, we estimated the proportion of lesions in the dataset based on the images with given manual annotations. Out of 163 manually annotated OCT volumes, 105 contained lesions (11x IRF – 66 B-scans, 78x SRF – 715 B-scans and 65x PED – 280 B-scans). This description has been added to the paper. We would also like to draw your attention to Table 3 in the appendix, which provides a more detailed breakdown of which biomarkers are present in which patients.

Finally, we would also like to comment on your remark about using FluidRegNet for unsupervised fluid segmentation in subsequent time points. Given the nature of CSCR, we consider a classic method to be unsuitable. Fluids do indeed (dis-)appear between time points; Figure 3 shows patients for whom this is the case. The initial segmentation of the very first time point is thus only needed for persistent fluids that are seldom throughout our dataset. For more clarity, we reformulated the respective sentences in Section 3.3.2.
Thank you very much for the review of our paper and your detailed remarks.

Firstly, we would like to comment on your remark about the missing novelty in the network architecture. The main novelty of our method lies in the sparse fluid seed approach and the training procedure to achieve meaningful appearance offsets (combination of loss functions and 3-step training). Network design has not been the focus of our work, which is why we used an established network architecture, with only slight modifications, namely separate input layers and output heads. Nevertheless, the gain in performance that can be attributed to the network architecture (compared to Voxelmorph) is considerable, as can be seen from the results in Table 1 comparing the “classical” version of FluidRegNet to Voxelmorph since both networks are trained with the same loss functions. In view of the limited space available, we have decided to leave the illustration of the detailed network architecture in the appendix but have expanded the network description in the main paper. 

Thank you for your suggestion to add a more detailed analysis of the limitations of the method. We implemented this in the discussion section.

Upon your remark we added a justification of the choice of the individual loss components in the paper. Another aspect that might not have been fully clear is how to find the weighting parameters in the loss function. This is indeed one of the major obstacles for adapting our method to different settings or registration problems since the weighting parameters need to be well balanced to assure a good registration performance and appearance seeds that are neither too small nor too big. We recommend finding the parameters by training FluidRegNet as a classical image registration network first using only the image distance and a spatial regularizer (evaluated on the entire image domain). Once you have found good hyperparameters for these, you can perform the pre-training step. The next step is the warming-up phase in which only the appearance output head is trained. This step is well suited to find a good weighting parameter for the sparsity loss. In all our experiments, the weighting parameters for the Dice loss and the Jacobian have proven less crucial, they only need to be “high enough” to give guidance to the registration and avoid inversions. A short version of this description has been added to the discussion section.
Thank you very much for reviewing our paper and your helpful remarks.

We agree that the figures are rather small and enlarged them in the new version of the paper. We also revised Table 2 to contain only two decimal places.

Regarding the evaluation of our method, you are right that we missed explaining which data is used for evaluation. A five-fold cross-validation has been used, where the images of 80% of the patients have been used for training and the remaining images for testing. Results have been calculated over all folds and finally averaged over all test images. This description has been added to the paper.