Semantic image segmentation is crucial to many biomedical imaging applications, such as performing population analyses, diagnosing disease, and planning treatments. When enough labeled data is available, supervised deep learning-based segmentation methods produce state-of-the-art results. However, in the medical domain, obtaining manual segmentation labels for medical images requires considerable expertise and time. In most clinical image datasets, there are very few manually labeled images. The problem of limited labeled data is exacerbated by differences in image acquisition procedures across machines and institutions, which can produce wide variations in resolution, image noise, and tissue appearance.
To overcome these challenges, many supervised biomedical segmentation methods focus on hand-engineered preprocessing steps and architectures [50, 54]. It is also common to use hand-tuned data augmentation to increase the number of training examples [2, 52, 54, 60, 62]. Data augmentation functions such as random image rotations or random nonlinear deformations are easy to implement, and have been shown to be effective at improving segmentation accuracy in some settings [52, 54, 60, 62]. However, these functions have limited ability to emulate diverse and realistic examples , and can be highly sensitive to the choice of parameters .
We propose to address the challenges of limited labeled data by learning to synthesize diverse and realistic labeled examples. Our novel, automated approach to data augmentation leverages unlabeled images. Using learning-based registration methods, we model the set of spatial and appearance transforms between images in the dataset. These models capture the anatomical and imaging diversity present in the unlabeled volumes. We then synthesize new examples by sampling transforms and applying them to a single labeled example.
We demonstrate our method on the task of one-shot segmentation of brain magnetic resonance imaging (MRI) scans. We use our method to synthesize new labeled training examples, enabling the training of a supervised segmentation network. This strategy outperforms state-of-the art one-shot biomedical segmentation approaches, including single-atlas segmentation and supervised segmentation with hand-tuned data augmentation.
2 Related work
2.1 Medical image segmentation
We focus on the segmentation of brain MR images, which is challenging for several reasons. Firstly, human brains exhibit substantial anatomical variations [27, 56, 73]. Secondly, MR image intensity can vary as a result of subject-specific noise, scanner protocol and quality, and other imaging parameters . This means that a tissue class can appear with different intensities across images – even images of the same MRI modality. Segmenting such scans based on appearance alone is a difficult task.
Many existing segmentation methods rely on scan pre-processing to mitigate these intensity-related challenges. Pre-processing methods can be costly to run, and developing techniques for realistic datasets is an active area of research [14, 70]. Our augmentation method tackles these intensity-related challenges from another angle: rather than removing intensity variations, it enables a segmentation method to be robust to the natural variations in MRI scans.
A large body of classical segmentation methods use atlas-based or atlas-guided segmentation, in which a labeled reference volume, or atlas, is aligned to a target volume using a deformation model, and the labels are propagated using the same deformation [6, 13, 21, 31]. When multiple atlases are available, they are each aligned to a target volume, and the warped atlas labels are fused [35, 40, 65, 75]. In atlas-based approaches, anatomical variations between subjects are captured by a deformation model, and the challenges of intensity variations are mitigated using pre-processed scans, or intensity-robust metrics such as normalized cross-correlation. However, ambiguities in tissue appearances (e.g., indistinct tissue boundaries, image noise) can still lead to inaccurate registration and segmentations. We aim to address this limitation by training a segmentation model on diverse realistic examples, making the segmenter more robust to such ambiguities. We focus on having a single atlas, and demonstrate that our strategy outperforms atlas-based segmentation. If more than one segmented example is available, our method can leverage them.
Supervised learning approaches to biomedical segmentation have gained popularity in recent years. To mitigate the need for large labeled training datasets, these methods often use data augmentation in conjunction with hand-engineered pre-processing steps and architectures [2, 39, 50, 54, 60, 62, 78]. For instance, multi-resolution image patches and convolutional weight-sharing are used in  for few-shot segmentation.
Semi-supervised and unsupervised approaches have also been proposed to combat the challenges of small training datasets. These methods do not require paired image and segmentation data. Rather, they leverage collections of segmentation data to build anatomical priors , to train an adversarial network , or to train a novel semantic constraint . In practice, collections of images are more readily available than segmentations. Rather than rely on segmentations, our method leverages a set of unlabeled images.
2.2 Spatial and appearance transform models
Models of shape and appearance have been used in a variety of image analyses. In medical image registration, a spatial deformation model is used to establish semantic correspondences between images. This mature field spans optimization-based methods [4, 7, 64, 67], and recent learning-based methods [8, 9, 19, 41, 59, 69, 76]. We leverage VoxelMorph [8, 9]
, a recent unsupervised learning-based method, to learn spatial transforms.
Many registration methods focus on intensity-normalized images or intensity-independent objective functions, and do not explicitly account for variations in image intensity. For unnormalized images, spatial and appearance transform models have been used together to register objects that differ in texture or appearance, as well as shape. Many works build upon the framework of Morphable Models  or Active Appearance Models (AAMs) [15, 16], in which statistical models of shape and texture are constructed. In the medical domain, AAMs have been used to localize anatomical landmarks [17, 55] and perform segmentation [49, 53, 74]. We build upon these concepts by using convolutional neural networks to learn models of unconstrained spatial and intensity transform fields. Rather than learning transform models for the end goal of registration or segmentation, we sample from these models to synthesize new training examples. As we show in our experiments, augmenting a segmenter’s training set in this way can produce more robust segmentations than performing segmentation using the transform models directly.
2.3 Few-shot segmentation of natural images
Few-shot segmentation is a challenging task in semantic segmentation, video object segmentation and interactive segmentation. Existing approaches focus mainly on natural images. Methods for few-shot semantic segmentation incorporate information from prototypical examples of the classes to be segmented [23, 66]. Few-shot video segmentation is frequently implemented by aligning objects in each frame to a labeled reference frame [36, 72]. Other approaches leverage large labeled datasets of supplementary information such as object appearances . Guided networks have been used to incorporate additional information (e.g., human-in-the-loop) to perform few-shot segmentation in various settings . Medical images present a different set of challenges from natural images; for instance, the visual differences between tissue classes are very subtle compared to the differences between objects in natural images.
2.4 Data augmentation
In image-based supervised learning tasks, data augmentation is commonly performed using simple parameterized transforms such as rotation and scaling. In the medical imaging domain, random smooth flow fields are often used to simulate anatomical variations [48, 60, 61]. These parameterized transforms can reduce overfitting and improve test performance [33, 42, 48, 60, 61]. However, the performance gains imparted by these transforms vary with the selection of transformation functions and parameter settings .
Recent works have proposed learning data augmentation transformations from data. Hauberg et al. 
focus on data augmentation for classifying MNIST digits. They learn digit-specific spatial transformations, and sample training images and transformations to create new examples aimed at improving classification performance. We learn an appearance model in addition to a spatial model, and we focus on the problem of MRI segmentation.
Ratner et al.  present a semi-automated approach to learning spatial and color transformations for data augmentation. They rely on user input to create compositions of simple parameterized transformation functions (e.g., rotation and contrast enhancement). They learn to generate new compositions of transform functions using a generative adversarial network. In contrast, our approach is fully automated.
We propose to improve one-shot biomedical image segmentation by synthesizing realistic training examples in a semi-supervised learning framework.
Let be a set of biomedical image volumes, and let the pair represent a labeled reference volume, or atlas, and its corresponding segmentation map. In our problem of brain MRI segmentation, each and is a grayscale 3D volume. We focus on the challenging case where only one labeled atlas is available, since it is often difficult in practice to obtain many segmented volumes. If more segmented volumes become available, our method can be easily extended to leverage them.
To perform data augmentation, we apply transforms to the labeled atlas . We first learn separate spatial and appearance transform models to capture the distribution of anatomical and appearance differences between the labeled atlas and each unlabeled volume. Using the two learned models, we synthesize labeled volumes by applying a spatial transform and an appearance transform to the atlas volume, and by warping the atlas label maps using the spatial transform. Compared to single-atlas segmentation, which suffers from uncertainty or errors in the spatial transform model, we use the same spatial transform to synthesize the volume and label map, ensuring that the newly synthesized volume is correctly labeled. These synthetic examples form a labeled dataset that characterizes the anatomical and appearance variations in the unlabeled dataset. Along with the atlas, this new training set enables us to train a supervised segmentation network. This process is outlined in Fig. 2.
3.1 Spatial and appearance transform models
MR images can exhibit substantial inter-scan variation in anatomy and appearance. We describe the differences between scans using a combination of spatial and intensity transforms. Specifically, we define a transform from one volume to another as a composition of a spatial transform and an intensity or appearance transform , i.e., .
We assume a spatial transform takes the form of a smooth voxel-wise displacement field . Following the medical registration literature, we define the deformation function , where is the identity function. We use to denote the application of the deformation to . To model the distribution of spatial transforms in our dataset, we compute the deformation that warps atlas to each volume using , where is a parametric function that we describe later. We write approximate inverse deformation of to as .
We model the appearance transform as a per-voxel addition in the spatial frame of the atlas. We compute this per-voxel volume using the function , where is a volume that has been registered to the atlas space using our learned spatial model. In summary, our spatial and appearance transforms are:
We aim to capture the distributions of the transforms and
between the atlas and the unlabeled volumes. We estimate the transform functionsand defined in Eqs. (1) and (2) using separate convolutional neural networks, with each network using the general architecture outlined in Fig. 3. Drawing on insights from Morphable Models  and Active Appearance Models [16, 17], we optimize the spatial and appearance models independently.
, a recent unsupervised learning-based approach with an open-source implementation. VoxelMorph learns to output a smooth displacement vector field that registers one image to another by jointly optimizing an image similarity loss and a displacement field smoothness term. We use a variant of VoxelMorph with normalized cross-correlation as the image similarity loss, enabling the estimation ofwith unnormalized input volumes.
We use a similar approach to learn the appearance model. Naively, one might define from Eq. (2) as a simple per-voxel subtraction of the volumes in the atlas space. However, this leads to produce extraneous details when the registration function is imperfect, resulting in image details that do not match the correspondingly warped anatomical labels. We instead design as a neural network that produces a per-voxel intensity change in an anatomically consistent manner. Specifically, we use an image similarity loss as well as a semantically-aware smoothness regularization. Given the network output , we define a smoothness regularization function based on the atlas segmentation map:
where is a binary image of anatomical boundaries computed from the atlas segmentation labels , and is the spatial gradient operator. Intuitively, this term discourages dramatic intensity changes within the same anatomical region.
In the total appearance transform model loss , we use mean squared error for the image similarity loss . In our experiments, we found that computing the image similarity loss in the spatial frame of the subject was helpful. We balance the similarity loss with the regularization term :
is a hyperparameter.
3.3 Synthesizing new examples
The models described in Eqs. (1) and (2) enable us to sample spatial and appearance transforms by sampling target volumes from an unlabeled dataset. Since the spatial and appearance targets can be different subjects, our method can combine the spatial variations of one subject with the intensities of another into a single synthetic volume . We create a labeled synthetic example by applying the transforms computed from the target volumes to the labeled atlas:
This process is visualized in steps 3 and 4 in Fig. 2. These new labeled training examples are then included in the labeled training set for a supervised segmentation network.
3.4 Segmentation network
The newly synthesized examples are useful for improving the performance of a supervised segmentation network. We demonstrate this using a network based on the state-of-the-art architecture described in 
. To account for GPU memory constraints, the network is designed to segment one slice at a time. We train the network on random slices from the augmented training set. We select the number of training epochs using early stopping on a validation set. We emphasize that the exact segmentation network architecture is not the focus of this work, since our method can be used in conjunction with any supervised segmentation network.
We implemented all models using Keras
and Tensorflow. The application of a spatial transform to an image is implemented using the differentiable 3D spatial transformer layer as described in 
, and a similar layer that uses nearest neighbor interpolation is used to transform segmentation maps. For simplicity, we capture the forward and inverse spatial transforms described in Section3.1 using two identical neural networks. For the appearance transform model, we use the hyperparameter setting . We train our transform models with a single pair of volumes in each batch, and train the segmentation model with a batch size of slices. All models are trained with a learning rate of . Our code is available at https://github.com/xamyzhao/brainstorm.
We demonstrate how our automatic augmentation method can be used to improve brain MRI segmentation. We focus on one-shot segmentation of unnormalized scans – a challenging but practical scenario. Intensity normalization methods such as bias field correction [26, 68, 71] can work poorly in realistic situations (e.g., clinical-quality scans, or scans with stroke  or traumatic brain injury).
We use the publicly available dataset of T1-weighted MRI brain scans described in . The dataset is compiled from eight databases: ADNI , OASIS , ABIDE , ADHD200 , MCIC , PPMI , HABS , and Harvard GSP . As in , we resample the brains to with 1mm isotropic voxels, and affinely align and crop the images to . We do not perform any intensity corrections. We obtain anatomical segmentation maps for all scans using FreeSurfer , and perform skull-stripping by zeroing out voxels with no anatomical label. For evaluation, we use segmentation maps of the anatomical labels described in .
We focus on the task of segmentation using a single labeled example. We randomly select brain scans to be available at training time. In practice, the atlas is usually selected to be close to the anatomical average of the population. We select our atlas from the training set by finding the most similar scan to the anatomical average computed in . This atlas is the single labeled example that is used in the training process of our method; the labels of the other training brains are not used. We use an additional scans as a validation set, and an additional scans as a held-out test set.
4.2 Segmentation baselines
We compare our method to the following baselines:
Single-atlas segmentation (SAS): We train the state-of-the-art registration algorithm described in  to register the labeled atlas to each training volume. At test time, we use the trained spatial transform model in a single-atlas segmentation framework: we register the atlas to each test volume and warp the atlas labels using the computed deformation field [6, 13, 21, 31, 40]. That is, for each test image , we compute and predict labels .
Data augmentation using single-atlas segmentation (SAS-aug): We use SAS results as labels for the unannotated training brains, which we then include as training examples for supervised segmentation. This adds new training examples to the segmenter training set. Even though SAS can produce imperfect labels because of mistakes or ambiguity in registration, training on multiple coarse labels can result in improved segmentation performance .
Hand-tuned random data augmentation (rand-aug): Random smooth deformations have been shown to be useful for data augmentation [48, 60, 61], and are particularly relevant in biomedical applications since they can simulate anatomical variations in tissues . Similarly to [48, 60, 61], we create a random smooth deformation field by first sampling random displacement vectors on a sparse grid, and then applying bilinear interpolation and spatial blurring. We evaluated several settings for the amplitude and smoothness of the deformation field, including the ones described in . We use the settings that result in the best segmentation performance on a validation set.
We synthesize variations in tissue imaging intensity using a random global intensity multiplicative factor, similar to [34, 39]. We sample this factor uniformly from the range , which we determined by inspection to match the intensities in the dataset. This is representative of how augmentation parameters are tuned in practice. This augmentation method synthesizes a new randomly transformed brain in each training iteration.
Supervised: We train a fully-supervised segmentation network that uses ground truth labels for all examples in our training dataset. Apart from the atlas labels, these labels are not available for any of the other methods. This method serves as an upper bound.
4.3 Variants of our method
Independent sampling (ours-indep): As described in Section 3.3, we sample spatial and appearance target images independently to compute . With unlabeled targets, we obtain spatial transforms and appearance transforms, enabling the synthesis of different labeled examples. Due to memory constraints, we synthesize a random labeled example in each training iteration, rather than adding all new examples to the training set.
(Ablation study) coupled sampling (ours-coupled): To highlight the efficacy of our independent transform models, we compare ours-indep to a variant of our method where we sample each of the spatial and appearance transforms from the same target image. This results in possible synthetic examples. As in ours-indep, we synthesize a random example in each training iteration.
Ours-indep + rand-aug: When training the segmenter, we alternate between training on examples synthesized using ours-indep, and examples synthesized using rand-aug
. The addition of hand-tuned augmentation to our synthetic augmentation could introduce additional variance that is unseen even in the unlabeled set, improving the robustness of the segmenter.
|Method||Dice score||Pairwise Dice improvement|
|SAS-aug||0.775 (0.147)||0.016 (0.041)|
|Rand-aug||0.765 (0.143)||0.006 (0.088)|
|Ours-coupled||0.795 (0.133)||0.036 (0.036)|
|Ours-indep||0.804 (0.130)||0.045 (0.038)|
|Ours-indep + rand-aug||0.815 (0.123)||0.056 (0.044)|
|Supervised (upper bound)||0.849 (0.092)||0.089 (0.072)|
brain scans. We report the mean Dice score (and standard deviation in parentheses) across allanatomical labels and all test subjects. We also report the mean pairwise improvement of each method over the SAS baseline.
4.4 Evaluation metrics
We evaluate the accuracy of each segmentation method in terms of Dice score , which quantifies the overlap between two anatomical regions. A Dice score of indicates perfectly overlapping regions, while indicates no overlap. The predicted segmentation labels are evaluated relative to anatomical labels generated using FreeSurfer .
4.5.1 Segmentation performance
Table 1 shows the segmentation accuracy attained by each method. Our methods outperform all baselines in mean Dice score across all evaluation labels, showing significant improvements over the next best baselines rand-aug (
using a paired t-test) andSAS-aug ().
In Figs. 4 and 5, we compare each method to the single-atlas segmentation baseline. Fig. 4 shows that our methods attain the most improvement on average, and are more consistent than hand-tuned random augmentation. Fig. 5 shows that ours-indep + rand-aug is consistently better than each baseline on every test subject. Ours-indep alone is always better than SAS-aug and SAS, and is better than rand-aug on of the test scans.
4.5.2 Synthesized images
Our independent spatial and appearance models enable the synthesis of a wide variety of brain appearances. Fig. 8 shows several examples where combining transforms from our models produces realistic results with accurate labels.
Why do we outperform single-atlas segmentation?
Our methods rely on the same spatial registration model that is used for SAS and SAS-aug. Both ours-coupled and SAS-aug augment the segmenter training set with new images.
To understand why our method produces better segmentations, we examine the augmented images. Our method warps the image in the same way as the labels, ensuring that the warped labels match the transformed image. On the other hand, SAS-aug applies the warped labels to the original image, so any errors or noise in the registration results in a mis-labeled new training example for the segmenter. Fig. 9 highlights examples where our method synthesizes image texture within the hippocampus label that is more consistent with the texture of the ground truth hippocampus, resulting in a more useful synthetic training example.
Our framework lends itself to several plausible future extensions. In Section 3.1, we discussed the use of an approximate inverse deformation function for learning the appearance transform in the reference frame of the atlas. Rather than learning a separate inverse spatial transform model, in the future we will leverage existing work in diffeomorphic registration [3, 5, 10, 19, 77].
We sample transforms from a discrete set of spatial and appearance transforms. This could be extended to span the space of transforms more richly, e.g., through interpolation between transforms, or using compositions of transforms.
We demonstrated our approach on brain MRIs. Since the method uses no brain- or MRI-specific information, it is feasible to extend it to other anatomy or imaging modalities, such as CT.
We presented a learning-based method for data augmentation, and demonstrated it on one-shot medical image segmentation.
We start with one labeled scan and a set of unlabeled examples. Using learning-based registration methods, we model the set of spatial and appearance transforms between the labeled and unlabeled examples. These transforms capture effects such as non-linear deformations and variations in imaging intensity. We synthesize new labeled examples by sampling transforms and applying them to the labeled example, producing a wide variety of realistic new scans.
We use these synthesized examples to train a supervised segmentation model. The segmenter out-performs existing one-shot segmentation methods on every example in our test set, approaching the performance of a fully supervised model. This framework enables segmentation in many applications, such as the clinical setting where time constraints permit the manual annotation of only a few scans.
In summary, this work shows that:
learning independent models of spatial and appearance transforms from unlabeled images enables the synthesis of diverse and realistic labeled examples, and
these synthesized examples can be used to train a segmentation model that out-performs existing methods in a one-shot scenario.
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