Hongming Li

Hongming Li, Shujian Yu, Jose Principe

We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation process. Distinct to the classical recurrent VAEs, our CR-VAE uses a multi-head decoder, in which the $p$-th head is responsible for generating the $p$-th dimension of $\mathbf{x}$ (i.e., $\mathbf{x}^p$). By imposing a sparsity-inducing penalty on the weights (of the decoder) and encouraging specific sets of weights to be zero, our CR-VAE learns a sparse adjacency matrix that encodes causal relations between all pairs of variables. Thanks to this causal matrix, our decoder strictly obeys the underlying principles of Granger causality, thereby making the data generating process transparent. We develop a two-stage approach to train the overall objective. Empirically, we evaluate the behavior of our model in synthetic data and two real-world human brain datasets involving, respectively, the electroencephalography (EEG) signals and the functional magnetic resonance imaging (fMRI) data. Our model consistently outperforms state-of-the-art time series generative models both qualitatively and quantitatively. Moreover, it also discovers a faithful causal graph with similar or improved accuracy over existing Granger causality-based causal inference methods. Code of CR-VAE is publicly available at https://github.com/hongmingli1995/CR-VAE.

Shujian Yu, Hongming Li, Sigurd Løkse et al.

The Cauchy-Schwarz (CS) divergence was developed by Príncipe et al. in 2000. In this paper, we extend the classic CS divergence to quantify the closeness between two conditional distributions and show that the developed conditional CS divergence can be simply estimated by a kernel density estimator from given samples. We illustrate the advantages (e.g., rigorous faithfulness guarantee, lower computational complexity, higher statistical power, and much more flexibility in a wide range of applications) of our conditional CS divergence over previous proposals, such as the conditional KL divergence and the conditional maximum mean discrepancy. We also demonstrate the compelling performance of conditional CS divergence in two machine learning tasks related to time series data and sequential inference, namely time series clustering and uncertainty-guided exploration for sequential decision making. The code of conditional CS divergence is available at https://github.com/SJYuCNEL/conditional_CS_divergence.

Xiaoyang Chen, Hao Zheng, Yuemeng Li et al.

A versatile medical image segmentation model applicable to images acquired with diverse equipment and protocols can facilitate model deployment and maintenance. However, building such a model typically demands a large, diverse, and fully annotated dataset, which is challenging to obtain due to the labor-intensive nature of data curation. To address this challenge, we propose a cost-effective alternative that harnesses multi-source data with only partial or sparse segmentation labels for training, substantially reducing the cost of developing a versatile model. We devise strategies for model self-disambiguation, prior knowledge incorporation, and imbalance mitigation to tackle challenges associated with inconsistently labeled multi-source data, including label ambiguity and modality, dataset, and class imbalances. Experimental results on a multi-modal dataset compiled from eight different sources for abdominal structure segmentation have demonstrated the effectiveness and superior performance of our method compared to state-of-the-art alternative approaches. We anticipate that its cost-saving features, which optimize the utilization of existing annotated data and reduce annotation efforts for new data, will have a significant impact in the field.

Hao Zheng, Hongming Li, Yong Fan

To achieve fast, robust, and accurate reconstruction of the human cortical surfaces from 3D magnetic resonance images (MRIs), we develop a novel deep learning-based framework, referred to as SurfNN, to reconstruct simultaneously both inner (between white matter and gray matter) and outer (pial) surfaces from MRIs. Different from existing deep learning-based cortical surface reconstruction methods that either reconstruct the cortical surfaces separately or neglect the interdependence between the inner and outer surfaces, SurfNN reconstructs both the inner and outer cortical surfaces jointly by training a single network to predict a midthickness surface that lies at the center of the inner and outer cortical surfaces. The input of SurfNN consists of a 3D MRI and an initialization of the midthickness surface that is represented both implicitly as a 3D distance map and explicitly as a triangular mesh with spherical topology, and its output includes both the inner and outer cortical surfaces, as well as the midthickness surface. The method has been evaluated on a large-scale MRI dataset and demonstrated competitive cortical surface reconstruction performance.

Bojian Hou, Hongming Li, Zhicheng Jiao et al.

Conventional survival analysis methods are typically ineffective to characterize heterogeneity in the population while such information can be used to assist predictive modeling. In this study, we propose a hybrid survival analysis method, referred to as deep clustering survival machines, that combines the discriminative and generative mechanisms. Similar to the mixture models, we assume that the timing information of survival data is generatively described by a mixture of certain numbers of parametric distributions, i.e., expert distributions. We learn weights of the expert distributions for individual instances according to their features discriminatively such that each instance's survival information can be characterized by a weighted combination of the learned constant expert distributions. This method also facilitates interpretable subgrouping/clustering of all instances according to their associated expert distributions. Extensive experiments on both real and synthetic datasets have demonstrated that the method is capable of obtaining promising clustering results and competitive time-to-event predicting performance.

Yang Liu, Hongming Li, Melissa Xiaohui Qin et al.

We present SemanticQA, an evaluation suite designed to assess language models (LMs) in semantic phrase processing tasks. The benchmark consolidates existing multiword expression (MwE) resources and reorganizes them into a unified testbed. It covers both general lexical phenomena, such as lexical collocations, and three fine-grained categories: idiomatic expressions, noun compounds, and verbal constructions. Through SemanticQA, we assess LMs of diverse architectures and scales in extraction, classification, and interpretation tasks, as well as sequential task compositions. We reveal substantial performance variation, particularly on tasks requiring semantic reasoning, highlighting differences in reasoning efficacy and semantic understanding of LMs, providing insights for pushing LMs with stronger comprehension on non-trivial semantic phrases. The evaluation harness and data of SemanticQA are available at https://github.com/jacklanda/SemanticQA.

Yang Liu, Melissa Xiaohui Qin, Hongming Li et al.

We introduce LexBench, a comprehensive evaluation suite enabled to test language models (LMs) on ten semantic phrase processing tasks. Unlike prior studies, it is the first work to propose a framework from the comparative perspective to model the general semantic phrase (i.e., lexical collocation) and three fine-grained semantic phrases, including idiomatic expression, noun compound, and verbal construction. Thanks to \ourbenchmark, we assess the performance of 15 LMs across model architectures and parameter scales in classification, extraction, and interpretation tasks. Through the experiments, we first validate the scaling law and find that, as expected, large models excel better than the smaller ones in most tasks. Second, we investigate further through the scaling semantic relation categorization and find that few-shot LMs still lag behind vanilla fine-tuned models in the task. Third, through human evaluation, we find that the performance of strong models is comparable to the human level regarding semantic phrase processing. Our benchmarking findings can serve future research aiming to improve the generic capability of LMs on semantic phrase comprehension. Our source code and data are available at https://github.com/jacklanda/LexBench

Hongming Li, Shujian Yu, Jose C. Principe

We develop a new neural network based independent component analysis (ICA) method by directly minimizing the dependence amongst all extracted components. Using the matrix-based R{é}nyi's $α$-order entropy functional, our network can be directly optimized by stochastic gradient descent (SGD), without any variational approximation or adversarial training. As a solid application, we evaluate our ICA in the problem of hyperspectral unmixing (HU) and refute a statement that "\emph{ICA does not play a role in unmixing hyperspectral data}", which was initially suggested by \cite{nascimento2005does}. Code and additional remarks of our DDICA is available at https://github.com/hongmingli1995/DDICA.

Hongming Li, Shujian Yu, Bin Liu et al.

This paper proposes \emph{Episodic and Lifelong Exploration via Maximum ENTropy} (ELEMENT), a novel, multiscale, intrinsically motivated reinforcement learning (RL) framework that is able to explore environments without using any extrinsic reward and transfer effectively the learned skills to downstream tasks. We advance the state of the art in three ways. First, we propose a multiscale entropy optimization to take care of the fact that previous maximum state entropy, for lifelong exploration with millions of state observations, suffers from vanishing rewards and becomes very expensive computationally across iterations. Therefore, we add an episodic maximum entropy over each episode to speedup the search further. Second, we propose a novel intrinsic reward for episodic entropy maximization named \emph{average episodic state entropy} which provides the optimal solution for a theoretical upper bound of the episodic state entropy objective. Third, to speed the lifelong entropy maximization, we propose a $k$ nearest neighbors ($k$NN) graph to organize the estimation of the entropy and updating processes that reduces the computation substantially. Our ELEMENT significantly outperforms state-of-the-art intrinsic rewards in both episodic and lifelong setups. Moreover, it can be exploited in task-agnostic pre-training, collecting data for offline reinforcement learning, etc.

Hongming Li, Yang Liu, Chao Huang

Modern language models (LMs) increasingly require two critical resources: computational resources and data resources. Data selection techniques can effectively reduce the amount of training data required for fine-tuning LMs. However, their effectiveness is closely related to computational resources, which always require a high compute budget. Owing to the resource limitations in practical fine-tuning scenario, we systematically reveal the relationship between data selection and uncertainty estimation of selected data. Although large language models (LLMs) exhibit exceptional capabilities in language understanding and generation, which provide new ways to alleviate data scarcity, evaluating data usability remains a challenging task. This makes efficient data selection indispensable. To mitigate these issues, we propose Entropy-Based Unsupervised Data Selection (EUDS) framework. Empirical experiments on sentiment analysis (SA), topic classification (Topic-CLS), and question answering (Q&A) tasks validate its effectiveness. EUDS establishes a computationally efficient data-filtering mechanism. Theoretical analysis and experimental results confirm the effectiveness of our approach. EUDS significantly reduces computational costs and improves training time efficiency with less data requirement. This provides an innovative solution for the efficient fine-tuning of LMs in the compute-constrained scenarios.

Hongming Li, Yong Fan

A novel unsupervised deep learning method is developed to identify individual-specific large scale brain functional networks (FNs) from resting-state fMRI (rsfMRI) in an end-to-end learning fashion. Our method leverages deep Encoder-Decoder networks and conventional brain decomposition models to identify individual-specific FNs in an unsupervised learning framework and facilitate fast inference for new individuals with one forward pass of the deep network. Particularly, convolutional neural networks (CNNs) with an Encoder-Decoder architecture are adopted to identify individual-specific FNs from rsfMRI data by optimizing their data fitting and sparsity regularization terms that are commonly used in brain decomposition models. Moreover, a time-invariant representation learning module is designed to learn features invariant to temporal orders of time points of rsfMRI data. The proposed method has been validated based on a large rsfMRI dataset and experimental results have demonstrated that our method could obtain individual-specific FNs which are consistent with well-established FNs and are informative for predicting brain age, indicating that the individual-specific FNs identified truly captured the underlying variability of individualized functional neuroanatomy.

Hongming Li, Yong Fan

We present a diffeomorphic image registration algorithm to learn spatial transformations between pairs of images to be registered using fully convolutional networks (FCNs) under a self-supervised learning setting. The network is trained to estimate diffeomorphic spatial transformations between pairs of images by maximizing an image-wise similarity metric between fixed and warped moving images, similar to conventional image registration algorithms. It is implemented in a multi-resolution image registration framework to optimize and learn spatial transformations at different image resolutions jointly and incrementally with deep self-supervision in order to better handle large deformation between images. A spatial Gaussian smoothing kernel is integrated with the FCNs to yield sufficiently smooth deformation fields to achieve diffeomorphic image registration. Particularly, spatial transformations learned at coarser resolutions are utilized to warp the moving image, which is subsequently used for learning incremental transformations at finer resolutions. This procedure proceeds recursively to the full image resolution and the accumulated transformations serve as the final transformation to warp the moving image at the finest resolution. Experimental results for registering high resolution 3D structural brain magnetic resonance (MR) images have demonstrated that image registration networks trained by our method obtain robust, diffeomorphic image registration results within seconds with improved accuracy compared with state-of-the-art image registration algorithms.

Yuemeng Li, Hongming Li, Yong Fan

Segmentation of brain structures from magnetic resonance (MR) scans plays an important role in the quantification of brain morphology. Since 3D deep learning models suffer from high computational cost, 2D deep learning methods are favored for their computational efficiency. However, existing 2D deep learning methods are not equipped to effectively capture 3D spatial contextual information that is needed to achieve accurate brain structure segmentation. In order to overcome this limitation, we develop an Anatomical Context-Encoding Network (ACEnet) to incorporate 3D spatial and anatomical contexts in 2D convolutional neural networks (CNNs) for efficient and accurate segmentation of brain structures from MR scans, consisting of 1) an anatomical context encoding module to incorporate anatomical information in 2D CNNs and 2) a spatial context encoding module to integrate 3D image information in 2D CNNs. In addition, a skull stripping module is adopted to guide the 2D CNNs to attend to the brain. Extensive experiments on three benchmark datasets have demonstrated that our method achieves promising performance compared with state-of-the-art alternative methods for brain structure segmentation in terms of both computational efficiency and segmentation accuracy.

Yuemeng Li, Hangfan Liu, Hongming Li et al.

Automatic segmentation of fine-grained brain structures remains a challenging task. Current segmentation methods mainly utilize 2D and 3D deep neural networks. The 2D networks take image slices as input to produce coarse segmentation in less processing time, whereas the 3D networks take the whole image volumes to generated fine-detailed segmentation with more computational burden. In order to obtain accurate fine-grained segmentation efficiently, in this paper, we propose an end-to-end Feature-Fused Context-Encoding Network for brain structure segmentation from MR (magnetic resonance) images. Our model is implemented based on a 2D convolutional backbone, which integrates a 2D encoding module to acquire planar image features and a spatial encoding module to extract spatial context information. A global context encoding module is further introduced to capture global context semantics from the fused 2D encoding and spatial features. The proposed network aims to fully leverage the global anatomical prior knowledge learned from context semantics, which is represented by a structure-aware attention factor to recalibrate the outputs of the network. In this way, the network is guaranteed to be aware of the class-dependent feature maps to facilitate the segmentation. We evaluate our model on 2012 Brain Multi-Atlas Labelling Challenge dataset for 134 fine-grained structure segmentation. Besides, we validate our network on 27 coarse structure segmentation tasks. Experimental results have demonstrated that our model can achieve improved performance compared with the state-of-the-art approaches.

Hongming Li, Mohamad Habes, David A. Wolk et al.

Introduction: It is challenging at baseline to predict when and which individuals who meet criteria for mild cognitive impairment (MCI) will ultimately progress to Alzheimer's disease (AD) dementia. Methods: A deep learning method is developed and validated based on MRI scans of 2146 subjects (803 for training and 1343 for validation) to predict MCI subjects' progression to AD dementia in a time-to-event analysis setting. Results: The deep learning time-to-event model predicted individual subjects' progression to AD dementia with a concordance index (C-index) of 0.762 on 439 ADNI testing MCI subjects with follow-up duration from 6 to 78 months (quartiles: [24, 42, 54]) and a C-index of 0.781 on 40 AIBL testing MCI subjects with follow-up duration from 18-54 months (quartiles: [18, 36,54]). The predicted progression risk also clustered individual subjects into subgroups with significant differences in their progression time to AD dementia (p<0.0002). Improved performance for predicting progression to AD dementia (C-index=0.864) was obtained when the deep learning based progression risk was combined with baseline clinical measures. Conclusion: Our method provides a cost effective and accurate means for prognosis and potentially to facilitate enrollment in clinical trials with individuals likely to progress within a specific temporal period.

Shi Yin, Zhengqiang Zhang, Hongming Li et al.

It remains challenging to automatically segment kidneys in clinical ultrasound images due to the kidneys' varied shapes and image intensity distributions, although semi-automatic methods have achieved promising performance. In this study, we developed a novel boundary distance regression deep neural network to segment the kidneys, informed by the fact that the kidney boundaries are relatively consistent across images in terms of their appearance. Particularly, we first use deep neural networks pre-trained for classification of natural images to extract high-level image features from ultrasound images, then these feature maps are used as input to learn kidney boundary distance maps using a boundary distance regression network, and finally the predicted boundary distance maps are classified as kidney pixels or non-kidney pixels using a pixel classification network in an end-to-end learning fashion. Experimental results have demonstrated that our method could effectively improve the performance of automatic kidney segmentation, significantly better than deep learning based pixel classification networks.

Hongming Li, Yong Fan

Multi-modal biological, imaging, and neuropsychological markers have demonstrated promising performance for distinguishing Alzheimer's disease (AD) patients from cognitively normal elders. However, it remains difficult to early predict when and which mild cognitive impairment (MCI) individuals will convert to AD dementia. Informed by pattern classification studies which have demonstrated that pattern classifiers built on longitudinal data could achieve better classification performance than those built on cross-sectional data, we develop a deep learning model based on recurrent neural networks (RNNs) to learn informative representation and temporal dynamics of longitudinal cognitive measures of individual subjects and combine them with baseline hippocampal MRI for building a prognostic model of AD dementia progression. Experimental results on a large cohort of MCI subjects have demonstrated that the deep learning model could learn informative measures from longitudinal data for characterizing the progression of MCI subjects to AD dementia, and the prognostic model could early predict AD progression with high accuracy.

Hongming Li, Pamela Boimel, James Janopaul-Naylor et al.

Recent radiomic studies have witnessed promising performance of deep learning techniques in learning radiomic features and fusing multimodal imaging data. Most existing deep learning based radiomic studies build predictive models in a setting of pattern classification, not appropriate for survival analysis studies where some data samples have incomplete observations. To improve existing survival analysis techniques whose performance is hinged on imaging features, we propose a deep learning method to build survival regression models by optimizing imaging features with deep convolutional neural networks (CNNs) in a proportional hazards model. To make the CNNs applicable to tumors with varied sizes, a spatial pyramid pooling strategy is adopted. Our method has been validated based on a simulated imaging dataset and a FDG-PET/CT dataset of rectal cancer patients treated for locally advanced rectal cancer. Compared with survival prediction models built upon hand-crafted radiomic features using Cox proportional hazards model and random survival forests, our method achieved competitive prediction performance.

Shi Yin, Qinmu Peng, Hongming Li et al.

It remains challenging to automatically segment kidneys in clinical ultrasound (US) images due to the kidneys' varied shapes and image intensity distributions, although semi-automatic methods have achieved promising performance. In this study, we propose subsequent boundary distance regression and pixel classification networks to segment the kidneys, informed by the fact that the kidney boundaries have relatively homogenous texture patterns across images. Particularly, we first use deep neural networks pre-trained for classification of natural images to extract high-level image features from US images, then these features are used as input to learn kidney boundary distance maps using a boundary distance regression network, and finally the predicted boundary distance maps are classified as kidney pixels or non-kidney pixels using a pixel classification network in an end-to-end learning fashion. We also adopted a data-augmentation method based on kidney shape registration to generate enriched training data from a small number of US images with manually segmented kidney labels. Experimental results have demonstrated that our method could effectively improve the performance of automatic kidney segmentation, significantly better than deep learning-based pixel classification networks.

Hongming Li, Yong Fan

Decoding brain functional states underlying different cognitive processes using multivariate pattern recognition techniques has attracted increasing interests in brain imaging studies. Promising performance has been achieved using brain functional connectivity or brain activation signatures for a variety of brain decoding tasks. However, most of existing studies have built decoding models upon features extracted from imaging data at individual time points or temporal windows with a fixed interval, which might not be optimal across different cognitive processes due to varying temporal durations and dependency of different cognitive processes. In this study, we develop a deep learning based framework for brain decoding by leveraging recent advances in sequence modeling using long short-term memory (LSTM) recurrent neural networks (RNNs). Particularly, functional profiles extracted from task functional imaging data based on their corresponding subject-specific intrinsic functional networks are used as features to build brain decoding models, and LSTM RNNs are adopted to learn decoding mappings between functional profiles and brain states. We evaluate the proposed method using task fMRI data from the HCP dataset, and experimental results have demonstrated that the proposed method could effectively distinguish brain states under different task events and obtain higher accuracy than conventional decoding models.

Hongming Li, Yong Fan

Dynamic functional connectivity analysis provides valuable information for understanding brain functional activity underlying different cognitive processes. Besides sliding window based approaches, a variety of methods have been developed to automatically split the entire functional MRI scan into segments by detecting change points of functional signals to facilitate better characterization of temporally dynamic functional connectivity patterns. However, these methods are based on certain assumptions for the functional signals, such as Gaussian distribution, which are not necessarily suitable for the fMRI data. In this study, we develop a deep learning based framework for adaptively detecting temporally dynamic functional state transitions in a data-driven way without any explicit modeling assumptions, by leveraging recent advances in recurrent neural networks (RNNs) for sequence modeling. Particularly, we solve this problem in an anomaly detection framework with an assumption that the functional profile of one single time point could be reliably predicted based on its preceding profiles within stable functional state, while large prediction errors would occur around change points of functional states. We evaluate the proposed method using both task and resting-state fMRI data obtained from the human connectome project and experimental results have demonstrated that the proposed change point detection method could effectively identify change points between different task events and split the resting-state fMRI into segments with distinct functional connectivity patterns.

Hongming Li, Xiaofeng Zhu, Yong Fan

We present a deep semi-nonnegative matrix factorization method for identifying subject-specific functional networks (FNs) at multiple spatial scales with a hierarchical organization from resting state fMRI data. Our method is built upon a deep semi-nonnegative matrix factorization framework to jointly detect the FNs at multiple scales with a hierarchical organization, enhanced by group sparsity regularization that helps identify subject-specific FNs without loss of inter-subject comparability. The proposed method has been validated for predicting subject-specific functional activations based on functional connectivity measures of the hierarchical multi-scale FNs of the same subjects. Experimental results have demonstrated that our method could obtain subject-specific multi-scale hierarchical FNs and their functional connectivity measures across different scales could better predict subject-specific functional activations than those obtained by alternative techniques.

Hongming Li, Theodore D. Satterthwaite, Yong Fan

Brain age prediction based on neuroimaging data could help characterize both the typical brain development and neuropsychiatric disorders. Pattern recognition models built upon functional connectivity (FC) measures derived from resting state fMRI (rsfMRI) data have been successfully used to predict the brain age. However, most existing studies focus on coarse-grained FC measures between brain regions or intrinsic connectivity networks (ICNs), which may sacrifice fine-grained FC information of the rsfMRI data. Whole brain voxel-wise FC measures could provide fine-grained FC information of the brain and may improve the prediction performance. In this study, we develop a deep learning method to use convolutional neural networks (CNNs) to learn informative features from the fine-grained whole brain FC measures for the brain age prediction. Experimental results on a large dataset of resting-state fMRI demonstrate that the deep learning model with fine-grained FC measures could better predict the brain age.

Hongming Li, Yong Fan

A novel non-rigid image registration algorithm is built upon fully convolutional networks (FCNs) to optimize and learn spatial transformations between pairs of images to be registered in a self-supervised learning framework. Different from most existing deep learning based image registration methods that learn spatial transformations from training data with known corresponding spatial transformations, our method directly estimates spatial transformations between pairs of images by maximizing an image-wise similarity metric between fixed and deformed moving images, similar to conventional image registration algorithms. The image registration is implemented in a multi-resolution image registration framework to jointly optimize and learn spatial transformations and FCNs at different spatial resolutions with deep self-supervision through typical feedforward and backpropagation computation. The proposed method has been evaluated for registering 3D structural brain magnetic resonance (MR) images and obtained better performance than state-of-the-art image registration algorithms.

Hongming Li, Mohamad Habes, Yong Fan

Increasing effort in brain image analysis has been dedicated to early diagnosis of Alzheimer's disease (AD) based on neuroimaging data. Most existing studies have been focusing on binary classification problems, e.g., distinguishing AD patients from normal control (NC) elderly or mild cognitive impairment (MCI) individuals from NC elderly. However, identifying individuals with AD and MCI, especially MCI individuals who will convert to AD (progressive MCI, pMCI), in a single setting, is needed to achieve the goal of early diagnosis of AD. In this paper, we propose a deep ordinal ranking model for distinguishing NC, stable MCI (sMCI), pMCI, and AD at an individual subject level, taking into account the inherent ordinal severity of brain degeneration caused by normal aging, MCI, and AD, rather than formulating the classification as a multi-category classification problem. The proposed deep ordinal ranking model focuses on the hippocampal morphology of individuals and learns informative and discriminative features automatically. Experiment results based on a large cohort of individuals from the Alzheimer's Disease Neuroimaging Initiative (ADNI) indicate that the proposed method can achieve better performance than traditional multi-category classification techniques using shape and radiomics features from structural magnetic resonance imaging (MRI) data.

Hongming Li, Yong Fan

We propose a novel non-rigid image registration algorithm that is built upon fully convolutional networks (FCNs) to optimize and learn spatial transformations between pairs of images to be registered. Different from most existing deep learning based image registration methods that learn spatial transformations from training data with known corresponding spatial transformations, our method directly estimates spatial transformations between pairs of images by maximizing an image-wise similarity metric between fixed and deformed moving images, similar to conventional image registration algorithms. At the same time, our method also learns FCNs for encoding the spatial transformations at the same spatial resolution of images to be registered, rather than learning coarse-grained spatial transformation information. The image registration is implemented in a multi-resolution image registration framework to jointly optimize and learn spatial transformations and FCNs at different resolutions with deep self-supervision through typical feedforward and backpropagation computation. Since our method simultaneously optimizes and learns spatial transformations for the image registration, our method can be directly used to register a pair of images, and the registration of a set of images is also a training procedure for FCNs so that the trained FCNs can be directly adopted to register new images by feedforward computation of the learned FCNs without any optimization. The proposed method has been evaluated for registering 3D structural brain magnetic resonance (MR) images and obtained better performance than state-of-the-art image registration algorithms.