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Sign Language Representation Learning (SLRL) is crucial for a range of sign language-related downstream tasks such as Sign Language Translation (SLT) and Sign Language Retrieval (SLRet). Recently, many gloss-based and gloss-free SLRL methods have been proposed, showing promising performance. Among them, the gloss-free approach shows promise for strong scalability without relying on gloss annotations. However, it currently faces suboptimal solutions due to challenges in encoding the intricate, context-sensitive characteristics of sign language videos, mainly struggling to discern essential sign features using a non-monotonic video-text alignment strategy. Therefore, we introduce an innovative pretraining paradigm for gloss-free SLRL, called C${^2}$RL, in this paper. Specifically, rather than merely incorporating a non-monotonic semantic alignment of video and text to learn language-oriented sign features, we emphasize two pivotal aspects of SLRL: Implicit Content Learning (ICL) and Explicit Context Learning (ECL). ICL delves into the content of communication, capturing the nuances, emphasis, timing, and rhythm of the signs. In contrast, ECL focuses on understanding the contextual meaning of signs and converting them into equivalent sentences. Despite its simplicity, extensive experiments confirm that the joint optimization of ICL and ECL results in robust sign language representation and significant performance gains in gloss-free SLT and SLRet tasks. Notably, C${^2}$RL improves the BLEU-4 score by +5.3 on P14T, +10.6 on CSL-daily, +6.2 on OpenASL, and +1.3 on How2Sign. It also boosts the R@1 score by +8.3 on P14T, +14.4 on CSL-daily, and +5.9 on How2Sign. Additionally, we set a new baseline for the OpenASL dataset in the SLRet task.

Continual learning (CL) aims to extend deep models from static and enclosed environments to dynamic and complex scenarios, enabling systems to continuously acquire new knowledge of novel categories without forgetting previously learned knowledge. Recent CL models have gradually shifted towards the utilization of pre-trained models (PTMs) with parameter-efficient fine-tuning (PEFT) strategies. However, continual fine-tuning still presents a serious challenge of catastrophic forgetting due to the absence of previous task data. Additionally, the fine-tune-then-frozen mechanism suffers from performance limitations due to feature channels suppression and insufficient training data in the first CL task. To this end, this paper proposes feature transformation tuning (FeTT) model to non-parametrically fine-tune backbone features across all tasks, which not only operates independently of CL training data but also smooths feature channels to prevent excessive suppression. Then, the extended ensemble strategy incorporating different PTMs with FeTT model facilitates further performance improvement. We further elaborate on the discussions of the fine-tune-then-frozen paradigm and the FeTT model from the perspectives of discrepancy in class marginal distributions and feature channels. Extensive experiments on CL benchmarks validate the effectiveness of our proposed method.

The nature of diversity in real-world environments necessitates neural network models to expand from closed category settings to accommodate novel emerging categories. In this paper, we study the open-vocabulary object detection (OVD), which facilitates the detection of novel object classes under the supervision of only base annotations and open-vocabulary knowledge. However, we find that the inadequacy of neighboring relationships between regions during the alignment process inevitably constrains the performance on recent distillation-based OVD strategies. To this end, we propose Neighboring Region Attention Alignment (NRAA), which performs alignment within the attention mechanism of a set of neighboring regions to boost the open-vocabulary inference. Specifically, for a given proposal region, we randomly explore the neighboring boxes and conduct our proposed neighboring region attention (NRA) mechanism to extract relationship information. Then, this interaction information is seamlessly provided into the distillation procedure to assist the alignment between the detector and the pre-trained vision-language models (VLMs). Extensive experiments validate that our proposed model exhibits superior performance on open-vocabulary benchmarks.

Class-incremental learning (CIL) has emerged as a means to learn new classes incrementally without catastrophic forgetting of previous classes. Recently, CIL has undergone a paradigm shift towards dynamic architectures due to their superior performance. However, these models are still limited by the following aspects: (i) Data augmentation (DA), which are tightly coupled with CIL, remains under-explored in dynamic architecture scenarios. (ii) Feature representation. The discriminativeness of dynamic feature are sub-optimal and possess potential for refinement. (iii) Classifier. The misalignment between dynamic feature and classifier constrains the capabilities of the model. To tackle the aforementioned drawbacks, we propose the Dynamic Feature Learning and Matching (DFLM) model in this paper from above three perspectives. Specifically, we firstly introduce class weight information and non-stationary functions to extend the mix DA method for dynamically adjusting the focus on memory during training. Then, von Mises-Fisher (vMF) classifier is employed to effectively model the dynamic feature distribution and implicitly learn their discriminative properties. Finally, the matching loss is proposed to facilitate the alignment between the learned dynamic features and the classifier by minimizing the distribution distance. Extensive experiments on CIL benchmarks validate that our proposed model achieves significant performance improvements over existing methods.

Domain generalization (DG) based Face Anti-Spoofing (FAS) aims to improve the model's performance on unseen domains. Existing methods either rely on domain labels to align domain-invariant feature spaces, or disentangle generalizable features from the whole sample, which inevitably lead to the distortion of semantic feature structures and achieve limited generalization. In this work, we make use of large-scale VLMs like CLIP and leverage the textual feature to dynamically adjust the classifier's weights for exploring generalizable visual features. Specifically, we propose a novel Class Free Prompt Learning (CFPL) paradigm for DG FAS, which utilizes two lightweight transformers, namely Content Q-Former (CQF) and Style Q-Former (SQF), to learn the different semantic prompts conditioned on content and style features by using a set of learnable query vectors, respectively. Thus, the generalizable prompt can be learned by two improvements: (1) A Prompt-Text Matched (PTM) supervision is introduced to ensure CQF learns visual representation that is most informative of the content description. (2) A Diversified Style Prompt (DSP) technology is proposed to diversify the learning of style prompts by mixing feature statistics between instance-specific styles. Finally, the learned text features modulate visual features to generalization through the designed Prompt Modulation (PM). Extensive experiments show that the CFPL is effective and outperforms the state-of-the-art methods on several cross-domain datasets., Comment: 11 pages, 4 figures

Striking a balance between precision and efficiency presents a prominent challenge in the bird's-eye-view (BEV) 3D object detection. Although previous camera-based BEV methods achieved remarkable performance by incorporating long-term temporal information, most of them still face the problem of low efficiency. One potential solution is knowledge distillation. Existing distillation methods only focus on reconstructing spatial features, while overlooking temporal knowledge. To this end, we propose TempDistiller, a Temporal knowledge Distiller, to acquire long-term memory from a teacher detector when provided with a limited number of frames. Specifically, a reconstruction target is formulated by integrating long-term temporal knowledge through self-attention operation applied to feature teachers. Subsequently, novel features are generated for masked student features via a generator. Ultimately, we utilize this reconstruction target to reconstruct the student features. In addition, we also explore temporal relational knowledge when inputting full frames for the student model. We verify the effectiveness of the proposed method on the nuScenes benchmark. The experimental results show our method obtain an enhancement of +1.6 mAP and +1.1 NDS compared to the baseline, a speed improvement of approximately 6 FPS after compressing temporal knowledge, and the most accurate velocity estimation.

Speech-driven 3D facial animation has improved a lot recently while most related works only utilize acoustic modality and neglect the influence of visual and textual cues, leading to unsatisfactory results in terms of precision and coherence. We argue that visual and textual cues are not trivial information. Therefore, we present a novel framework, namely PMMTalk, using complementary Pseudo Multi-Modal features for improving the accuracy of facial animation. The framework entails three modules: PMMTalk encoder, cross-modal alignment module, and PMMTalk decoder. Specifically, the PMMTalk encoder employs the off-the-shelf talking head generation architecture and speech recognition technology to extract visual and textual information from speech, respectively. Subsequently, the cross-modal alignment module aligns the audio-image-text features at temporal and semantic levels. Then PMMTalk decoder is employed to predict lip-syncing facial blendshape coefficients. Contrary to prior methods, PMMTalk only requires an additional random reference face image but yields more accurate results. Additionally, it is artist-friendly as it seamlessly integrates into standard animation production workflows by introducing facial blendshape coefficients. Finally, given the scarcity of 3D talking face datasets, we introduce a large-scale 3D Chinese Audio-Visual Facial Animation (3D-CAVFA) dataset. Extensive experiments and user studies show that our approach outperforms the state of the art. We recommend watching the supplementary video.

Despite the fundamental importance of solid-solid transformations in many technologies, the microscopic mechanisms remain poorly understood. Here, we explore the atomistic mechanisms at the migrating interface during solid-solid phase transformations between the topologically closed-packed A15 and body-centred cubic phase in tungsten. The high energy barriers and slow dynamics associated with this transformation require the application of enhanced molecular sampling approaches. To this end, we performed metadynamics simulations in combination with a path collective variable derived from a machine learning classification of local structural environments, which allows the system to freely sample the complex interface structure. A disordered region of varying width forming at the migrating interface is identified as a key physical descriptor of the transformation mechanisms, facilitating the atomic shuffling and rearrangement necessary for structural transformations. Furthermore, this can directly be linked to the differences in interface mobility for distinct orientation relationships as well as the formation of interfacial ledges during the migration along low-mobility directions.

Nowadays, transformer networks have demonstrated superior performance in many computer vision tasks. In a multi-view 3D reconstruction algorithm following this paradigm, self-attention processing has to deal with intricate image tokens including massive information when facing heavy amounts of view input. The curse of information content leads to the extreme difficulty of model learning. To alleviate this problem, recent methods compress the token number representing each view or discard the attention operations between the tokens from different views. Obviously, they give a negative impact on performance. Therefore, we propose long-range grouping attention (LGA) based on the divide-and-conquer principle. Tokens from all views are grouped for separate attention operations. The tokens in each group are sampled from all views and can provide macro representation for the resided view. The richness of feature learning is guaranteed by the diversity among different groups. An effective and efficient encoder can be established which connects inter-view features using LGA and extract intra-view features using the standard self-attention layer. Moreover, a novel progressive upsampling decoder is also designed for voxel generation with relatively high resolution. Hinging on the above, we construct a powerful transformer-based network, called LRGT. Experimental results on ShapeNet verify our method achieves SOTA accuracy in multi-view reconstruction. Code will be available at https://github.com/LiyingCV/Long-Range-Grouping-Transformer., Comment: Accepted to ICCV 2023

Sign Language Translation (SLT) is a challenging task due to its cross-domain nature, involving the translation of visual-gestural language to text. Many previous methods employ an intermediate representation, i.e., gloss sequences, to facilitate SLT, thus transforming it into a two-stage task of sign language recognition (SLR) followed by sign language translation (SLT). However, the scarcity of gloss-annotated sign language data, combined with the information bottleneck in the mid-level gloss representation, has hindered the further development of the SLT task. To address this challenge, we propose a novel Gloss-Free SLT based on Visual-Language Pretraining (GFSLT-VLP), which improves SLT by inheriting language-oriented prior knowledge from pre-trained models, without any gloss annotation assistance. Our approach involves two stages: (i) integrating Contrastive Language-Image Pre-training (CLIP) with masked self-supervised learning to create pre-tasks that bridge the semantic gap between visual and textual representations and restore masked sentences, and (ii) constructing an end-to-end architecture with an encoder-decoder-like structure that inherits the parameters of the pre-trained Visual Encoder and Text Decoder from the first stage. The seamless combination of these novel designs forms a robust sign language representation and significantly improves gloss-free sign language translation. In particular, we have achieved unprecedented improvements in terms of BLEU-4 score on the PHOENIX14T dataset (>+5) and the CSL-Daily dataset (>+3) compared to state-of-the-art gloss-free SLT methods. Furthermore, our approach also achieves competitive results on the PHOENIX14T dataset when compared with most of the gloss-based methods. Our code is available at https://github.com/zhoubenjia/GFSLT-VLP., Comment: Accepted to ICCV'23

The availability of handy multi-modal (i.e., RGB-D) sensors has brought about a surge of face anti-spoofing research. However, the current multi-modal face presentation attack detection (PAD) has two defects: (1) The framework based on multi-modal fusion requires providing modalities consistent with the training input, which seriously limits the deployment scenario. (2) The performance of ConvNet-based model on high fidelity datasets is increasingly limited. In this work, we present a pure transformer-based framework, dubbed the Flexible Modal Vision Transformer (FM-ViT), for face anti-spoofing to flexibly target any single-modal (i.e., RGB) attack scenarios with the help of available multi-modal data. Specifically, FM-ViT retains a specific branch for each modality to capture different modal information and introduces the Cross-Modal Transformer Block (CMTB), which consists of two cascaded attentions named Multi-headed Mutual-Attention (MMA) and Fusion-Attention (MFA) to guide each modal branch to mine potential features from informative patch tokens, and to learn modality-agnostic liveness features by enriching the modal information of own CLS token, respectively. Experiments demonstrate that the single model trained based on FM-ViT can not only flexibly evaluate different modal samples, but also outperforms existing single-modal frameworks by a large margin, and approaches the multi-modal frameworks introduced with smaller FLOPs and model parameters., Comment: 12 pages, 7 figures

The existing multi-modal face anti-spoofing (FAS) frameworks are designed based on two strategies: halfway and late fusion. However, the former requires test modalities consistent with the training input, which seriously limits its deployment scenarios. And the latter is built on multiple branches to process different modalities independently, which limits their use in applications with low memory or fast execution requirements. In this work, we present a single branch based Transformer framework, namely Modality-Agnostic Vision Transformer (MA-ViT), which aims to improve the performance of arbitrary modal attacks with the help of multi-modal data. Specifically, MA-ViT adopts the early fusion to aggregate all the available training modalities data and enables flexible testing of any given modal samples. Further, we develop the Modality-Agnostic Transformer Block (MATB) in MA-ViT, which consists of two stacked attentions named Modal-Disentangle Attention (MDA) and Cross-Modal Attention (CMA), to eliminate modality-related information for each modal sequences and supplement modality-agnostic liveness features from another modal sequences, respectively. Experiments demonstrate that the single model trained based on MA-ViT can not only flexibly evaluate different modal samples, but also outperforms existing single-modal frameworks by a large margin, and approaches the multi-modal frameworks introduced with smaller FLOPs and model parameters., Comment: 7 pages, 4 figures, conference

Insight into structural and thermodynamic properties of nanoparticles is crucial for designing optimal catalysts with enhanced activity and stability. We present a semi-automated workflow for parameterizing the atomic cluster expansion (ACE) from ab initio data. The main steps of the workflow are the generation of training data from accurate electronic structure calculations, an efficient fitting procedure supported by active learning and uncertainty indication, and a thorough validation. We apply the workflow to the simulation of binary Pt-Rh nanoparticles that are important for catalytic applications. We demonstrate that the Pt-Rh ACE is able to reproduce accurately a broad range of fundamental properties of the elemental metals as well as their compounds while retaining an outstanding computational efficiency. This enables a direct comparison of simulations to high resolution experiments.

In recent years, many video tasks have achieved breakthroughs by utilizing the vision transformer and establishing spatial-temporal decoupling for feature extraction. Although multi-view 3D reconstruction also faces multiple images as input, it cannot immediately inherit their success due to completely ambiguous associations between unstructured views. There is not usable prior relationship, which is similar to the temporally-coherence property in a video. To solve this problem, we propose a novel transformer network for Unstructured Multiple Images (UMIFormer). It exploits transformer blocks for decoupled intra-view encoding and designed blocks for token rectification that mine the correlation between similar tokens from different views to achieve decoupled inter-view encoding. Afterward, all tokens acquired from various branches are compressed into a fixed-size compact representation while preserving rich information for reconstruction by leveraging the similarities between tokens. We empirically demonstrate on ShapeNet and confirm that our decoupled learning method is adaptable for unstructured multiple images. Meanwhile, the experiments also verify our model outperforms existing SOTA methods by a large margin. Code will be available at https://github.com/GaryZhu1996/UMIFormer., Comment: Accepted by ICCV 2023

Motion recognition is a promising direction in computer vision, but the training of video classification models is much harder than images due to insufficient data and considerable parameters. To get around this, some works strive to explore multimodal cues from RGB-D data. Although improving motion recognition to some extent, these methods still face sub-optimal situations in the following aspects: (i) Data augmentation, i.e., the scale of the RGB-D datasets is still limited, and few efforts have been made to explore novel data augmentation strategies for videos; (ii) Optimization mechanism, i.e., the tightly space-time-entangled network structure brings more challenges to spatiotemporal information modeling; And (iii) cross-modal knowledge fusion, i.e., the high similarity between multimodal representations caused to insufficient late fusion. To alleviate these drawbacks, we propose to improve RGB-D-based motion recognition both from data and algorithm perspectives in this paper. In more detail, firstly, we introduce a novel video data augmentation method dubbed ShuffleMix, which acts as a supplement to MixUp, to provide additional temporal regularization for motion recognition. Secondly, a Unified Multimodal De-coupling and multi-stage Re-coupling framework, termed UMDR, is proposed for video representation learning. Finally, a novel cross-modal Complement Feature Catcher (CFCer) is explored to mine potential commonalities features in multimodal information as the auxiliary fusion stream, to improve the late fusion results. The seamless combination of these novel designs forms a robust spatiotemporal representation and achieves better performance than state-of-the-art methods on four public motion datasets. Specifically, UMDR achieves unprecedented improvements of +4.5% on the Chalearn IsoGD dataset. Our code is available at https://github.com/zhoubenjia/MotionRGBD-PAMI., Comment: Accepted to TPAMI 2023

Deep learning technology has made great progress in multi-view 3D reconstruction tasks. At present, most mainstream solutions establish the mapping between views and shape of an object by assembling the networks of 2D encoder and 3D decoder as the basic structure while they adopt different approaches to obtain aggregation of features from several views. Among them, the methods using attention-based fusion perform better and more stable than the others, however, they still have an obvious shortcoming -- the strong independence of each view during predicting the weights for merging leads to a lack of adaption of the global state. In this paper, we propose a global-aware attention-based fusion approach that builds the correlation between each branch and the global to provide a comprehensive foundation for weights inference. In order to enhance the ability of the network, we introduce a novel loss function to supervise the shape overall and propose a dynamic two-stage training strategy that can effectively adapt to all reconstructors with attention-based fusion. Experiments on ShapeNet verify that our method outperforms existing SOTA methods while the amount of parameters is far less than the same type of algorithm, Pix2Vox++. Furthermore, we propose a view-reduction method based on maximizing diversity and discuss the cost-performance tradeoff of our model to achieve a better performance when facing heavy input amount and limited computational cost.

Vision Transformers (ViTs) have shown promising performance compared with Convolutional Neural Networks (CNNs), but the training of ViTs is much harder than CNNs. In this paper, we define several metrics, including Dynamic Data Proportion (DDP) and Knowledge Assimilation Rate (KAR), to investigate the training process, and divide it into three periods accordingly: formation, growth and exploration. In particular, at the last stage of training, we observe that only a tiny portion of training examples is used to optimize the model. Given the data-hungry nature of ViTs, we thus ask a simple but important question: is it possible to provide abundant ``effective'' training examples at EVERY stage of training? To address this issue, we need to address two critical questions, \ie, how to measure the ``effectiveness'' of individual training examples, and how to systematically generate enough number of ``effective'' examples when they are running out. To answer the first question, we find that the ``difficulty'' of training samples can be adopted as an indicator to measure the ``effectiveness'' of training samples. To cope with the second question, we propose to dynamically adjust the ``difficulty'' distribution of the training data in these evolution stages. To achieve these two purposes, we propose a novel data-centric ViT training framework to dynamically measure the ``difficulty'' of training samples and generate ``effective'' samples for models at different training stages. Furthermore, to further enlarge the number of ``effective'' samples and alleviate the overfitting problem in the late training stage of ViTs, we propose a patch-level erasing strategy dubbed PatchErasing. Extensive experiments demonstrate the effectiveness of the proposed data-centric ViT training framework and techniques.

Decoupling spatiotemporal representation refers to decomposing the spatial and temporal features into dimension-independent factors. Although previous RGB-D-based motion recognition methods have achieved promising performance through the tightly coupled multi-modal spatiotemporal representation, they still suffer from (i) optimization difficulty under small data setting due to the tightly spatiotemporal-entangled modeling;(ii) information redundancy as it usually contains lots of marginal information that is weakly relevant to classification; and (iii) low interaction between multi-modal spatiotemporal information caused by insufficient late fusion. To alleviate these drawbacks, we propose to decouple and recouple spatiotemporal representation for RGB-D-based motion recognition. Specifically, we disentangle the task of learning spatiotemporal representation into 3 sub-tasks: (1) Learning high-quality and dimension independent features through a decoupled spatial and temporal modeling network. (2) Recoupling the decoupled representation to establish stronger space-time dependency. (3) Introducing a Cross-modal Adaptive Posterior Fusion (CAPF) mechanism to capture cross-modal spatiotemporal information from RGB-D data. Seamless combination of these novel designs forms a robust spatialtemporal representation and achieves better performance than state-of-the-art methods on four public motion datasets. Our code is available at https://github.com/damo-cv/MotionRGBD., Comment: open sourced; codes and models are available:https://github.com/damo-cv/MotionRGBD; transformer-based method

Face presentation attack detection (PAD) is essential to secure face recognition systems primarily from high-fidelity mask attacks. Most existing 3D mask PAD benchmarks suffer from several drawbacks: 1) a limited number of mask identities, types of sensors, and a total number of videos; 2) low-fidelity quality of facial masks. Basic deep models and remote photoplethysmography (rPPG) methods achieved acceptable performance on these benchmarks but still far from the needs of practical scenarios. To bridge the gap to real-world applications, we introduce a largescale High-Fidelity Mask dataset, namely CASIA-SURF HiFiMask (briefly HiFiMask). Specifically, a total amount of 54,600 videos are recorded from 75 subjects with 225 realistic masks by 7 new kinds of sensors. Together with the dataset, we propose a novel Contrastive Context-aware Learning framework, namely CCL. CCL is a new training methodology for supervised PAD tasks, which is able to learn by leveraging rich contexts accurately (e.g., subjects, mask material and lighting) among pairs of live faces and high-fidelity mask attacks. Extensive experimental evaluations on HiFiMask and three additional 3D mask datasets demonstrate the effectiveness of our method.

How to utilize deep learning methods for graph classification tasks has attracted considerable research attention in the past few years. Regarding graph classification tasks, the graphs to be classified may have various graph sizes (i.e., different number of nodes and edges) and have various graph properties (e.g., average node degree, diameter, and clustering coefficient). The diverse property of graphs has imposed significant challenges on existing graph learning techniques since diverse graphs have different best-fit hyperparameters. It is difficult to learn graph features from a set of diverse graphs by a unified graph neural network. This motivates us to use a multiplex structure in a diverse way and utilize a priori properties of graphs to guide the learning. In this paper, we propose MxPool, which concurrently uses multiple graph convolution/pooling networks to build a hierarchical learning structure for graph representation learning tasks. Our experiments on numerous graph classification benchmarks show that our MxPool has superiority over other state-of-the-art graph representation learning methods.

Nucleation during solidification in multi-component alloys is a complex process that comprises the competition between different crystalline phases as well as chemical composition and ordering. Here, we combine transition interface sampling with an extensive committor analysis to investigate the atomistic mechanisms during the initial stages of nucleation in $\text{Ni}_3\text{Al}$. The formation and growth of crystalline clusters from the melt are strongly influenced by the interplay between three descriptors: the size, crystallinity, and chemical short-range order of the emerging nuclei. We demonstrate that it is essential to include all three features in a multi-dimensional reaction coordinate to correctly describe the nucleation mechanism, where in particular the chemical short-range order plays a crucial role in the stability of small clusters. The necessity of identifying multi-dimensional reaction coordinates is expected to be of key importance for the atomistic characterization of nucleation processes in complex, multi-component systems.

Face anti-spoofing is essential to prevent face recognition systems from a security breach. Much of the progresses have been made by the availability of face anti-spoofing benchmark datasets in recent years. However, existing face anti-spoofing benchmarks have limited number of subjects ($\le\negmedspace170$) and modalities ($\leq\negmedspace2$), which hinder the further development of the academic community. To facilitate face anti-spoofing research, we introduce a large-scale multi-modal dataset, namely CASIA-SURF, which is the largest publicly available dataset for face anti-spoofing in terms of both subjects and modalities. Specifically, it consists of $1,000$ subjects with $21,000$ videos and each sample has $3$ modalities (i.e., RGB, Depth and IR). We also provide comprehensive evaluation metrics, diverse evaluation protocols, training/validation/testing subsets and a measurement tool, developing a new benchmark for face anti-spoofing. Moreover, we present a novel multi-modal multi-scale fusion method as a strong baseline, which performs feature re-weighting to select the more informative channel features while suppressing the less useful ones for each modality across different scales. Extensive experiments have been conducted on the proposed dataset to verify its significance and generalization capability. The dataset is available at https://sites.google.com/qq.com/face-anti-spoofing/welcome/challengecvpr2019?authuser=0, Comment: Accepted by TBIOM; Journal extension of our previous conference paper: arXiv:1812.00408