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Graph Convolutional Networks (GCNs) are one of the most popular architectures that are used to solve classification problems accompanied by graphical information. We present a rigorous theoretical understanding of the effects of graph convolutions in multi-layer networks. We study these effects through the node classification problem of a non-linearly separable Gaussian mixture model coupled with a stochastic block model. First, we show that a single graph convolution expands the regime of the distance between the means where multi-layer networks can classify the data by a factor of at least $1/\sqrt[4]{\mathbb{E}{\rm deg}}$, where $\mathbb{E}{\rm deg}$ denotes the expected degree of a node. Second, we show that with a slightly stronger graph density, two graph convolutions improve this factor to at least $1/\sqrt[4]{n}$, where $n$ is the number of nodes in the graph. Finally, we provide both theoretical and empirical insights into the performance of graph convolutions placed in different combinations among the layers of a network, concluding that the performance is mutually similar for all combinations of the placement. We present extensive experiments on both synthetic and real-world data that illustrate our results.

Many recent state-of-the-art (SOTA) optical flow models use finite-step recurrent update operations to emulate traditional algorithms by encouraging iterative refinements toward a stable flow estimation. However, these RNNs impose large computation and memory overheads, and are not directly trained to model such stable estimation. They can converge poorly and thereby suffer from performance degradation. To combat these drawbacks, we propose deep equilibrium (DEQ) flow estimators, an approach that directly solves for the flow as the infinite-level fixed point of an implicit layer (using any black-box solver), and differentiates through this fixed point analytically (thus requiring $O(1)$ training memory). This implicit-depth approach is not predicated on any specific model, and thus can be applied to a wide range of SOTA flow estimation model designs. The use of these DEQ flow estimators allows us to compute the flow faster using, e.g., fixed-point reuse and inexact gradients, consumes $4\sim6\times$ times less training memory than the recurrent counterpart, and achieves better results with the same computation budget. In addition, we propose a novel, sparse fixed-point correction scheme to stabilize our DEQ flow estimators, which addresses a longstanding challenge for DEQ models in general. We test our approach in various realistic settings and show that it improves SOTA methods on Sintel and KITTI datasets with substantially better computational and memory efficiency.

Making generative models 3D-aware bridges the 2D image space and the 3D physical world yet remains challenging. Recent attempts equip a Generative Adversarial Network (GAN) with a Neural Radiance Field (NeRF), which maps 3D coordinates to pixel values, as a 3D prior. However, the implicit function in NeRF has a very local receptive field, making the generator hard to become aware of the global structure. Meanwhile, NeRF is built on volume rendering which can be too costly to produce high-resolution results, increasing the optimization difficulty. To alleviate these two problems, we propose a novel framework, termed as VolumeGAN, for high-fidelity 3D-aware image synthesis, through explicitly learning a structural representation and a textural representation. We first learn a feature volume to represent the underlying structure, which is then converted to a feature field using a NeRF-like model. The feature field is further accumulated into a 2D feature map as the textural representation, followed by a neural renderer for appearance synthesis. Such a design enables independent control of the shape and the appearance. Extensive experiments on a wide range of datasets show that our approach achieves sufficiently higher image quality and better 3D control than the previous methods.

In this paper, we consider the challenging task of simultaneously locating and recovering multiple hands from single 2D image. Previous studies either focus on single hand reconstruction or solve this problem in a multi-stage way. Moreover, the conventional two-stage pipeline firstly detects hand areas, and then estimates 3D hand pose from each cropped patch. To reduce the computational redundancy in preprocessing and feature extraction, we propose a concise but efficient single-stage pipeline. Specifically, we design a multi-head auto-encoder structure for multi-hand reconstruction, where each head network shares the same feature map and outputs the hand center, pose and texture, respectively. Besides, we adopt a weakly-supervised scheme to alleviate the burden of expensive 3D real-world data annotations. To this end, we propose a series of losses optimized by a stage-wise training scheme, where a multi-hand dataset with 2D annotations is generated based on the publicly available single hand datasets. In order to further improve the accuracy of the weakly supervised model, we adopt several feature consistency constraints in both single and multiple hand settings. Specifically, the keypoints of each hand estimated from local features should be consistent with the re-projected points predicted from global features. Extensive experiments on public benchmarks including FreiHAND, HO3D, InterHand2.6M and RHD demonstrate that our method outperforms the state-of-the-art model-based methods in both weakly-supervised and fully-supervised manners.

This paper proposes a numerical method based on the Adomian decomposition approach for the time discretization, applied to Euler equations. A recursive property is demonstrated that allows to formulate the method in an appropriate and efficient way. To obtain a fully numerical scheme, the space discretization is achieved using the classical DG techniques. The efficiency of the obtained numerical scheme is demonstrated through numerical tests by comparison to exact solution and the popular Runge-Kutta DG method results.

The content based image retrieval aims to find the similar images from a large scale dataset against a query image. Generally, the similarity between the representative features of the query image and dataset images is used to rank the images for retrieval. In early days, various hand designed feature descriptors have been investigated based on the visual cues such as color, texture, shape, etc. that represent the images. However, the deep learning has emerged as a dominating alternative of hand-designed feature engineering from a decade. It learns the features automatically from the data. This paper presents a comprehensive survey of deep learning based developments in the past decade for content based image retrieval. The categorization of existing state-of-the-art methods from different perspectives is also performed for greater understanding of the progress. The taxonomy used in this survey covers different supervision, different networks, different descriptor type and different retrieval type. A performance analysis is also performed using the state-of-the-art methods. The insights are also presented for the benefit of the researchers to observe the progress and to make the best choices. The survey presented in this paper will help in further research progress in image retrieval using deep learning.

Deep learning techniques have received much attention in the area of image denoising. However, there are substantial differences in the various types of deep learning methods dealing with image denoising. Specifically, discriminative learning based on deep learning can ably address the issue of Gaussian noise. Optimization models based on deep learning are effective in estimating the real noise. However, there has thus far been little related research to summarize the different deep learning techniques for image denoising. In this paper, we offer a comparative study of deep techniques in image denoising. We first classify the deep convolutional neural networks (CNNs) for additive white noisy images; the deep CNNs for real noisy images; the deep CNNs for blind denoising and the deep CNNs for hybrid noisy images, which represents the combination of noisy, blurred and low-resolution images. Then, we analyze the motivations and principles of the different types of deep learning methods. Next, we compare the state-of-the-art methods on public denoising datasets in terms of quantitative and qualitative analysis. Finally, we point out some potential challenges and directions of future research.

Applying artificial intelligence techniques in medical imaging is one of the most promising areas in medicine. However, most of the recent success in this area highly relies on large amounts of carefully annotated data, whereas annotating medical images is a costly process. In this paper, we propose a novel method, called FocalMix, which, to the best of our knowledge, is the first to leverage recent advances in semi-supervised learning (SSL) for 3D medical image detection. We conducted extensive experiments on two widely used datasets for lung nodule detection, LUNA16 and NLST. Results show that our proposed SSL methods can achieve a substantial improvement of up to 17.3% over state-of-the-art supervised learning approaches with 400 unlabeled CT scans.

Generative Adversarial Networks (GANs) can produce images of surprising complexity and realism, but are generally modeled to sample from a single latent source ignoring the explicit spatial interaction between multiple entities that could be present in a scene. Capturing such complex interactions between different objects in the world, including their relative scaling, spatial layout, occlusion, or viewpoint transformation is a challenging problem. In this work, we propose to model object composition in a GAN framework as a self-consistent composition-decomposition network. Our model is conditioned on the object images from their marginal distributions to generate a realistic image from their joint distribution by explicitly learning the possible interactions. We evaluate our model through qualitative experiments and user evaluations in both the scenarios when either paired or unpaired examples for the individual object images and the joint scenes are given during training. Our results reveal that the learned model captures potential interactions between the two object domains given as input to output new instances of composed scene at test time in a reasonable fashion.

Image captioning is a challenging task that combines the field of computer vision and natural language processing. A variety of approaches have been proposed to achieve the goal of automatically describing an image, and recurrent neural network (RNN) or long-short term memory (LSTM) based models dominate this field. However, RNNs or LSTMs cannot be calculated in parallel and ignore the underlying hierarchical structure of a sentence. In this paper, we propose a framework that only employs convolutional neural networks (CNNs) to generate captions. Owing to parallel computing, our basic model is around 3 times faster than NIC (an LSTM-based model) during training time, while also providing better results. We conduct extensive experiments on MSCOCO and investigate the influence of the model width and depth. Compared with LSTM-based models that apply similar attention mechanisms, our proposed models achieves comparable scores of BLEU-1,2,3,4 and METEOR, and higher scores of CIDEr. We also test our model on the paragraph annotation dataset, and get higher CIDEr score compared with hierarchical LSTMs