The problems of computing graph colorings and clique covers are central challenges in combinatorial optimization. Both of these are known to be NP-hard, and thus computationally intractable in the worst-case instance. A prominent approach for computing approximate solutions to these problems is the celebrated Lov\'asz theta function $\vartheta(G)$, which is specified as the solution of a semidefinite program (SDP), and hence tractable to compute. In this work, we move beyond the worst-case analysis and set out to understand whether the Lov\'asz theta function recovers clique covers for random instances that have a latent clique cover structure, possibly obscured by noise. We answer this question in the affirmative and show that for graphs generated from the planted clique model we introduce in this work, the SDP formulation of $\vartheta(G)$ has a unique solution that reveals the underlying clique-cover structure with high-probability. The main technical step is an intermediate result where we prove a deterministic condition of recovery based on an appropriate notion of sparsity.
Object detection in remote sensing images relies on a large amount of labeled data for training. However, the increasing number of new categories and class imbalance make exhaustive annotation impractical. Few-shot object detection (FSOD) addresses this issue by leveraging meta-learning on seen base classes and fine-tuning on novel classes with limited labeled samples. Nonetheless, the substantial scale and orientation variations of objects in remote sensing images pose significant challenges to existing few-shot object detection methods. To overcome these challenges, we propose integrating a feature pyramid network and utilizing prototype features to enhance query features, thereby improving existing FSOD methods. We refer to this modified FSOD approach as a Strong Baseline, which has demonstrated significant performance improvements compared to the original baselines. Furthermore, we tackle the issue of spatial misalignment caused by orientation variations between the query and support images by introducing a Transformation-Invariant Network (TINet). TINet ensures geometric invariance and explicitly aligns the features of the query and support branches, resulting in additional performance gains while maintaining the same inference speed as the Strong Baseline. Extensive experiments on three widely used remote sensing object detection datasets, i.e., NWPU VHR-10.v2, DIOR, and HRRSD demonstrated the effectiveness of the proposed method.
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, Chevallier et al. proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well-suited for large-scale Earth-system data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment.
Image Segmentation is one of the core tasks in Computer Vision and solving it often depends on modeling the image appearance data via the color distributions of each it its constituent regions. Whereas many segmentation algorithms handle the appearance models dependence using alternation or implicit methods, we propose here a new approach to directly estimate them from the image without prior information on the underlying segmentation. Our method uses local high order color statistics from the image as an input to tensor factorization-based estimator for latent variable models. This approach is able to estimate models in multiregion images and automatically output the regions proportions without prior user interaction, overcoming the drawbacks from a prior attempt to this problem. We also demonstrate the performance of our proposed method in many challenging synthetic and real imaging scenarios and show that it leads to an efficient segmentation algorithm.
Fusion-based hyperspectral image (HSI) super-resolution aims to produce a high-spatial-resolution HSI by fusing a low-spatial-resolution HSI and a high-spatial-resolution multispectral image. Such a HSI super-resolution process can be modeled as an inverse problem, where the prior knowledge is essential for obtaining the desired solution. Motivated by the success of diffusion models, we propose a novel spectral diffusion prior for fusion-based HSI super-resolution. Specifically, we first investigate the spectrum generation problem and design a spectral diffusion model to model the spectral data distribution. Then, in the framework of maximum a posteriori, we keep the transition information between every two neighboring states during the reverse generative process, and thereby embed the knowledge of trained spectral diffusion model into the fusion problem in the form of a regularization term. At last, we treat each generation step of the final optimization problem as its subproblem, and employ the Adam to solve these subproblems in a reverse sequence. Experimental results conducted on both synthetic and real datasets demonstrate the effectiveness of the proposed approach. The code of the proposed approach will be available on //github.com/liuofficial/SDP.
Video post-processing methods can improve the quality of compressed videos at the decoder side. Most of the existing methods need to train corresponding models for compressed videos with different quantization parameters to improve the quality of compressed videos. However, in most cases, the quantization parameters of the decoded video are unknown. This makes existing methods have their limitations in improving video quality. To tackle this problem, this work proposes a diffusion model based post-processing method for compressed videos. The proposed method first estimates the feature vectors of the compressed video and then uses the estimated feature vectors as the prior information for the quality enhancement model to adaptively enhance the quality of compressed video with different quantization parameters. Experimental results show that the quality enhancement results of our proposed method on mixed datasets are superior to existing methods.
Data uncertainties, such as sensor noise or occlusions, can introduce irreducible ambiguities in images, which result in varying, yet plausible, semantic hypotheses. In Machine Learning, this ambiguity is commonly referred to as aleatoric uncertainty. Latent density models can be utilized to address this problem in image segmentation. The most popular approach is the Probabilistic U-Net (PU-Net), which uses latent Normal densities to optimize the conditional data log-likelihood Evidence Lower Bound. In this work, we demonstrate that the PU- Net latent space is severely inhomogenous. As a result, the effectiveness of gradient descent is inhibited and the model becomes extremely sensitive to the localization of the latent space samples, resulting in defective predictions. To address this, we present the Sinkhorn PU-Net (SPU-Net), which uses the Sinkhorn Divergence to promote homogeneity across all latent dimensions, effectively improving gradient-descent updates and model robustness. Our results show that by applying this on public datasets of various clinical segmentation problems, the SPU-Net receives up to 11% performance gains compared against preceding latent variable models for probabilistic segmentation on the Hungarian-Matched metric. The results indicate that by encouraging a homogeneous latent space, one can significantly improve latent density modeling for medical image segmentation.
Existing knowledge graph (KG) embedding models have primarily focused on static KGs. However, real-world KGs do not remain static, but rather evolve and grow in tandem with the development of KG applications. Consequently, new facts and previously unseen entities and relations continually emerge, necessitating an embedding model that can quickly learn and transfer new knowledge through growth. Motivated by this, we delve into an expanding field of KG embedding in this paper, i.e., lifelong KG embedding. We consider knowledge transfer and retention of the learning on growing snapshots of a KG without having to learn embeddings from scratch. The proposed model includes a masked KG autoencoder for embedding learning and update, with an embedding transfer strategy to inject the learned knowledge into the new entity and relation embeddings, and an embedding regularization method to avoid catastrophic forgetting. To investigate the impacts of different aspects of KG growth, we construct four datasets to evaluate the performance of lifelong KG embedding. Experimental results show that the proposed model outperforms the state-of-the-art inductive and lifelong embedding baselines.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.
Inspired by recent development of artificial satellite, remote sensing images have attracted extensive attention. Recently, noticeable progress has been made in scene classification and target detection.However, it is still not clear how to describe the remote sensing image content with accurate and concise sentences. In this paper, we investigate to describe the remote sensing images with accurate and flexible sentences. First, some annotated instructions are presented to better describe the remote sensing images considering the special characteristics of remote sensing images. Second, in order to exhaustively exploit the contents of remote sensing images, a large-scale aerial image data set is constructed for remote sensing image caption. Finally, a comprehensive review is presented on the proposed data set to fully advance the task of remote sensing caption. Extensive experiments on the proposed data set demonstrate that the content of the remote sensing image can be completely described by generating language descriptions. The data set is available at //github.com/2051/RSICD_optimal