The goal of few-shot segmentation (FSS) is to segment unlabeled images belonging to previously unseen classes using only a limited number of labeled images. The main objective is to transfer label information effectively from support images to query images. In this study, we introduce a novel meta-learning framework called layer-wise mutual information (LayerMI), which enhances the propagation of label information by maximizing the mutual information (MI) between support and query features at each layer. Our approach involves the utilization of a LayerMI Block based on information-theoretic co-clustering. This block performs online co-clustering on the joint probability distribution obtained from each layer, generating a target-specific attention map. The LayerMI Block can be seamlessly integrated into the meta-learning framework and applied to all convolutional neural network (CNN) layers without altering the training objectives. Notably, the LayerMI Block not only maximizes MI between support and query features but also facilitates internal clustering within the image. Extensive experiments demonstrate that LayerMI significantly enhances the performance of baseline and achieves competitive performance compared to state-of-the-art methods on three challenging benchmarks: PASCAL- $5^{i}$ , COCO- $20^{i}$ , and FSS-1000.

In this work, we address the challenging issue of few-shot segmentation. Existing methods mainly explore the target object through the semantic similarity between the query and support pixels. However, the semantic similarity often fails to deal well with the target objects with large variations in appearance and the error predictions along the boundary. To this end, we propose a novel spatial similarity guidance network (S2GNet), which adaptively integrates spatial information with semantic information for building a target-aware correlation region to enhance the target object localization. To promote the overall spatial position understanding of the target object, we exploit boundaries as crucial guidance for spatial information. Thus we jointly train a boundary detection task and a segmentation task in an end-to-end way. With that, a target-aware attention module is further proposed to capture the target correlation region by combining the spatial similarity with the semantic similarity for each pair of pixels in the query image, which refines the location of the target object effectively and improves the segmentation performance. Extensive experiments on both PASCAL-5iand COCO-20idatasets show that our approach can achieve state-of-the-art performances.

In this paper, we address the problem of fusing multi-focus images in same scenes. We propose a gradient guidance progressive network for multi-focus image fusion. We explicitly extract gradient features of images, and introduce the gradient guidance progressive module to integrate effectively features. In the module, we employ low-resolution features with large receptive fields to detect focused areas far away from boundaries. While for high-resolution features incorporating detailed gradient features, we only focus on optimizing outputs near boundaries. Benefiting from the separate operations on both areas far away from and near boundaries, the proposed method makes accurate focus region detection with detailed boundaries. Experimental results demonstrate the effectiveness and superiority of the proposed method compared with the state-of-the-art methods.

Few-shot segmentation has got a lot of concerns recently. Existing methods mainly locate and recognize the target object based on a cross-guided way that applies masked target object features of support(query) images to make a feature matching with query(support) images. However, there are some differences between support images and query images because of large appearance and scale variation, which will lead to inaccurate and incomplete segmentation. This problem inspired us to explore the local coherence of the image to guide the segmentation. We try to get some target pixels in the query image and apply these pixels to search for more target pixels in the query image. In this work, we propose a novel network that combines a universal cross-guided branch with a new pseudo-interacting guided branch. Specifically, we first employ the universal cross-guided branch to produce a pseudo-labeling that represents the probability of each pixel belonging to the target object. Then we design a pseudo-interacting guided branch, which applies some pixels with high probabilities based on generated pseudo-labeling to segment the target object in the query image and revises the results of the cross-guided branch simultaneously. Extensive experiments show that our approach outperforms state-of-the-art methods on both PASCAL-5iand COCO-20idatasets.

Few-shot segmentation refers to learn a segmentation model that can be generalized to novel classes with limited labeled images. Establishing the correspondence between support images and query images effectively has a considerable effect on guiding the segmentation of query images. Most existing methods mainly adopt a trained classification network as the backbone, nevertheless, the classification tasks only focus on the most discriminate regions of the target rather than the targets' integrity and the most discriminate regions may not be part of the target we need to segment while multiple classes object included in images. Besides, there exists another question that the most discriminate regions of the target in support image also do not necessarily appear in query images because of occlusion or incomplete object. All these may cause the correspondence between two images inaccurately. To tackle these problems, we propose a Target-aware Network(TaNet). Our network has two objectives: (1) increasing both intra-object similarity and inter-object dissimilarity for query image and support image to make each object more complete rather than highlight the most discriminate regions; (2) adaptively generating target-aware correspondence between support images and query images. Experiments on PASCAL-5iand COCO-20ishow that our method achieves state-of-the-art performance.

An approach to CEGAR-based model checking which has proved to be successful on large models employs Craig interpolation to efficiently construct parsimonious abstractions. Following this design, we introduce new applications, universal safety interpolant and existential error interpolant, of Craig interpolation that can systematically reduce the program state space to be explored for safety verification. Whenever the universal safety interpolant is implied by the current path, all paths emanating from that location are guaranteed to be safe. Dually whenever the existential error interpolant is implied by the current path, there is guaranteed to be an unsafe path from the location. We show how these interpolants are computed and applied in safety verification. We have implemented our approach in a tool named InterpChecker by building on an open source software model checker. Experiments on a large number of benchmark programs show that both the interpolations and the auxiliary optimization strategies are effective in improving scalability of software model checking.

Counter-example guided abstraction refinement (CEGAR) is widely used in software model checking. With an abstract model, the state space is largely reduced, however, a counterexample found in such a model that does not satisfy the desired property may not exist in the concrete model. Therefore, how to check whether a reported counterexample is spurious is a key problem in the abstraction-refinement loop. Next, in the case that a spurious counterexample is found, the abstract model needs to be further refined where an NP-hard state separation problem is often involved. Thus, how to refine the abstract model efficiently has attracted a great attention in the past years. In this paper, by re-analyzing spurious counterexamples, a new formal definition of spurious paths is given. Based on it, efficient algorithms for detecting spurious counterexamples are presented. By the new algorithms, when dealing with infinite counterexamples, the finite prefix to be analyzed will be polynomially shorter than the one dealt with by the existing algorithms. Moreover, in practical terms, the new algorithms can naturally be parallelized that enables multi-core processors contributes more in spurious counterexample checking. In addition, a novel refining approach by adding extra Boolean variables to the abstract model is presented. With this approach, not only the NP-hard state separation problem can be avoided, but also a smaller refined abstract model can be obtained. Experimental results show that the new algorithms perform well in practice.