# A Hierarchical Fusion SAR Image Change-Detection Method Based on HF-CRF Model
## 1 Introduction
[35] introduced the pyramidal attention layer structure into the full convolutional network framework to further extract multi-scale variation information from the difference-feature maps processed by the original network encoder structure. Song et al. [36] proposed AGCDetNet by combining a fully convolutional network with an attention mechanism. The network takes into account the joint use of a spatial attention mechanism and channel attention mechanism. The paper verifies that AGCDetNet is able to enhance the discrimination of changing targets and backgrounds while improving the performance of feature representation for changing information. Lv et al. [37] proposed a hybrid attention semantic segmentation network (HAssNet), which incorporates a spatial attention mechanism and a channel attention mechanism based on a fully convolutional network [38]. This approach effectively utilizes multi-scale extracted features and global correlation to locate and segment targets in the image. Nevertheless, most of the work only uses the deep features of CNN to build semantic feature descriptions, which ignores the fine-grained information contained in the shallow features [39]. Du et al. [40] designed a bilateral semantic fusion twin network (BSFNet) integrating shallow and deep semantic features in order to better map dual-temporal images to semantic feature domains for comparison, and obtained pixel-level change results with more complete structures. The UNet network [41] has outstanding performance in the field of semantic segmentation, and has been widely adopted into the field of remote sensing change detection. Zhi, Z et al. [42] proposed a UNet-based CLNet network with a cross-layer structure to improve the change-detection accuracy by improving the way of contextual information fusion. By incorporating the advantages of dense connections for multi-scale information mining within UNet++, Li et al. [43] introduced multiple sources of information to supplement the channel information of remote sensing imagesin their framework. The resulting model exhibits excellent performance across various datasets. Chen et al. [44] combined the attention mechanism with UNet to design the Siamese_AUNet twin neural network. The model performs well in solving the problems related to weak change detection and noise suppression. Furthermore, for change detection, the conditional random field (CRF) based on probabilistic graphical models (PGM) [45] and the Markov random field (MRF) [46] have been introduced. Zhang et al. [47] used the CRF model to improve the traditional change-detection method. A half-normal CRF (HNCRF) method is proposed to construct the interaction between pixel points in the spatial analysis of difference images, which is effective when the change region is small. Lv et al. [48] proposed a hybrid conditional random field (HCRF) model that combining traditional random field methods with object-based techniques. The improved model fully exploits the spectral spatial information, thereby enhancing the change-detection performance of high-spatial-resolution remote sensing images, improving the traditional change-detection method with the CRF model. A half-normal CRF (HNCRF) method is proposed to construct the interaction between pixel points in the process of the spatial analysis of difference images, which is effective when the change region is not significant. However, CRF ignores the image-global-distribution relationship. The localization accuracy of the fully connected conditional random field (FCCRF) [49; 50], coupled with the recognition ability of the deep convolutional neural network shows better boundary localization in the change-detection results. Y. Shang et al. [51] introduced a novel approach to mitigate the issue of excessive feature smoothing in the fully connected conditional random field (FCCRF) model by incorporating region boundary constraints.