# Convolutional Sparse Modular Fusion Algorithm for Non-Rigid Registration of Visible-Infrared Images
## 1 Introduction  
A single-type camera often encounters difficulty accurately capturing an entire imaging scene due to environmental interference or hardware malfunctions [1]. To improve scene perception, leveraging multiple cameras to capture images of different modalities can offer a more comprehensive perception of scene details. Visible-infrared image fusion technology is designed to extract complementary information from these various modalities and integrate them into a single final coherent image. This technique effectively harnesses the strengths of each modality, resulting in a versatile fused image that retains crucial information. Traditional multimodal image fusion methods primarily rely on classic fusion frameworks. However, these approaches are often prone to high human error and have limited generalization capability. Consequently, deep learning-based frameworks have been more favored. An example of a deep learning multimodal image fusion method is shown in Figure 1. In the realms of feature extraction and attention mechanisms, [PERSON] et al. [2]proposed the GRPAFusion framework, which leverages gradient residuals and pyramid attention to achieve multi-scale feature correction and fusion. [PERSON] et al. [3] developed the PIAFusion network, employing illumination-aware encoding to enhance cross-modal integration capabilities. In the research of semantic-oriented fusion methods, [PERSON] et al. [4] introduced the PSFusion network, which utilizes semantic perception to improve the detection accuracy of infrared-visible light fusion. [PERSON] et al. [5] proposed KDFuse, which narrows the cross-modal gap by designing a semantic-fusion information interaction mechanism. Concurrently, [PERSON] et al. [6] developed the SeAFusion network, and [PERSON] et al. [7] created the HFSNet framework, both innovatively combining semantic segmentation with image fusion, thereby providing novel insights for image analysis in complex scenarios. In the application of Transformer architectures, [PERSON] et al. [8] proposed a dual-branch feature decomposition fusion network, demonstrating exceptional performance in visible-infrared image and medical image fusion tasks. [PERSON] et al. [9] developed DCAFusion based on Swin Transformer, significantly enhancing the utilization efficiency of complementary information. On the other hand, [PERSON] et al. [10] proposed the TUFusion algorithm, which overcomes the bottleneck of multimodal fusion through the development of a composite attention strategy. Additionally, [PERSON] et al. [11] introduced an implicit degradation estimation model, effectively reducing information loss in fusion through feature aggregation. Despite the notable progress in fusion effects achieved by the methods above, there remain several common challenges that urgently need to be addressed: Firstly, fusion methods based on deep learning typically require substantial computational resources, leading to high computational costs when processing high-resolution images; Secondly, many methods rely on complex network structures, increasing the difficulty of model training and deployment; Furthermore, the dependency of some methods on high-level visual tasks such as semantic segmentation also limits their generalizability and application scope to a certain extent. In the research field of multimodal image fusion, image registration serves as a critical preprocessing step, with its accuracy directly influencing the quality of fusion. However, due to inherent characteristic differences in source images acquired by different sensors, poor registration often leads to the generation of fusion artifacts, as illustrated in Figure 1. To address this challenge, researchers have proposed various innovative registration methods. In traditional-based registration techniques, [PERSON] et al. [12] enhanced infrared-visible light registration by optimizing Euclidean evaluation. [PERSON] et al. [13] employed co-analysis shearlet transform in conjunction with a classified dictionary and the PCCN model to extract visual features.