## 1 Introduction
Building on a similar network structure as previous approaches, they enhanced the robustness of homography estimation to lighting variations by learning the homography relationship through minimizing the pixel intensity difference between two images. This method eliminates the need for labeled data. However, it performs poorly on images with significant viewpoint differences and lacks scale and rotation invariance. In recent years, there has been increasing research on unsupervised homography estimation [16; 17; 18; 19; 20]. Unsupervised learning methods eliminate the complex process of labeling training data, reducing the impact of human bias. These methods are better suited to adapt to complex and changing environments and demonstrate improved generalization ability when handling variations in real-world conditions, such as different lighting conditions, motion blur, shifts, and rotations. [PERSON] et al. [16] proposed an unsupervised learning model that learns feature representations for homography estimation and image comparison. This model calculates loss in the feature space rather than in the pixel space, achieving robustness to varying lighting conditions. [PERSON] et al. [17] extended this work by adding perceptual loss computation [21], further enhancing the robustness of deep homography estimation methods to lighting changes. However, both of these new unsupervised homography estimation methods are not applicable to scenes with small image overlapping regions and low similarity. [PERSON] et al. [18] proposed a new unsupervised learning framework that improves homography estimation by learning motion bases. This approach can estimate global homography transformations and handle local homography transformations at a finer granularity, thus improving the accuracy of homography estimation. However, due to the complex feature extraction and learning processes involved, this method requires significant computational resources and time, making it unsuitable for industrial applications. To address the issues mentioned above, this paper proposes an improved unsupervised homography estimation model based on existing models, tailored for the specific industrial context of stamping process monitoring. By incorporating a special deformation convolution module and a GN normalization layer into the backbone network, the model enhances its rotational invariance when handling large-scale, high-resolution images. A multi-scale, multi-stage network architecture is developed, utilizing unsupervised training through minimizing pixel-level photometric loss at each stage, which progressively refines the homography transformations between images from coarse to fine, improving the accuracy of homography estimation and enhancing the model's learning ability for scale invariance. To make the model suitable for the specific industrial application of the stamping process and improve its robustness against complex environmental changes such as lighting variations and vibration disturbances, the training dataset integrates stamping surveillance image data with random perturbations, lighting, contrast, and blur for data augmentation, addressing the issue of dataset scarcity in specific industrial applications of deep learning. The remainder of this paper is organized as follows. Section 2 first describes the network structure of the unsupervised single-response estimation model, improves on it by introducing a special deformation convolution module and a GN normalization layer, and constructs a multi-scale, multi-stage overall network structure and establishes a multi-stage coupling relation, minimizing the luminosity loss function. Comparison and ablation experiments are carried out in Section 3 to analyze the effectiveness of the method of this paper, and conclusions are summarized in Section 4.