# A Zero-Watermarking Algorithm Based on Scale-Invariant Feature Reconstruction Transform
## 2 Related Work  
### Feature Matrix Based on SIFT  
Scale-invariant feature transform (SIFT) is a local feature descriptor algorithm that is widely used in the field of image processing. Taking human visual perception as an example, our eyes have the ability to perceive differences in the size and clarity of objects. The scale space construction step of SIFT is inspired by this observation. It uses the process of upsampling and downsampling to simulate the perception of distance in an image and employs Gaussian convolution kernels to model different levels of smoothness or blurriness. The SIFT algorithm was proposed by Canadian professor [PERSON] in 1999. It detects and describes local features in multi-scale space, rendering the generated descriptors scale-invariant. It exhibits strong robustness in handling image transformations such as rotation, illumination changes, and image-capture position shifts. Consequently, SIFT finds wide application in image stitching and specialized image-matching fields. [PERSON] et al. [8] utilized the SIFT algorithm to generate a series of images with different stylistic patterns, resolving the issue of resolution differences between style and content images. They performed feature extraction on these images and generated the matching patches required for image synthesis. This algorithm assists in finding the correct style of image, facilitating image-correction and -matching processes. [PERSON] et al. [9] applied SIFT to feature point extraction and image-matching in synthetic aperture radar (SAR) satellite images, thereby improving the efficiency of SAR image-matching. Apart from image-matching techniques, SIFT is also used in various information processing tasks such as biometrics feature recognition [10] and the sets of feature descriptors [11]. By simplifying the computational complexity through local feature calculations, SIFT significantly enhances the efficiency of the corresponding algorithm. In the application field of zero-watermarking technology, the process of extracting copyright information from digital images does not involve the image-matching step in the traditional SIFT algorithm. In order to reduce unnecessary computational complexity, this paper proposes an improved feature matrix construction algorithm, the scale-invariant feature reconstruction transformation (SIFRT) descriptor algorithm. After using the SIFT algorithm to extract image keypoints and compute feature descriptors, this algorithm standardizes the keypoints' descriptors and decomposes the resulting matrix into eigenvectors. The purpose of this step is to retain vectors with abundant feature information while eliminating redundant data from vectors with less feature information. The theoretical basis is that SIFT descriptors are composed of feature vectors from various local regions of the image, with each region further decomposed into multiple subregions. When calculating the gradient histograms of regions with low contrast or unclear textures, their contribution may be small and ignored by the thresholding step of gradient magnitude, leading to an excess of zero-value elements in the keypoints' descriptors. Although these zero-value elements can enhance the redundancy and discriminability of the algorithm during feature-point-matching, the zero-watermarking algorithm only involves a single image as the computational target and does not require matching or stitching between two images. Users are more concerned about the stability and discriminability of the feature matrix. Therefore, it is necessary for the new algorithm to compress the traditional SIFT feature descriptors to ensure that the constructed feature matrix contains as much rich feature information as possible, reducing redundant information used for image-matching. The SIFT algorithm proposed in this article reduces the redundant data in the traditional 128-dimensional SIFT descriptors. The collected feature descriptors are used to generate the dataset for algorithm training.