# A Novel Perceptual Hash Algorithm for Multispectral Image Authentication
## 2 Preliminaries  
### Overview of Perceptual Hash  
As shown in Figure 1, perceptual hash algorithms generally consist of the following stages: preprocessing, feature extraction, feature quantification, hash generation.  
Pre-processing generally removes redundant information in an image, making it easier to extract features from the image later on. Feature extraction is to extract the principle features of the image using a specific extraction method. Feature compression is to fuzzy up the extracted features in order to enhance robustness. Hash generation is to make the quantitative characteristics more abstract, because the quantitative features may lead to a large amount of data being suitable as an output sequence. For image authentication, a perceptual hash algorithm should possess the following properties:  
1. Compactness: The hash value of the image should be as compact as possible, so that it is easier to transport, store and use.
2. Sensitivity to tampering: Visually distinct images should have significantly different hash values.
3. Perceptual robustness: The hash generation should be insensitive to a certain level of distortion with respect to the input image.
4. Security: Calculation of image hashing depends on a secret key, that is, different secret keys can generate significantly different hash values for the same image.  
For the authentication of an MS image, the perceptual hash algorithm has to be sensitive to malicious tampering operations and to be robust to content-preserving ones. Compared with normal images, MS images have higher requirements for measurement accuracy, and their pixels with coordinates can be used for measuring geometrical locations after the image has been corrected and processed, which means the authentication algorithm should have high authentication precision and be able to detect micro-tampering of the image.  
Figure 1: Framework of perceptual hash algorithms.  
The simplest way to generate multispectral image perceptual hashing is to generate the hash value for each band. However, this would lead to a huge data volume of hash values, while the perceptual hash values should be as compact as possible to be convenient for data authentication. In addition, there are some correlations between each band, which result in high redundancy and a great amount of computation time wasted in hash generation.  
In this paper, we separate the bands into several band subsets with a clustering algorithm to reduce the content redundancy, and then we adopt a band fusion-based feature extraction technique to obtain the compact feature of each band subset, which could be suitable for hashing computation. Furthermore, grid division is adopted to divide each band into grids and make the hash value more sensitive to local modification in the MS images.  
On the other hand, feature extraction is a key stage of the perceptual hash. For remote sensing image authentication, edge characteristics based on perceptual hash can achieve higher precision [16]. The sensing images would have little value if the edge characteristics had been greatly changed. Additionally, edge characteristics contain effective information for applications such as object extraction, image segmentation and target recognition. Therefore, we adopt edge features as the perceptual feature to generate perceptual hash value.