The Image Encryption, Retrieval And Classification Algorithm Based On The Fractal Theory

With the popularity of the computer and the rapid development of multimedia technology, image information is growing rapidly, especially for multimedia that involves audio, image, or video. How to effectively manage these resources has become a focus of many scholars’study. It is difficult to describe the overall part or part of fractal sets by Euclidean geometry. Its complex internal structure, such as self-similarity, pseudo randomness and complexity, makes the fractal sets widely used in nonlinear science in the scientific research. How to use the fractal theory to encrypt image, and to use the fractal dimension to describe the image features for image recognition has become a hot discussion.In this paper, we proposed three methods based on the characteristics of classical fractal set. We proposed a set of indices based on M-J fractal dictionary encoding by using the statistical characteristics of the indices. Also, we proposed a novel compression-encryption scheme based on the fractal dictionary and Julia set. At last, based on the fractal dimension, an approach for pattern recognition in stained HEp-2 cell IIF images, which is critical for the immune diseases diagnosis, was presented. The details are as follows:1、Generalized Julia set has rich and no rule contents. Additionally, the internal Julia sets will have significant changes with different position. Actually, it has been proved that the points closer to the Julia set border have a more pronounced border’s features, i.e., closed set, density, non-differentiability, and sensitivity to initial conditions. Based on these characteristics, we select an inner set of the generalized Julia set as initial stream cipher, and make the encryption with the fractal codes based on fractal dictionary, with diffusion followed. The experiments showed that the image compression based on fractal dictionary not only saves time consumption, but also gives a good quality of image reconstruction with a satisfying PSNR. Furthermore, when the size of the Julia set is proper, the key space is large and it has a high sensitivity for cipher to both key and plaintext. The ciphertext passed the sp800-22 test suite, showing that the encryption system can resist external attacks, especially for the chosen plaintext attack and known plaintext attacks. At last, the encryption time is no more 15% of the compression time, making it easy to realize real-time compression and encryption.2、In the fractal dictionary coding, we regarded the dictionary as the shared medium. Therefore, the coding parameters based on the fractal dictionary represents the spatial relations with the encoded image and the dictionary. According to the relations, we proposed a set of indices based on M-J fractal dictionary encoding for image retrieval. They are dictionary of collage error (DE), dictionary of BTC (DB) and joint of dictionary of BTC and s (JDBS). The experiments showed that DE, DB, and JDBS indices are close for similar texture images, and different for different texture images. Subsequently, the proposed method was a better performance than other methods. In our scheme, JDSE+DB provided a 79.18% average retrieval rate at the maximum, and its computational complexity was tolerated. In addition, JDSE+DB and DS+DE+DB not only had low computational complexity, but also provided competitive retrieval rate, compared to existing methods.3、Indirect immunofluorescence (IIF) with HEp-2 cells is considered as a powerful, sensitive and comprehensive technique for analyzing antinuclear autoantibodies (ANAs). However, the IIF method is hard to diagnosis repeatability due to the subjective. Computer-Aided Diagnosis (CAD) system supports the physician’s decision and overcome current method limitations. Based on the Minkowski-Bouligand dimension, a new fractal dimension algorithm for pattern recognition in stained HEp-2 cell IIF images is proposed, combining with the morphological descriptor and pixel difference feature descriptor. The experiments showed that the fractal descriptor makes the overall accuracy 54.5% with a mild precision changes in each pattern. When combining with other two descriptors, the overall accuracy achieves more than 67% with a mildly variation in class precision. Based on the comparison with the previous literature methods, the proposed method works better in some of the class predictions with the least vector length. We arrive the conclusion that the join of the fractal descriptor enhance the overall accuracy and serves better for the hybrid descriptor on each class in general.