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Since different regions of an image have different importance, therefore only the important information of the image regions, which the users are really interested in, needs to be encrypted and protected emphatically in some special multimedia applications. However, the regions of interest (ROI) are always some irregular parts, such as the face and the eyes. Assuming the bulk data in transmission without being damaged, we propose a chaotic image encryption algorithm for ROI. ROI with irregular shapes are chosen and detected arbitrarily. Then the chaos-based image encryption algorithm with scrambling, S-box and diffusion parts is used to encrypt the ROI. Further, the whole image is compressed with Huffman coding. At last, a message authentication code (MAC) of the compressed image is generated based on chaotic maps. The simulation results show that the encryption algorithm has a good security level and can resist various attacks. Moreover, the compression method improves the storage and transmission efficiency to some extent, and the MAC ensures the integrity of the transmission data.

The nature of mathematics has been the subject of heated debate among mathematicians and philosophers throughout the ages. The realist and anti-realist positions have had longstanding debate over this problem, but some of the most important recent development has focused on the interpretations; each of the above positions has its own interpretation of the nature of mathematics. I argue in this paper a contextualist interpretation of mathematics, it elucidates the essential features of mathematical context. That is, being integral and having concrete structure, mathematical context is a recontextualizational process with determinate boundary.