Computer algebra algorithms and image set compression and encryption

计算机代数算法和图像集压缩和加密

• 批准号: 288300-2007
• 负责人: Cheng, Howard
• 金额: $ 1.09万
• 依托单位: University of Lethbridge
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=366495
• 关键词: Computer; algebra; algorithms; image; set

We propose to study problems from two distinct areas of computer science: computer algebra and image processing.Computer algebra is the study of algorithms which perform mathematical computations symbolically rather than numerically.  Because of its ability to handle symbolic quantities and its lack of numerical errors, computer algebra has many applications in mathematical research, engineering, and mathematical education.  Despite advances in this area, many problems remain impractical to solve.  A common issue encountered in computer algebra is the so-called "intermediate expression swell."  In many problems, the size of the input is small but the size of the intermediate results during the calculations can grow significantly.  If this growth is not controlled, an algorithm cannot finish its computation due to time and memory constraints.  The goal in the proposed research in computer algebra is to design and analyze algorithms to control this growth for a variety of problems in computer algebra.  This study will improve our understanding of such problems and provide practical improvements to the current algorithms.In a separate direction, we propose to study issues related to the storage of large image sets.  We plan to investigate compression methods to reduce storage requirements, as well as encryption algorithms for security.  We are also interested in the interaction among compression, encryption, and efficient image retrieval.  The results from this study  have many applications as the use of large image databases have become more common (e.g. medical and satellite images).

我们建议从计算机科学的两个不同领域研究问题：计算机代数和图像处理。计算机代数是对以符号方式而不是数字方式执行数学计算的算法的研究。由于它能够处理符号量并且没有数值错误，计算机代数在数学研究、工程和数学教育中有许多应用。尽管在这一领域取得了进展，许多问题仍然无法解决。2在计算机代数中遇到的一个常见问题是所谓的“中间表达式膨胀”。“在许多问题中，输入的大小很小，但计算过程中的中间结果的大小可能会显着增长。如果这种增长不受控制，由于时间和内存的限制，算法无法完成其计算。计算机代数研究的目标是设计和分析算法，以控制计算机代数中各种问题的增长。本研究将提高我们对这些问题的理解，并提供对当前算法的实际改进。在一个单独的方向，我们建议研究与大型图像集存储相关的问题。我们计划研究压缩方法以减少存储需求，以及加密算法以提高安全性。我们还对压缩，加密，和有效的图像检索。这项研究的结果有许多应用，因为大型图像数据库的使用已经变得越来越普遍（例如医学和卫星图像）。