Fractal-based methods in analysis and signal image processing

基于分形的分析和信号图像处理方法

• 批准号: 238898-2006
• 负责人: Kunze, Herbert
• 金额: $ 0.66万
• 依托单位: University of Guelph
• 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=362166
• 关键词: Fractal; based; methods; analysis; signal

Fractal-based approximation methods take advantage of mathematical self-similarity in the object being analyzed. Finding such self-similarity in a digital signals/images facilitates the construction of fractal-based algorithms for image operations such as compression and denoising.  Such operations are of great concern when images are transmitted over a computer or cell phone connection, for example.  A very recent advancement involves the construction of "orbital pictures" via fractal-based techniques.  A simple example of an orbital picture is a field of corn or flowers disappearing off to the horizon.  Besides allowing for such images to be rendered with remarkable speed on a computer, there are other applications of these ideas to image representation. Finding such self-similarity in experimentally observed data can enable us to approximate the values of parameters in the mathematical model of the phenomenon being studied.  If the mathematical model is unknown, we may be able to determine its form.  Scientific research in a wide range of areas requires efficient model identification and parameter estimation techniques.

基于分形的近似方法利用了被分析对象的数学自相似性。在数字信号/图像中发现这种自相似性有助于构建基于分形的图像操作算法，如压缩和去噪。当图像通过计算机或手机连接传输时，例如，最近的一项进展涉及通过分形构建“轨道图像”，一个简单的例子，一个轨道图片是一个领域的玉米或鲜花消失在地平线上。除了允许这样的图像被渲染在计算机上以显着的速度，还有其他应用这些想法的图像表示。在实验观测数据中发现这种自相似性可以使我们能够近似地估计所研究现象的数学模型中的参数值。如果数学模型是未知的，我们可以确定它的形式。在广泛的领域中，科学研究需要有效的模型识别和参数估计技术。