正交多项式变换及其在图像压缩与分析中的应用研究

Image transform is an important tool in image processing and computer vision, and it is also an effective way to solve the problems in high efficiency compression and intelligent analysis of big data for images and videos. Orthogonal polynomials transform is a recently proposed image transform technology, and have been widely used in the field of the invariant image recognition due to its kernel function has the properties of good orthogonality, perfect symmetry, fast recursive, and so on. However, the existing studies on orthogonal polynomials transform encounter the problems that the model for orthogonal transform are not well studied, the applications in invariant image recognition have low robustness and the applications in image compression and fusion are not introduced. All of these problems limit the applications and further study of orthogonal polynomials transform severely. This proposal studies the orthogonal polynomials transform from perspectives of mathematical model and the actual applications, and the major research contents include: the fractional order orthogonal polynomials transform, generalized orthogonal polynomials transform model, image compression based on the orthogonal polynomials transform, local feature extraction based on the orthogonal polynomials transform, image fusion based on orthogonal polynomials transform, etc. Through the research of this proposal, it is expected to complete the orthogonal polynomials transform theory system, to establish the open framework of loss and loss-less image compression based on the orthogonal polynomials transform, to solve the bottleneck problems of orthogonal polynomials transform based invariant image recognition, to expand the applications of the orthogonal polynomials transform, to provide more theoretical and technical supports for the development of image compression, analysis and other corresponding industries.

图像变换是图像处理与机器视觉研究中的重要工具，也是图像大数据高效压缩与智能分析的有效解决途径。作为近年来提出的图像变换技术，正交多项式变换由于其核函数具有良好的正交性、对称性和快速迭代性等优点，被广泛地应用于图像不变性识别等领域。但目前的研究还存在着在理论体系不完善、图像识别中鲁棒性低、在图像压缩与融合方面的研究还未展开等问题，限制了正交多项式变换的进一步研究和应用。本项目从正交多项式变换模型与实际应用角度出发，研究分数阶正交多项式变换、通用正交多项式变换模型、基于正交多项式变换的图像压缩、基于正交多项式变换的局部特征构造以及正交多项式变换在图像融合中的应用等问题。通过本项目的研究有望建立完善的正交多项式变换理论体系，构建基于正交多项式变换的有损与无损图像压缩开放框架，解决正交多项式变换在图像识别中的瓶颈问题，扩展正交多项式变换的应用领域，为图像压缩与分析等相关产业发展提供理论和技术支持。

图像变换作为图像处理技术里的一个重要基础理论，一直以来都是图像视频处理的研究热点，从图像底层的处理到图像分析再到图像理解都会涉及许多图像变换技术，图像变换技术也是图像大数据存储与分析研究中行之有效的手段。本项目从正交多项式变换模型与实际应用角度出发，研究分数阶正交多项式变换、通用正交多项式变换模型、基于正交多项式变换的图像压缩、基于正交多项式变换的局部特征构造以及正交多项式变换在图像融合中的应用等问题。通过本项目的研究有望建立完善的正交多项式变换理论体系，构建基于正交多项式变换的有损与无损图像压缩开放框架，解决正交多项式变换在图像识别中的瓶颈问题，扩展正交多项式变换的应用领域，为图像压缩与分析等相关产业发展提供理论和技术支持。