广义极坐标矩及其在仿射不变特征提取中的应用

Affine transform is the approximate model to describe the relations between the images for one object viewed from angles. Therefore, affine invariant feature extraction plays a key role in object recognition and registration. Moment invariants are important solutions to the problem. Traditional moments are defined by inner product. Affine invariant feature can only be constructed by moments with integer order. However, moment invariants with high order are sensitive to noise, and as results only a few low order moments can be used. To address this problem, quasi pre-inner product is proposed,and generic polar coordinate moments are constructed to extract affine invariant features in this application. The proposed quasi pre-inner product is defined by a modifying of the repeated integral used in the traditional inner product. A function of the integral along radial direction is employed to eliminate the angular factor due to shearing in affine transformation. This research will go deep into studying the following aspects. First,the robustness of the extracted affine invariant features to noise will be invested. Second, construct affine invariants by low degree(order) generic polar coordinate moments to improve the robustness of moments to the noise. Third, establish the linear equations by generic polar coordinate moments, and design accurate affine transform parameters estimation methods with small computational complexity. This project is promising to breakthrough the limitation that only a few low order moments can be applied for affine invariant feature extraction. The proposed quasi pre- inner product also opens up new ways for feature extraction.

目标在不同场景获得的图像存在各种变化，提取不随视点不同而改变的图像特征尤为重要。仿射变换是描述同一目标在不同视点获取图像间关系的近似模型，仿射不变的特征提取是目标识别或配准的关键问题，图像矩技术是解决该问题的重要方法。传统矩以传统内积定义，仅能利用正整数阶矩提取仿射不变特征，然而高阶矩对噪声敏感，因此仅有有限几个低阶矩构造的仿射不变量可用。本项申请引入拟准内积，并以之定义广义极坐标矩。拟准内积以变形累次积分定义，为消除在仿射变换前后非线性变化因子，引入径向方向积分的变换函数。将展开以下几方面工作：探讨拟准内积核函数的选取对广义极坐标矩抗噪性能影响机理；构造更多低阶仿射不变矩量以提高矩量法的抗噪性能；建立关于广义极坐标矩的线性方程组，给出精确且计算量小的仿射变换参数恢复算法。本申请可以打破仅有有限几个低阶矩量可用于提取仿射不变特征的瓶颈，提出的拟准内积也为仿射不变特征的提取引入了新方法。

主要预期指标是发表学术论文20篇，有10篇论文被SCI等收录，培养硕士生2- 4名。迄今为止，已在SCI 检索的期刊上发表标注项目号的论文16 篇，另有2 篇SCI 检索论文录用待发表；已发表标注项目号的EI 检索论文6 篇。除SCI 、EI检索的论文外，还参编教材一部，发表国外、国内刊物论文若干，项目负责人指导培养硕士生7名，项目组成员培养研究生若干。不计学位论文，共发表28 篇（不含待发表2 篇）论文。所有28份都标注了项目批准号，超预期指标完成了项目。.利用拟准内积定义的广义极坐标矩，设计出了一系列提取不变特征的算法：提出了分数阶矩以及Mellin极坐标矩（Mellin polar coordinate moment），这些矩直接利用变形累次积分定义，极经方向积分可充分利用仿射变换映直线为直线这一特性，而选择了极经方向积分的变换函数,又能方便地消除仿射变换前后极角因子的影响，利用这些矩给出了构造仿射不变量的方法，传统图像矩构造的仿射不变量仅是这些不变量的特例，并且可构造出比传统矩构造不变量抗噪性能更优的不变量；提出了广义质心的概念，给出了广义质心点保持仿射变换前后对应关系的条件，从而利用构造的广义质心点可建立线性方程组求解仿射变换中的参数，实现仿射变换参数的恢复，该算法计算量小，并且对灰度和二值图像都适用；重点讨论了核函数为幂函数时广义极坐标的抗噪性能，结果显示一般内部核函数幂指数越大，抗噪性能越差，应选择内部核函数幂指数较小的广义极坐标矩提取不变特征；改造了传统正交矩，提出了分数阶的Zernike矩和广义雅可比傅里叶矩；结合Radon、Fourier、Mellin等变换，提出了RMT(Radon Mellin Transform)变换，设计出提取旋转和伸缩不变特征的算法；提出了Mellin中心投影变换以及无需参数化的中心投影变换。