融合多尺度稀疏与稠密特征结构的透视不变图像匹配模型研究

Based on the theory that receptive fields of cells at one level of the visual system are formed from input by cells at a lower level of the visual system, the feature with multi-scale representation and perspective invariance is considered as the key research object of this project, and the research is aimed at solving two limits of classic visual feature extraction and matching models. The first limit is that the classic models do not have perspective invariance; the second is that classic models is deficient in deep fusion of scattered and dense feature structures.The main innovations of this research include creative objectives, creative concepts, creative ideas, and creative methods. There are two creative objectives in this research. The first objective is to construct a local dense feature extraction and matching model with perspective invariance; the second is to present a visual feature definition with deep fusion of scatterd and dense structures, and construct a multi-scale feature extraction and matching model with perspective invariance. There are three creative concepts in this research. The first concept is the feature point with perspective invariance; the second concept is the projective Gaussian kernel, which is transformed from normal Guassian kernel with projection transformation; and the third concept is the visual feature with fusion of scattered and dense structures. There are three creative ideas in this research. First, projective transformation is applied to adapt to perspective deformation of local feature. Second, before applying projective transformation to a image, convolution with projective Gaussian kernel is applied to perform anti-aliasing and obtain perpective invariance. Third, the fusion mechanism of scatterd and dense feature structures is realized with the mlti-scale representation of visual feature, these two feature structures are rectified with each other in feature matching procedure, and finally perspective invariance of the feature is obtained. There are two creative methods in this research, which are local dense feature extraction and matching method with perspective invariance,and feature matching method based on fusion mechanism of scattered and dense structures with multi-scale representation.

基于人类视觉系统中多层视觉神经细胞的接受域由低层向高层逐层合并的基本结构，本项目以透视不变的多尺度视觉特征为研究对象，旨在解决现有视觉特征提取与匹配模型中的两个关键局限：现有模型不具有透视不变性；稀疏与稠密特征结构缺乏深度融合。主要创新点包括：（1）新目标：1）构造透视不变的局部稠密特征提取与匹配模型，2）建立深入融合稀疏与稠密结构的视觉特征定义，并构造透视不变的多尺度特征提取与匹配模型；（2）新概念：1）透视不变特征点，2）射影高斯核，3）稀密结构融合的视觉特征；（3）新思路：1）使用射影变换适应局部特征的透视形变，从而提高匹配精度，2）基于射影高斯核生成射影变换图像，兼顾反走样与透视不变性，3）在多尺度视觉特征框架中融合稀疏与稠密特征结构，使二者在匹配过程中相互校正，从而获取透视不变性；（4）新方法：1）透视不变的局部特征提取与匹配方法；2）多尺度框架中稀密结构融合的特征匹配方法。

本项目的研究目标包括：（1）构造透视不变的局部特征提取与匹配模型；（2）建立深入融合稀疏与稠密结构的视觉特征定义，并构造透视不变的多尺度特征提取与匹配模型。目标（1）已完成，项目组已提出映射适应卷积（MA-convolution）的数学定义，构建了映射适应卷积理论，并完成了相关核心定理的数学证明。作为标准卷积理论的自然扩展形式，映射适应卷积理论实质上构造了针对微分同胚映射下chirp信号的理想滤波器，基于这一不可或缺的基础理论，项目组构建了微分同胚映射不变的信号模拟模型（包括成像模拟）、特征提取与匹配模型。映射适应卷积理论揭示了如下两个关键结论：1）微分同胚映射不能与标准卷积交换，但是，如果将标准卷积视为映射适应卷积的特殊情况，微分同胚映射与映射适应卷积的运算顺序可以交换，并且服从映射分配律；2）标准卷积与映射适应卷积不能整体交换，但服从单点交换律。基于上述两个关键结论，映射适应卷积理论解决了标准卷积理论中的一个基础性矛盾：标准卷积无法兼具映射适应性与抗混叠（反走样）性质；换言之，映射适应卷积在理论上自然地兼具映射不变性质与抗混叠性质。由于映射适应卷积兼具这两种关键性质，映射适应卷积理论在均匀采样与非均匀采样方法间构建了一座等价变换的桥梁，该理论实质上是所有微分同胚映射下非均匀采样方法的系统化理论，可广泛应用于计算机视觉、计算机图形学、信号处理与分析等领域。目标（2）已部分完成，基于映射适应卷积理论，具有微分同胚映射不变性（包括透视不变性）的多尺度特征提取与匹配模型已经得到构建，并且项目组已提出融合稀疏与稠密特征结构的特征提取与匹配算法。虽然映射适应卷积的空间域理论已经完整，但是，准确获得融合稀疏与稠密结构的视觉特征定义需要进一步完善映射适应卷积理论中的频率域理论，其中包含求解复合函数的傅里叶变换这一困难的问题，这一部分工作尚未彻底完成，这也是目前项目组的研究重点。