摘要
点模式匹配是计算机视觉和模式识别领域的一个重要而基础的问题，在图像配准、立体视觉、图像检索、目标识别与跟踪、医学图像分析、景象匹配导航等方面有着广阔的应用背景。由于实际应用中所提取到的点集通常会出现噪声、出格点和缺失点等复杂情况，而且点集之间的几何变换关系既可能是低维的刚体变换，也可能是更复杂的高维非刚体变换，这样就使得有着广泛应用的点模式匹配本身仍然是一个十分具有挑战性的任务。
针对目前已有的点模式匹配算法所存在的问题，本论文根据待匹配点模式之间所满足的几何变换模型的不同，对刚体变换和非刚体变换下的点模式匹配问题分别展开深入研究，提出了一系列新的适用于不同几何变换模型的鲁棒的点模式匹配算法：
在相似变换下的点模式匹配方法研究中，论文首先提出了一种新的基于点集的不变特征—相对形状上下文，然后将该不变特征分别与概率松弛标记法和谱匹配方法相结合，提出了基于相对形状上下文与概率松弛标记法的点模式匹配算法和基于相对形状上下文与谱匹配方法的点模式匹配算法。相比于其它经典算法，本文所提的两种新算法均具有较强的针对噪声、出格点的鲁棒性，且都能适用于一定程度的透视变换情况。而在相同的参数设置下，前者具备更强的抗出格点能力，而后者则具备更强的抗噪声能力。
在仿射变换下的点模式匹配方法研究中，为了解决传统的一致性点漂移算法存在的局部最优性和收敛速度随点集大小增加而下降等问题，论文提出了一种新的基于全局最优的快速一致性点漂移算法。该算法首先将点集进行正交标准形约简，利用约简后点集的重要性质，推导出不完全观测数据的对数似然函数在全局最优解附近凸函数区域的边界值，再以该边界值为基础，采用多重初始化策略来实现全局最优。最后，提出了基于置信域的全局收敛二次平方迭代期望最大化算法，实现了全局优化算法的超线性收敛。通过实验验证了该算法是有效的、快速的以及鲁棒性较强的。
在非刚体变换下的有标记点模式匹配方法研究中，当归纳分析了经典的非刚体几何变换模型以及经典的基于微分同胚的非刚体变换模型所存在的问题后，论文提出了一种新的基于恒定动量矢量的快速大形变微分同胚非刚体变换有标记点模式匹配算法，该方法利用拉格朗日坐标系下的恒定动量矢量以及时间依赖的多尺度再生核来构造速度矢量场，然后采用基于规则化控制参数的确定性退火机制来搜索最优动量矢量，从而得到最优的微分同胚变换形变场。通过比较实验发现，新方法不仅适用于大形变的微分同胚非刚体变换的情况，而且与经典的基于微分同胚的方法相比，匹配精度较高，时空复杂度较低，并在匹配精确性与形变光滑性之间达到了较好的平衡兼顾。
在非刚体变换下的无标记点模式匹配方法研究中，提出了一种新的高斯混合模型与基于恒定动量矢量的大形变微分同胚变换相结合的非刚体点模式匹配算法，该方法将以高斯混合模型为基础的软匹配方法与上述非刚体变换下有标记点模式匹配研究中所提出来的基于恒定动量矢量的快速大形变微分同胚非刚体几何变换模型相结合，利用高斯混合模型概率密度函数的参数估计方法来迭代求解最优的恒定动量矢量参数。新算法在复杂实际应用中不仅能得到满足微分同胚条件的大形变光滑可微形变场，同时还具备较高的匹配精度以及较强的鲁棒性。
Point Pattern Matching (PPM) is one of important and fundamental problems incomputer vision and pattern recognition, which is widely used in many applications,such as imaging registration, stereovision, image retrieval, object recognition andtracking, medical imaging analysis, image matching for navigation, etc. It is still achallenging task due to the existence of the noise, the outliers and the missing points inthe extracted point pattern from the realistic applications; moreover, the geometricdeformation between point pattern can also be from the low-dimensional rigidtransformations to the high-dimensional non-rigid transformations.
Considering the difficulties of current point pattern mathing methods andaccording to the diversity of geometric distortion, the thesis lucubrates on the rigid andnon-rigid point pattern matching problems respectively, and then develops a series ofnew and robust point pattern matching methods, which can be suitable for differentgeometirc transformations.
In the research on the problems of PPM which under similarity transformations,the thesis firstly propose a new point-set based invariant feature which name as RelativeShape Context (RSC). After combining the invariant feture with probabilistic relaxationlabelling and spectral matching method, the thesis presents one PPM algorithm whichbased on relative shape context and probabilistic relaxation labelling (RSC-PRL) andthe other PPM algorithm which based on relative shape context and spectral matchingmethod respectively. Compared with the other classical PPM methods under similaritytransformation, the two proposed novel methods all are more robust to noise andoutliers, and even can be applicable to some certain extant of pespective distortion.Under the same parameters setup, the RSC-PRL method is more robust to outliers thanthe RSC-SM method and inversely the RSC-SM method is more robust to noise thanthe RSC-PRL method.
In the research on the problems of PPM which under affine transformations, theCoherent Point Drift (CPD) is one of popular point pattern matching algorithms becauseof its robustness. However, The CPD is local optimization and its convergent rate isslower along with the size of point-set become larger. For resolving these problems, thethesis develops a Global Optimal and Fast algorithm which based on CPD (GOF-CPD).The orthogonal normalization first reduce the general affine case to the orthogonal case,and the convex region boundary of the unoberserved data’s logarithmic likelihoodnearby the global optimal solutions are deduced by the properties of normalizedpoint-sets. Then, the Multi-start strategy based on the convex region boundary isintroduced to achieve the global optimization. Finally, a new iterative scheme, calledthe Trust Region based global convergent SQUARed iterative EM (TR-gSQUAREM) is proposed to achieve the superlinear convergence. Experiments show that the proposedalgorithm is efficient, speedy and robust.
In the research on the problems of non-rigid landmark matching, the thesisproposes a novel methods which name as the Fast Large Deformation DiffeomorphicLandmarks Matching Based on Stationary Momentum (SM-FLDDLM) for the purposeof resolving the limitations of the known classical non-rigid transformation models andthe classical diffeomorphic non-rigid transformation models. The SM-FLDDLMmethod estimates the velocity vector fields by means of the Lagrangian stationarymomentum vector and time-dependent multi-scales reproducing kernels. The optimaldiffeomorphic deformation fields can be gained by the searching of optimal momentumvectors using the determinate simulative anneal based on the regularization controlsparameter. The results of comparative experiments show that the SM-FLDDLM methodis not only suitable for the large deformation diffeomorphic non-rigid transformation,but also has higher matching precision and lesser time and space consumes than thoseclassical diffeomorphic landmark mathing methods. Note that the proposed method canachieve a better balance between the accuracy of matching and the smoothness ofnon-rigid deformation.
In the research on the problems of non-rigid unlabeled point pattern matching, thethesis develops a new diffeomorphic non-rigid PPM algorithm which combines theGaussian Mixture Model and Large Deformation Diffeomorphism Matching Based onStationary Momentum (GMM-SMLDDM). The GMM-SMLLDM method integratesthe soft matching technique which based on Gaussian Mixture Model with the non-rigidtransformation model which based on the above proposed SM-FLDDLM method. Theoptimal stationary momentum can be finded by the maximum likelihood estimation ofthe parameters Gaussian Mixture Model. The proposed novel method performs well inthe practical applications which under large deformation diffeomorphism and also havehigher matching accuracy and stronger robustness.
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