A fast pattern matching algorithm derived by transformational and assertional reasoning

Highly optimised algorithms are, in general, hard to understand. This is a consequence of the designer's sacrifice of clarity and modularity in favour of efficiency. In this paper we present a formal derivation of a rather ingenious algorithm, viz., the fast pattern matching algorithm of Boyer and Moore. The development illustrates that transformational programming combined with assertional reasoning provides an appropriate approach for developing and understanding highly optimised algorithms.This research has been carried out within the NFT-project STOP (Specification and Transformation Of Programs) and partially sponsored by NWO (Netherlands Organisation for Scientific Research) under grant NFI-FW3315.     

Inexact Bayesian point pattern matching for linear transformations

We introduce a novel Bayesian inexact point pattern matching model that assumes that a linear transformation relates the two sets of points. The matching problem is inexact due to the lack of one-to-one correspondence between the point sets and the presence of noise. The algorithm is itself inexact; we use variational Bayesian approximation to estimate the posterior distributions in the face of a problematic evidence term. The method turns out to be similar in structure to the iterative closest point algorithm.     

A fast expected time algorithm for the 2-D point pattern matching problem

Point set pattern matching is an integral part of many pattern recognition problems. We study a randomized algorithm for the alignment approach to model-based recognition.Under certain mild assumptions we show that if our scene is a set of n points and our model is a set of m<n points our algorithm has expected running time for finding an occurrence of the model in the scene. This is significantly faster than any existing algorithms in the literature. We then describe some experimental results on randomly generated data using a practical version of our algorithm. These results agree well with the theoretical analysis.     

Spectral correspondence for point pattern matching

This paper investigates the correspondence matching of point-sets using spectral graph analysis. In particular, we are interested in the problem of how the modal analysis of point-sets can be rendered robust to contamination and drop-out. We make three contributions. First, we show how the modal structure of point-sets can be embedded within the framework of the EM algorithm. Second, we present several methods for computing the probabilities of point correspondences from the modes of the point proximity matrix. Third, we consider alternatives to the Gaussian proximity matrix. We evaluate the new method on both synthetic and real-world data. Here we show that the method can be used to compute useful correspondences even when the level of point contamination is as large as 50%. We also provide some examples on deformed point-set tracking.     

Real-time model based geometric reasoning for vision-guided navigation

This paper describes results of a real-time model based geometric reasoning module for autonomous vision-guided road following. Vision-guided road following requires extracting road boundaries from images in real time to guide the navigation of autonomous vehicles on a roadway. The detected road region boundary is error prone due to imperfect image segmentation. To achieve robust system performance, a geometric reasoning module that uses spatial and temporal constraints to perform model based reasoning is used. Local geometric supports for each road edge segment are collected and recorded and a global consistency checking is performed to obtain a consistent interpretation of the raw data. Cases involving incomplete sensor data, curved roads where only one side of the road is visible, and incorrect segmentation due to shadows, road patches, or unusual road conditions, can usually be detected and corrected. The image segmentation results are what the vision system sees. The geometric reasoning results are what the vision system perceives. This reasoning module has been integrated into a road following system which is capable of supporting autonomous robot road following at 24 km/hr.     

基于向量积点匹配的轮廓层间插值算法

利用向量积的性质,使用线性插值算法,结合基于角度和距离算法的思想提出了一种新的层间轮廓的点匹配及插值算法.该算法适用于一对一与一对多插值,不仅对一般问题插值的效果良好,而且成功地解决了弹性插值中不能解决的示例.一系列数据的实验结果表明,该算法是一种可行的层间轮廓线性插值算法.     

A fast algorithm for order-preserving pattern matching

Given a text T and a pattern P, the order-preserving pattern matching (OPPM) problem is to find all substrings in T which have the same relative orders as P. The OPPM has been studied in the fields of finding some patterns affected by relative orders, not by their absolute values. In this paper, we present a method of deciding the order-isomorphism between two strings even when there are same characters. Then, we show that the bad character rule of the Horspool algorithm for generic pattern matching problems can be applied to the OPPM problem and we present a space-efficient algorithm for computing shift tables for text search. Finally, we combine our bad character rule with the KMP-based algorithm to improve the worst-case running time. We give experimental results to show that our algorithm is about 2 to 6 times faster than the KMP-based algorithm in reasonable cases.     

一种基于混合匹配的指纹识别方法

为克服传统的基于细节点匹配的不足,对基于点模式匹配算法与改进的2DPCA匹配算法的混合识别算法进行了改进。改进后的算法在点模式匹配算法中加入改进的2DPCA算法的初匹配得分权重,提高了点模式匹配算法的准确性;并利用点模式匹配算法对2DPCA算法的匹配结果进行二次匹配,同时也提高了2DPCA算法匹配的准确率。     

A new point matching algorithm for non-rigid registration

Feature-based methods for non-rigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, feature-based non-rigid matching requires us to automatically solve for correspondences between two sets of features. In addition, there could be many features in either set that have no counterparts in the other. This outlier rejection problem further complicates an already difficult correspondence problem. We formulate feature-based non-rigid registration as a non-rigid point matching problem. After a careful review of the problem and an in-depth examination of two types of methods previously designed for rigid robust point matching (RPM), we propose a new general framework for non-rigid point matching. We consider it a general framework because it does not depend on any particular form of spatial mapping. We have also developed an algorithm—the TPS–RPM algorithm—with the thin-plate spline (TPS) as the parameterization of the non-rigid spatial mapping and the softassign for the correspondence. The performance of the TPS–RPM algorithm is demonstrated and validated in a series of carefully designed synthetic experiments. In each of these experiments, an empirical comparison with the popular iterated closest point (ICP) algorithm is also provided. Finally, we apply the algorithm to the problem of non-rigid registration of cortical anatomical structures which is required in brain mapping. While these results are somewhat preliminary, they clearly demonstrate the applicability of our approach to real world tasks involving feature-based non-rigid registration.