Point Pattern Matching Problem Research Articles

A new algorithm for the small-field astrometric point-pattern matching problem

The small-field astrometric point-pattern matching problem is a fundamental problem in astronomy, that although considered a long time ago still lacks a formal definition. It can be textually stated as: given two lists of positions of stars, find the common stars between these lists, taking into account rotation, translation, reflection and scaling operations. It is expected that there might be missing stars between the lists. In this work, we give the astronomical context, review some heuristic methods adopted in the literature, present distance matrix formulations for the problem and propose a new algorithm to solve it.

A Local Structural Descriptor for Image Matching via Normalized Graph Laplacian Embedding.

This paper investigates graph spectral approaches to the problem of point pattern matching. Specifically, we concentrate on the issue of how to effectively use graph spectral properties to characterize point patterns in the presence of positional jitter and outliers. A novel local spectral descriptor is proposed to represent the attribute domain of feature points. For a point in a given point-set, weight graphs are constructed on its neighboring points and then their normalized Laplacian matrices are computed. According to the known spectral radius of the normalized Laplacian matrix, the distribution of the eigenvalues of these normalized Laplacian matrices is summarized as a histogram to form a descriptor. The proposed spectral descriptor is finally combined with the approximate distance order for recovering correspondences between point-sets. Extensive experiments demonstrate the effectiveness of the proposed approach and its superiority to the existing methods.

Image registration using a point-line duality based line matching method

In the paper, a Point-Line Duality (PLD), i.e. a line in the image (x–y) space corresponds to a point in the dual (θ–ρ) space, based line matching method is proposed for image registration. First, edge points are detected in a template image and a target image. The edge points are linked and segmented into chains. The chains are fitted to lines, and the lines are mapped to dual points in the dual space. To improve stability and efficiency, a point merging algorithm is proposed to deal with the fragmentary line segments that should belong to a single line. As a result, a line matching problem is converted to a point pattern matching problem. Finally, a point pattern matching algorithm is proposed to determine registration parameters and to determine matched line pairs. Experimental results demonstrate that the proposed method is effective for images under rigid body transformation, occlusion, and illumination change.

Point Pattern Matching Algorithm for Planar Point Sets under Euclidean Transform

Point pattern matching is an important topic of computer vision and pattern recognition. In this paper, we propose a point pattern matching algorithm for two planar point sets under Euclidean transform. We view a point set as a complete graph, establish the relation between the point set and the complete graph, and solve the point pattern matching problem by finding congruent complete graphs. Experiments are conducted to show the effectiveness and robustness of the proposed algorithm.

Fast matching of large point sets under occlusions

The problem of isometric point-pattern matching can be modeled as inference in small tree-width graphical models whose embeddings in the plane are said to be 'globally rigid'. Although such graphical models lead to efficient and exact solutions, they cannot generally handle occlusions, as even a single missing point may 'break' the rigidity of the graph in question. In addition, such models can efficiently handle point sets of only moderate size. In this paper, we propose a new graphical model that is not only adapted to handle occlusions but is much faster than previous approaches for solving the isometric point-pattern matching problem. We can match point-patterns with thousands of points in a few seconds.

Approximate input sensitive algorithms for point pattern matching

We study input sensitive algorithms for point pattern matching under various transformations and the Hausdorff metric as a distance function. Given point sets P and Q in the plane, the problem of point pattern matching is to determine whether P is similar to some portion of Q, where P may undergo transformations from a group G of allowed transformations. All algorithms are based on methods for extracting small subsets from Q that can be matched to a small subset of P. The runtime is proportional to the number k of these subsets. Let d be the number of points in P that are needed to define a transformation in G. The key observation is that for some set B ⊂ P of cardinality larger than d, the number of subsets of Q of this cardinality that match B, is practically small, as the problem becomes more constrained. We present methods to extract efficiently all these subsets in Q. We provide algorithms for homothetic, rigid and similarity transformations in the plane and give a general method that works for any dimension and for any group of transformations. The runtime of our algorithms depends roughly linearly on the number of subsets k, in addition to an n log n factor. Thus our approximate matching algorithms run roughly in time O ( n log n + km log n ) , where m and n are the number of points in P and Q, respectively. The constants hidden in the big O vary depending on the group of transformations G.

基于偏最小二乘方法的谱特征匹配方法

We investigate the spectral approaches to the problem of point pattern matching, and present a spectral feature descriptors based on partial least square (PLS). Given keypoints of two images, we define the position similarity matrices respectively, and extract the spectral features from the matrices by PLS, which indicate geometric distribution and inner relationships of the keypoints. Then the keypoints matching is done by bipartite graph matching. The experiments on both synthetic and real-world data corroborate the robustness and invariance of the algorithm.

Graphical Models and Point Pattern Matching

This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.

Correspondence matching using kernel principal components analysis and label consistency constraints

This paper investigates spectral approaches to the problem of point pattern matching. We make two contributions. First, we consider rigid point-set alignment. Here we show how kernel principal components analysis (kernel PCA) can be effectively used for solving the rigid point correspondence matching problem when the point-sets are subject to outliers and random position jitter. Specifically, we show how the point- proximity matrix can be kernelised, and spectral correspondence matching transformed into one of kernel PCA. Second, we turn our attention to the matching of articulated point-sets. Here we show label consistency constraints can be incorporated into definition of the point proximity matrix. The new methods are compared to those of Shapiro and Brady and Scott and Longuet-Higgins, together with multidimensional scaling. We provide experiments on both synthetic data and real world data.

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 O(n( log m) 3/2) 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.

An applied point pattern matching problem: comparing 2D patterns of protein spots

It is shown how to use various ideas from computational geometry to derive a new algorithmic solution to the matching problem of 2D patterns of protein spots obtained by the 2D gel electrophoresis technique. The algorithm especially relies on a data structure derived from the incremental Delaunay triangulation of a point set and several heuristics to cope with distortions and noise inherent to the electrophoresis process. The main feature of the presented solution is that interactive landmark setting is optional and not necessary.

An Application of Point Pattern Matching in Astronautics

We consider a point pattern matching problem occuring in astronautics: Given are pictures from a camera of unknown orientation, showing a section of the starry sky. We want to determine the orientation of the camera by matching the constellations in the pictures with a star catalogue. This problem occurs for satellite attitude determination with star field sensors. We present a new solution, which uses incremental Delaunay triangulation.