Point Set Matching Research Articles

Matching point sets with respect to the Earth Mover's Distance

The Earth Mover's Distance (EMD) between two weighted point sets (point distributions) is a distance measure commonly used in computer vision for color-based image retrieval and shape matching. It measures the minimum amount of work needed to transform one set into the other one by weight transportation. We study the following shape matching problem: Given two weighted point sets A and B in the plane, compute a rigid motion of A that minimizes its Earth Mover's Distance to B. No algorithm is known that computes an exact solution to this problem. We present simple FPTASs and polynomial-time ( 2 + ϵ ) -approximation algorithms for the minimum Euclidean EMD between A and B under translations and rigid motions.

ALGORITHMS FOR POINT SET MATCHING WITH k-DIFFERENCES

The largest common point set problem (LCP) is, given two point set P and Q in d-dimensional Euclidean space, to find a subset of P with the maximum cardinality that is congruent to some subset of Q. We consider a special case of LCP in which the size of the largest common point set is at least (|P| + |Q| - k)/2. We develop efficient algorithms for this special case of LCP and a related problem. In particular, we present an O(k3n1.34 + kn2 log n) time algorithm for LCP in two-dimensions, which is much better for small k than an existing O(n3.2 log n) time algorithm, where n = max {|P|,|Q|}.

Multi-modal image registration using local frequency representation and computer-aided design (CAD) models

Given two images of roughly the same scene, image registration is the process of determining the transformation that nearly maps one image to another. While some efficient procedures have been developed lately, the registration of images acquired from sensors operating in different modalities is still a challenging problem. In general, such images have different gray level characteristics and the features in the two images to be registered are often not well preserved, rendering registration techniques such as those based on feature extraction and area correlation generally not efficient, and hence not feasible in all cases. In this paper, we propose a new algorithm for multi-sensor image registration based on using the local frequency representation of the images together with image representation of computer-aided design (CAD) models that permit region-of-interest-to-region-of-interest, ROI-to-ROI, space to solve image registration problem (instead of relying only on the captured images to solve image registration problem using image-to-image space). The key point underlying the proposed approach is the employment of local frequency representations of CAD models images to efficiently determine sets of matching points from the images to be registered, which in turn enables obtaining correspondence between these sets for estimating the transformation parameters. Performance evaluation results reported here indicate that the proposed technique is robust and yields promising results for multi-modal image registration.

Approximating the problem, not the solution: An alternative view of point set matching

This work discusses the issue of approximation in point set matching. In general, one may have two classes of approximations when tackling a matching problem: (1) an algorithmic approximation which consists in using suboptimal procedures to infer the assignment, and (2), a representational approximation which involves a simplified and suboptimal model for the original data. Matching techniques have typically relied on the first approach by retaining the complete model and using suboptimal techniques to solve it. In this paper, we show how a technique based on using exact inference in simple Graphical Models, an instance of the second class, can significantly outperform instances of techniques from the first class. We experimentally compare this method with well-known Spectral and Relaxation methods, which are exemplars of the first class. We have performed experiments with synthetic and real-world data sets which reveal significant performance improvement in a wide operating range.

Similarity K-d tree method for sparse point pattern matching with underlying non-rigidity

We propose a method for matching non-affinely related sparse model and data point-sets of identical cardinality, similar spatial distribution and orientation. To establish a one-to-one match, we introduce a new similarity K -dimensional tree. We construct the tree for the model set using spatial sparsity priority order. A corresponding tree for the data set is then constructed, following the sparsity information embedded in the model tree. A matching sequence between the two point sets is generated by traversing the identically structured trees. Experiments on synthetic and real data confirm that this method is applicable to robust spatial matching of sparse point-sets under moderate non-rigid distortion and arbitrary scaling, thus contributing to non-rigid point-pattern matching.

A new image registration method for grey images

The proposed algorithm relies on a group of new formulas for calculating tangent slope so as to address angle feature of edge curves of image. It can utilize tangent angle features to estimate automatically and fully the rotation parameters of geometric transform and enable rough matching of images with huge rotation difference. After angle compensation, it can search for matching point sets by correlation criterion, then calculate parameters of affine transform, enable higher-precision emendation of rotation and transferring. Finally, it fulfills precise matching for images with relax-tense iteration method. Compared with the registration approach based on wavelet direction-angle features, the matching algorithm with tangent feature of image edge is more robust and realizes precise registration of various images. Furthermore, it is also helpful in graphics matching.

Registration of digital retinal images using landmark correspondence by expectation maximization

A method for registering pairs of digital images of the retina is presented, using a small set of intrinsic control points whose matching is not known. Control point matching is then achieved by calculating similarity transformation (ST) coefficients for all possible combinations of control point pairs. The cluster of coefficients associated with the matched control point pairs is identified by calculating the Euclidean distance between each set of ST coefficients and its Rth nearest neighbour, followed by use of the Expectation–Maximization (EM) algorithm. Registration is then achieved using linear regression to optimize similarity, bilinear or second order polynomial transformations for the matching control point pairs. Results are presented of (a) the cross-modal image registration of an optical image and a fluorescein angiogram, (b) temporal registration of two images of an infant eye, and (c) mono-modal registration of a set of seven standard field optical photographs. For cross-modal registration, using a set of independent matched control points, points are mapped with an estimated accuracy of 2.9 pixels for 575×480 pixel images. Bilinear and second-order polynomial transformation models all prove to be appropriate for the final registration transform.

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.

Approximate congruence in nearly linear time

The problem of geometric point set matching has been studied extensively in the domain of computational geometry, and has many applications in areas such as computer vision, computational chemistry, and pattern recognition. One of the commonly used metrics is the bottleneck distance, which for two point sets P and Q is the minimum over all one-to-one mappings f :P→Q of max p∈ P d( p, f( p)), where d is the Euclidean distance. Much effort has gone into developing efficient algorithms for minimising the bottleneck distance between two point sets under groups of transformations. However, the algorithms that have thus far been developed suffer from running times that are large polynomials in the size of the input, even for approximate formulations of the problem. In this paper we define a point set similarity measure that includes both the bottleneck distance and the Hausdorff distance as special cases. This measure relaxes the condition that the mapping must be one-to-one, but guarantees that only a few points are mapped to any point. Using a novel application of Hall's Theorem to reduce the geometric matching problem to a combinatorial matching problem, we present near-linear time approximation schemes for minimising this distance between two point sets in the plane under isometries; we note here that the best known algorithms for congruence under the bottleneck measure run in time O (n 2.5) . We also obtain a combinatorial bound on the metric entropy of certain families of geometric objects. This result yields improved algorithms for approximate congruence, and may be of independent interest.

Geometric Applications of a Randomized Optimization Technique

We propose a simple, general, randomized technique to reduce certain geometric optimization problems to their corresponding decision problems. These reductions increase the expected time complexity by only a constant factor and eliminate extra logarithmic factors in previous, often more complicated, deterministic approaches (such as parametric searching). Faster algorithms are thus obtained for a variety of problems in computational geometry: finding minimal k -point subsets, matching point sets under translation, computing rectilinear p -centers and discrete 1-centers, and solving linear programs with k violations.

Computational Micrograph Registration with Sieve Processes

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Affine point matching

An algorithm for matching point sets equivalent up to an affine transformation is shown.

Automatic derivation of initial match points for paired digital images of skin

Computerized matching of skin images has been suggested as a means of screening for changes indicative of malignant melanoma. Matching or “registering” each lesion in a pair of images plays an important role in this process. Point-pattern matching algorithms based upon correlation or geometric transformations of the image pairs have been shown to be effective for this registration but require knowledge of one or more “initial match” points which are known to be the same on both images. A method is described for automatically finding these initial match points with a high degree of success. Our algorithm uses the so-called “Gabriel graph” representation of the paired images to select sets of probable matching points. Performance of the algorithm has been measured in realistic trials, using images of patients with large numbers of pigmented lesions. Results show that the single best match chosen is correct greater than 99% of the time, while over 93% of the first three consecutive matches will be chosen correctly. It is likely that these results can be improved through the use of additional nonpositional information or additional image processing.

Matching and motion estimation of three-dimensional point and line sets using eigenstructure without correspondences

This paper presents moment-based algorithms for matching and motion estimation of three-dimensional (3D) point or line sets without correspondences and application of these algorithms to object tracking over long image sequences. The motion analysis is performed by identifying two sets of coordinate directions based on the relative position of points (or lines) before and after the motion. Since these coordinate vectors are motion invariant, the relationship between them gives parameters of rigid motion. However, we need to determine the set matching before and after the motion estimation algorithms can be applied. We propose several measures suitable for matching of 3D point (and line) sets. We also evaluate these approaches with simulated data and develop criteria for determining the sensitivity to noise. Finally, we apply the proposed algorithm to a time sequence of experimental data (moving vehicle) on which 3D points were determined by stereo matching.

Estimating the kinematics and structure of a rigid object from a sequence of monocular images

The problem considered involves the use of a sequence of noisy monocular images of a three-dimensional moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth. A set of object match points is assumed to be available, consisting of fixed features on the object, the image plane coordinates of which have been extracted from successive images in the sequence. Structure is defined as the 3-D positions of these object feature points, relative to each other. Rotational motion occurs about the origin of an object-centered coordinate system, while translational motion is that of the origin of this coordinate system. In this work, which is a continuation of the research done by the authors and reported previously (ibid., vol.PAMI-8, p.90-9, Jan. 1986), results of an experiment with real imagery are presented, involving estimation of 28 unknown translational, rotational, and structural parameters, based on 12 images with seven feature points.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Recursive 3-D motion estimation from a monocular image sequence

Consideration is given to the design and application of a recursive algorithm to a sequence of images of a moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth in the sense that it can be modeled by retaining an arbitrary number of terms in the appropriate Taylor series expansions. Translational motion involves a standard rectilinear model, while rotational motion is described with quaternions. Neglected terms of the Taylor series are modeled as process noise. A state-space model is constructed, incorporating both kinematic and structural states, and recursive techniques are used to estimate the state vector as a function of time. A set of object match points is assumed to be available. The problem is formulated as a parameter estimation and tracking problem which can use an arbitrarily large number of images in a sequence. The recursive estimation is done using an iterated extended Kalman filter (IEKF), initialized with the output of a batch algorithm run on the first few frames. Approximate Cramer-Rao lower bounds on the error covariance of the batch estimate are used as the initial state estimate error covariance of the IEKF. The performance of the recursive estimator is illustrated using both real and synthetic image sequences. >

Performance bounds for estimating three-dimensional motion parameters from a sequence of noisy images

The problem considered here involves the use of a sequence of monocular images of a three-dimensional moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth. A set of object match points is assumed to be available, consisting of fixed features on the object, the image plane coordinates of which have been extracted from successive images in the sequence. The measured data are the noisy image plane coordinates of this set of object match points, taken from each image in the sequence. In previous papers [ IEEE Trans. Pattern Anal. Mach. Intell.PAMI-8, 90 ( 1986); in Proceedings of the IEEE Workshop on Motion: Representation and Analysis ( Institute of Electrical and Electronics Engineers, New York, 1986), p. 95; in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition ( Institute of Electrical and Electronics Engineers, New York, 1986), p. 176] we discussed model-based approaches for motion and structure estimation from a long sequence of images. We examine here the performance of such techniques by using a Cramer–Rao lower bounds on the estimation error variance. This method permits a priori prediction of estimation accuracy as a function of a number of factors, including the number of images in the sequence, the time at which each image is made, the number of feature points used, the image-plane noise level, and the type of motion that is involved. Theoretical performance predictions are compared with the statistics of Monte Carlo simulation, and it is shown that the actual estimation accuracy is close to the Cramer–Rao bounds in most cases. These results also show that noisy sequences with fewer than four images often do not contain enough information to permit accurate estimation of motion and structure parameters. This conclusion is consistent with the observed instability of so-called two-frame estimation methods in the presence of noise.

Disparity Analysis of Images

An algorithm for matching images of real world scenes is presented. The matching is a specification of the geometrical disparity between the images and may be used to partially reconstruct the three-dimensional structure of the scene. Sets of candidate matching points are selected independently in each image. These points are the locations of small, distinct features which are likely to be detectable in both images. An initial network of possible matches between the two sets of candidates is constructed. Each possible match specifies a possible disparity of a candidate point in a selected reference image. An initial estimate of the probability of each possible disparity is made, based on the similarity of subimages surrounding the points. These estimates are iteratively improved by a relaxation labeling technique making use of the local continuity property of disparity that is a consequence of the continuity of real world surfaces. The algorithm is effective for binocular parallax, motion parallax, and object motion. It quickly converges to good estimates of disparity, which reflect the spatial organization of the scene.

Dynamics ofT=2 Σ-π system.-I.

A dynamical calculation using Balazs typesN/D method is performed for theT=2 Σ-π system inP 3/2 state. Self-consistent solutions for the position and residue of a resonance are obtained for a wide range of the relevant Yukawa coupling constants and different sets of matching points. Some remarks are made regarding interpretation of the results

On the Parametrization of the Three-Dimensional Rotation Group

Parameterization of group of rotations of Euclidean three-dimensional space applied to integration of rigid body motion equations