Curve matching is one instance of the fundamental correspondence problem. Our exible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations. A syntactic representation is constructed for both curves, and an edit transformation which maps one curve to the other is found using dynamic programming. We present extensive...

Shape matching is an important ingredient in shape retrieval, recognition and classification, alignment and registration, and approximation and simplification. This paper treats various aspects that are needed to solve shape matching problems: choosing the precise problem, selecting the properties of the similarity measure that are needed for the problem, choosing the specific similarity measure, and constructing the algorithm to compute the similarity. The focus is on methods that lie close to the field of computational geometry.

Abstract—This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data.

Abstract—We present a novel approach to finding a correspondence (alignment) between two curves. The correspondence is based on a notion of an alignment curve which treats both curves symmetrically. We then define a similarity metric based on the alignment curve using two intrinsic properties of the curve, namely, length and curvature. The optimal correspondence is found by an efficient dynamic-programming method both for aligning pairs of curve segments and pairs of closed curves, and is effective in the presence of a variety of transformations of the curve. Finally, the correspondence is shown in application to handwritten character recognition, prototype formation, and object recognition, and is potentially useful in other applications such as registration and tracking. Index Terms—Curve alignment, recognition, dynamic programming, prototypes, correspondence.

A fundamental open problem in computer vision---determining pose and correspondence between two sets of points in space---is solved with a novel, fast [O(nm)], robust and easily implementable algorithm. The technique works on noisy 2D or 3D point sets that may be of unequal sizes and may differ by non-rigid transformations. Using a combination of optimization techniques such as deterministic annealing and the softassign, which have recently emerged out of the recurrent neural network/statistical physics framework, analog objective functions describing the problems are minimized. Over thirty thousand experiments, on randomly generated points sets with varying amounts of noise and missing and spurious points, and on hand-written character sets demonstrate the robustness of the algorithm. Keywords: Point-matching, pose estimation, correspondence, neural networks, optimization, softassign, deterministic annealing, affine. 1 Introduction Matching the representations of two images has long...

We present a novel method for the geometric alignment of autoradiographs of the brain. The method is based on finding the spatial mapping and the one-to-one correspondences (or homologies) between point features extracted from the images and rejecting non-homologies as outliers. In this way, we attempt to account for the local natural and artifactual differences between the autoradiograph slices. We have executed the resulting automated algorithm on a set of left prefrontal cortex autoradiograph slices, specifically demonstrated its ability to perform point outlier rejection, validated it using synthetically generated spatial mappings and provided a visual comparison against the well known iterated closest point (ICP) algorithm. Visualization of a stack of aligned left prefrontal cortex autoradiograph slices is also provided.

Abstract--Based on 2-D cluster approach, a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns. Theorems and algorithms are developed to determine the matching pairs support of each point pair and its transformation parameters (scaling s and rotation 0) on a two-parameter space (s,O). Experiments are conducted both on real and synthetic data. The experimental results show that the proposed matching algorithm can handle translation, rotation, and scaling differences under noisy or distorted condition. The computational time is just about 0.5 s for 50 to 50 point matching on Sun-4 workstation. Copyright © 1997 Pattern Recognition Society. Published by Elsevier Science Ltd. Point pattern matching Affine transformation Maximum matching pairs support Hough transform Inexact matching Registration 1.

General information about a class of objects, such as human faces or teeth, can help to solve the otherwise ill-posed problem of reconstructing a complete surface from sparse 3D feature points or 2D projections of points. We present a technique that uses a vector space representation of shape (3D Morphable Model) to infer missing vertex coordinates. Regularization derived from a statistical approach makes the system stable and robust with respect to noise by computing the optimal tradeoff between fitting quality and plausibility. We present a direct, non-iterative algorithm to calculate this optimum efficiently, and a method for simultaneously compensating unknown rigid transformations. The system is applied and evaluated in two different fields: (1) reconstruction of 3D faces at unknown orientations from 2D feature points at interactive rates, and (2) restoration of missing surface regions of teeth for CAD-CAM production of dental inlays and other medical applications. I.

This thesis presents an integrated approach in modeling, extracting, detecting and classifying deformable contours directly from noisy images. We begin by conducting a case study on regularization, formulation and initialization of the active contour models (snakes). Using minimax principle, we derive a regularization criterion whereby the values can be automatically and implicitly determined along the contour. Furthermore, we formulate a set of energy functionals which yield snakes that contain Hough transform as a special case. Subsequently, we consider the problem of modeling and extracting arbitrary deformable contours from noisy images. We combine a stable, invariant and unique contour model with Markov random field to yield prior distribution that exerts influence over an arbitrary global model while allowing for deformation. Under the Bayesian framework, contour extraction turns into posterior estimation, which is in turn equivalent to energy minimization in a generalized active...

Abstract—For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database. Index Terms—Integral invariants, shape, shape matching, shape distance, shape retrieval. 1